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Friday, June 30, 2017

-ေဒၚစုဟာလဲ-ျမိဳထဲမွာဆူေနတဲ့ၾကြက္ေတြကုိ-ပုေလြမွဳတ္ျပီးျမိဳ ့ျပင္ေခၚထုတ္သြားကာ-ေျခာက္ကမ္းဘားကေန-ပင္လယ္ထဲခုံခ်ခုိင္ေနတဲ့ပုေလြသမားတဦးသာျဖစ္ေနပါတယ္။

1 july 2017.
Image result for pied piper of HAMELIN

Aung Myint
June 30, 2015 ·
အရွင္ဥတၱမ - သုိ ့ (၃၀-၆-၁၅)
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(NLD ဟာ ကုလားအားေပးဆုိတာဟုတ္ပါသလား ) ဆုိတဲ့ ေခါင္းစဥ္ကုိတပ္ျပီး ရွင္ျပထားတာအထူးေကာင္းမြန္ပါတယ္။ ပီဒီပီ ပါတီက အဓိကစိတ္၀င္စါးတာကေတာ့ ေအာက္ပါအပုိဒ္ပါဘဲ-
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ဒီမိုကေရစီဝါဒမွာ တကယ့္နိဳင္ငံ႔ေခါင္း
ေဆာင္ဆိုတာ လူမဟုတ္ပါဘူးဒကာၾကီး။
ျပည္သူ႔ဆႏၵနဲ႔အညီေရးဆြဲထားတဲ႔ ဖြဲ႔စည္းအုပ္
ခ်ဳပ္ပံု အေျခခံဥပေဒပါ။
ဒီမိုကေရစီမွာ သမၼတလည္းသူလုပ္ခ်င္
တာလုပ္လို႔မရသလို တိုင္းသူျပည္သားေတြ
ကလည္းသူတို႔လုပ္ခ်င္တိုင္းလုပ္လို႔မရပါဘူး။
အျပန္အလွန္ထိန္းေက်ာင္းတဲ႔စနစ္ပါ။
တိုင္းျပည္မွာတရားဝင္ေနထိုင္တဲ႔ျပည္သူ
အမ်ားစုရဲ႕ဆႏၵနဲ႔ ေရးဆြဲတဲ႔ ဥပေဒနဲ႔အညီ
အုပ္ခ်ဳပ္ရပါတယ္။
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အရွင္ဥတၱမ ေ၇းသားတဲ့အခ်က္ေတြဟာလုိင္းမွန္ကုိေရးထားတာျဖစ္ပါတယ္။ သုိ ့ေသာ္အဲ့ဒီအခ်က္-တကယ္ျဖစ္ေျမာက္လာဘုိ ့-၂၀၀၈စစ္ဖြဲ ့စည္းပုံကုိလက္ခံျပီးက်ိဳး စားေနတဲ့-အင္အယ္ဒီမလုပ္ႏွိဳင္ပါဘူး
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-ေဒၚစုဟာလဲ-ျမိဳထဲမွာဆူေနတဲ့ၾကြက္ေတြကုိ-ပုေလြမွဳတ္ျပီးျမိဳ ့ျပင္ေခၚထုတ္သြားကာ-ေျခာက္ကမ္းဘားကေန-ပင္လယ္ထဲခုံခ်ခုိင္ေနတဲ့ပုေလြသမားတဦးသာျဖစ္ေနပါတယ္။
Pied piper of Hamelin could could kill rats.
Daw su is trying to silence the democrats.


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Image result for pied piper of HAMELIN

The Pied Piper of Hamelin (German: Rattenfänger von Hameln, also known as the Pan Piper, the Rat-Catcher of Hamelin) is the title character of a legend from the town of Hamelin (Hameln), Lower Saxony, Germany.

