Author Topic: Space, Astrophysics and Cosmology  (Read 96737 times)

Offline CL3

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Re: Space, Astrophysics and Cosmology
« Reply #555 on: December 11, 2016, 12:40:46 PM »
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The metric raises and lowers indices according to

gij Vj = Vi

Where the thing on the left hand side means a sum over j :

Vi = gi0 V0 + gi1 V1 + gi2 V2 + gi3 V3

This idea generalises to two indices as in these examples:

gijFjk = Fki

gklgijFjk = gklFki= Fil

That is, to lower both of the indices one applies the metric twice.

So when you have a contraction of two 2-index objects like this:

FijFij = FijgikgjlFkl


Explicitly, using the Minkowski metric and taking Fij to be a matrix of 1s

Fij =

Code: [Select]
|  1  1  1  1 |
|  1  1  1  1 |
|  1  1  1  1 |
|  1  1  1  1 |

Fij = giaFaj

Code: [Select]
| -1 -1 -1 -1 |
|  1  1  1  1 |
|  1  1  1  1 |
|  1  1  1  1 |

Fij= giagjbFab

Code: [Select]
|  1 -1 -1 -1 |
| -1  1  1  1 |
| -1  1  1  1 |
| -1  1  1  1 |

as you said.

Does that clear things up at all?
« Last Edit: December 11, 2016, 12:42:53 PM by CL3 »


Offline Gan_HOPE326

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Re: Space, Astrophysics and Cosmology
« Reply #556 on: December 11, 2016, 01:57:19 PM »
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Does that clear things up at all?


Yep, thanks, it's pretty much how I figured. I still can't figure out how all the signs come and go in some passages (I'm looking at the calculation of the propagator for the photon in QED). I probably just don't get the full implications of the notation used. I tried working out a simpler 1+1 dimensional case (because 3+1 of course would be huge) and still don't find it. I follow pretty well the logic of what's going on but the finest details of the maths escape me and that's pretty frustrating because it's from deriving those that come all the nice conclusions (here in particular it's demonstrating how photons can mediate repelling force while gravitons can't. The general sense of it is that every rank of the tensor introduces one Minkowski symbol and therefore for rank 2 the two minus signs cancel each other out and we're back in the same situation (sign-wise) as for a scalar field, but of course that's just a qualitative understanding.

On other news, did you hear the rumours about echoes hinting at a firewall or some other weird fuzzy event horizon shit going on in the LIGO gravitational waves detection experiment?



Offline notimportant

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Re: Space, Astrophysics and Cosmology
« Reply #557 on: January 22, 2017, 11:17:34 PM »
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http://www.telegraph.co.uk/news/science/11719914/Astronomers-discover-monster-black-holes.html

Well, this is interesting enough. Some crazy person sent an email to my university email account (and probably that of every other scientist whose email he could find...) linking to this article, but going on to call it bullshit and denying that black holes exist, and presumably trying to convince me of this (I think he was trying?) while talking shit about a load of famous scientists. So thanks to the crazy dude for bringing this piece of news to my attention.

Terrible person whoever it was they should lock him up. Such heresy. Maybe it was a woman, though.

Offline CL3

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Re: Space, Astrophysics and Cosmology
« Reply #558 on: May 19, 2017, 06:51:38 PM »
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A slide from a cosmology conference today



Translation notes from physicist-speak for those who want the jokes explained:

(click to show/hide)
« Last Edit: May 19, 2017, 09:39:03 PM by CL3 »


Offline Jin Kanzaki

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Re: Space, Astrophysics and Cosmology
« Reply #559 on: June 19, 2017, 11:03:01 PM »
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Hey guys, I got a question because fuck the vague explanations in my professor's scripts.

In case of microscopes or telescopes, what's the difference between resolution and localization precision.
I mean, I know they imply something different, but isn't localization precision just a consequence of resolution?

I mean, the better you can discern how big and where the thing is, the more precisely can you determine its exact position, right?

This is literally the entirety of my professor's explanation:

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Offline Gan_HOPE326

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Re: Space, Astrophysics and Cosmology
« Reply #560 on: June 19, 2017, 11:49:23 PM »
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Hey guys, I got a question because fuck the vague explanations in my professor's scripts.

In case of microscopes or telescopes, what's the difference between resolution and localization precision.
I mean, I know they imply something different, but isn't localization precision just a consequence of resolution?

I mean, the better you can discern how big and where the thing is, the more precisely can you determine its exact position, right?

This is literally the entirety of my professor's explanation:



From that plot I imagine the difference would be:

- resolution is the ability to tell that two lumps are different. It requires discerning that the intensity goes down, then up again in between.
- localization is the ability to tell where a single lump is located. Even if there's no doubt it's only one, there is still a limit on the precision with which one can determine its actual position

For example, with a digital camera, localization would depend on the amount of pixels of the sensor, while resolution would also be a function of their sensitivity.

Offline Jin Kanzaki

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Re: Space, Astrophysics and Cosmology
« Reply #561 on: June 20, 2017, 01:33:22 AM »
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From that plot I imagine the difference would be:

- resolution is the ability to tell that two lumps are different. It requires discerning that the intensity goes down, then up again in between.
- localization is the ability to tell where a single lump is located. Even if there's no doubt it's only one, there is still a limit on the precision with which one can determine its actual position

For example, with a digital camera, localization would depend on the amount of pixels of the sensor, while resolution would also be a function of their sensitivity.
Ahhh, ok.
Thanks.
But that also means that localization precision is dependent on resolution to some degree, while the opposite is not the case, right?
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Offline CL3

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Re: Space, Astrophysics and Cosmology
« Reply #562 on: June 20, 2017, 10:09:48 AM »
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That sounds reasonable. I don't think I ever encountered this distinction in my studies, but I only worked with telescopes, really.

More specifically are we talking about PALM or some similar fluorescence microscopy technique? If so then maybe part of the distinction is "can determine that there are two things there, and what they are" vs "can determine there are two things there and how far apart they are, but not really their identities".



Offline Jin Kanzaki

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Re: Space, Astrophysics and Cosmology
« Reply #563 on: June 21, 2017, 06:21:15 PM »
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That sounds reasonable. I don't think I ever encountered this distinction in my studies, but I only worked with telescopes, really.

More specifically are we talking about PALM or some similar fluorescence microscopy technique? If so then maybe part of the distinction is "can determine that there are two things there, and what they are" vs "can determine there are two things there and how far apart they are, but not really their identities".


Thank you!

Yes, we actually are talking about fluorescence microscopy.
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