Pied Piper of Hamelin - Wikipedia

https://en.wikipedia.org/wiki/Pied_Piper_of_Hamelin

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စစ္အစုိးရကုိဆန္ ့က်င္တဲ့သူေတြကုိ-ဘယ္ဆႏၵျပမွဳ ့မွာမွမပါေစေတာ့ဘဲ-စစ္အာဏာရွင္ မ်ားေအာက္မွာအာဏာမွ်ေ၀မဲ့ပုံစံေခၚေဆာင္သြားတာကုိတာေတြ ့ရပါတယ္။
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ေဒၚစုကုိ (Immaculate lady) အျပစ္ကင္းစင္ျပီး-ေျပာသမွ်လုပ္သမွ်မွန္တဲ့သူ-လုိ ့ေထာက္ခံေနၾကသူမ်ားကုိလဲေတြ ့ရပါတယ္။-လူဆုိတာ-အျပစ္မကင္းတဲ့သူေတြ-လုိ ့ခရစၥယံဘာသာကေဟာထားသလုိ-ဗုဒ္ဓျမတ္ဘုရားကလဲ-လူေတြဟာအရူးၾကီးဘဲလုိ ့ေရးထားပါတယ္။အဲ့ဒါေၾကာင့္-သူတုိ ့ေခါင္းေဆာင္ရဲ ့ေၾကာက္စရာေကာင္းတဲ့ အမွားေတြကုိျပန္လည္ျမင္ေတြ ့သုံးသပ္ႏွိႈင္ၾကဘုိ ့လုိပါတယ္။
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ေဒၚစုုကုိသိပ္ေျမွာက္ၾကလုိ ့-ေဒၚစုကလဲ-သိပ္ေျမာက္ျပီးအမွားအယြင္းေတြလုပ္ကုိင္ေျပာ ဆုိခဲ့တဲ့သမုိင္းေၾကာင္းေတြအမ်ားၾကီးရွိတာေၾကာင့္- ဦးဇင္းေရးေပးလုိက္တဲ့-(ဒီမုိကေရ စီမွာ-တကယ့္ေခါင္းေဆာင္ဆုိတာလူမဟုတ္ပါဘူး) ဆုိတဲ့အပုိဒ္ကုိ အင္အယ္ဒီေတြ မ်ားမ်ားဖတ္ျပီး-အဖန္ဖန္-ျပန္လည္းသုံးသပ္ၾကဘုိ ့လုိပါတယ္။
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ဒီမုိကေရစီစနစ္မွာအမ်ားနဲ့တုိင္ပင္လုပ္ကုိင္ရမဲ့-ကိစၥေတြရွိတာကုိ-ေဒၚစုတဦးတည္းၾကီး-ဇြတ္ထုိးဆုံးျဖတ္လုိ ့-မွားယြင္းမွဳ ့ေတြမ်ားစြာေတြ ့ေနရပါတယ္။-စစ္တပ္ကုိ၀င္ေပါင္းျပီး -၂၀၀၈ စစ္အာဏာရွင္စနစ္ကုိလက္ခံခဲ့တယ္။ကုိယ္လုိခ်င္တာမရေတာ့-အဲ့ဒီ၂၀၀၈ဖြဲ ့စည္းပုံကုိအျပစ္တင္တယ္။- ၂၀၀၈ဖြဲ ့စည္းပုံဟာ-စစ္အာဏာရွင္မ်ားက အဆင့္ဆင့္ခံ တပ္မ်ိဳးနဲ ့ေရးဆြဲထားတဲ့ဖြဲ ့စည္းပုံမုိ ့လုိ ့- အခုလုိ- ့(-ဒို ့လုိခ်င္တာေတြျပင္ေပးဆုိျပီး) ခေလးေတာင္းေတာင္းဆုိေနခဲ့ျခင္းဟာ-ဘြင္းဘြင္းၾကီးျမင္ေနရတဲ့-အေတာ္ကုိမွားယြင္တဲ့-အမွားလုပ္ရပ္တခုျဖစ္ပါတယ္။ လူသတ္သမားစစ္အစုိးရကဘယ္လုိမွမေပးႏွိဳင္ပါဘူး။အခ်ိန္ကုန္လူပန္းသာျဖစ္ခဲ့တာေတြ ့ရပါတယ္။
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အဓိကအားျဖင့္-နိဳင္ငံျခားသားယူသူကုိဘယ္နိဳင္ငံကမွသမတမေပးႏွိဳင္သည့္ကိစၥကုိ-သမတျဖစ္မွဆုိျပီး-အတင္းသူ ့ေနာက္လုိက္ေတြကုိဦးေဆာင္တုိက္ပြဲ၀င္ခဲ့တာဟာလဲ-ဦးေဏွာက္ရွိသူေခါင္းေဆာင္ေကာင္းတဥိး၏လုပ္ရပ္မဟုတ္ဘူးဆုိတာျမင္ေတြ ့ရပါတယ္။
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ဒါေတာင္-အခုအခ်ိန္အထိ-အင္အယ္ဒီေနာက္လုိက္ေတြဟာ-ဒုံရင္းဒုံရင္းဦးေဏွာက္ဘဲ- သူတုိ ့ေခါင္းေဆာင္သမတျဖစ္ဘုိ ့ကုိဘဲ-လုိက္ေနၾကတုံးရွိပါေသးတယ္။ ေဒၚစုကလဲ -သူပါတီ အစုိးရျဖစ္ဘုိ ့-ေနာက္မဟာျဗဴဟာခ်ျပီးၾကိဳးစားေနျပန္ပါျပီ။
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ဒီကိစၥမွာရွင္းေအာင္ေျပာရရင္-စစ္အာဏာရွင္မ်ားျပဳတ္မက်မျခင္း-အတုိက္အခံပါတီေတြ ကုိသူတုိ ့ေအာက္မွာဖြဲ ့ေပးတဲ့အစုိးရထဲမွာအဖြဲ့၀င္ေတြအေနႏွင့္သာ-ဖြဲ ့ေပးထားမွာပါဘဲ။
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အဲ့ဒီ-လုိစစ္အာဏာရွင္မ်ား၇ဲ ့ေအာက္မွာလုပ္ရမ့ဲအစုိးရဘ၀ကုိအတင္းလုိက္ေနျခင္းဟာ-အမွားတခုထပ္လုပ္ေနျခင္းျဖစ္တယ္ဆုိတာ-ျပည္သူအမ်ားျမင္ၾကဘုိ ့လုိပါတယ္။ဒီပုံစံနဲ ့လုိက္တုိးလုိ ့ကေတာ့-စစ္အာဏာရွင္ေတြဟာ-စစ္အာဏာရွင္ေတြဘဲဆက္ျဖစ္ေနမယ္ဆုိ တာ ျမင္ၾကဘုိ ့လုိပါတယ္။
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ယဥ္ျပခ်င္တာက-ေတာင္အာဖရိကနိဳင္ငံကနယ္ဆင္မင္ေဒလားဟာ-အဲ့ဒိလုိပုံစံေတြကုိ လက္မခံပါဘူး။လုံး၀လြတ္ေျမာက္မွဳ ့အတြက္အသက္ေပးတုိက္ပဲြ၀င္ခဲ့လုိ့ ့ကမၻာေက်ာ္ သြားတာပါ။
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အခုျဖစ္ေနတာက-၀င္ကမၻာလုိ - သြားခဲ့တဲ့လမ္းကပိတ္ေနလုိ ့ျပန္ဆုတ္ေနရျပီး-ဆက္သြားရမဲ့လမ္းေတြအားလုံးလုိလုိကပိတ္ထားျခင္းခံေနပါတယ္။ သုိ ့ေသာ္-အခုလုိပိတ္ေနတဲ့(အပိတ္ခံထားရတဲ့)လမ္းေၾကာင္းကုိဘဲ-အင္အယ္ဒီေတြက-ေခါင္းနဲ ့တုိးေနၾကတဲ့အတြက္(လုိင္းေပ်ာက္ေနၾကျခင္း)ျဖစ္ပါတယ္။
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၄င္းတုိ ့အခုလုိုလုပ္ေနတာဟာထြက္ေပါက္ကုိေရာက္လိမ့္မယ္လုိ ့-မျမင္ပါ။ စစ္အာဏာ ရွင္ေတြကုိဖါယ္ရွားႏွိဳင္မယ္လုိ ့မျမင္ပါ။ပုိမုိၾကီးထြားေအာင္အလုပ္အေၾကြးျပဳေေနတာနဲ ့တာတူပါတယ္။
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အေၾကာင္းကလဲ-အေပၚစည္းယူျပီးေစါင့္ၾကည့္ေနတဲ့စစ္အာဏာရွင္ေတြကနည္းအမ်ိဳး မ်ိဳးနဲ ့ညစ္ပါတ္မွာမုိ ့-သမင္ေမြးရင္း-က်ားစါးရင္း ဆုိသလုိ-လုပ္သမွ်အဖတ္မတင္ဘဲ-အခ်ိန္ကုန္လူပန္းသာျဖစ္ပါလိမ့္မယ္။
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ပီဒီပီပါတီက-အဲ့ဒါေၾကာင့္-အဲ့ဒီလုိ-လူယုတ္မာၾကီးမ်ားဖြဲ ့ထားတဲ့- စစ္အစုိးရကုိ-ျဖစ္တဲ့-ရတဲ့နည္းနဲ ့သပိတ္ေမွာက္ၾကဘုိ ့ျပည္သူကုိတုိက္တြန္းလွ်က္ရွိပါတယ္။
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ဗုိလ္ခ်ဳပ္ေအာင္ဆန္းဦးေဆာင္ျပီးေရးဆြဲေပးခဲ့တဲ့၄၇ခုဖြဲ ့စည္းအုပ္ခ်ဳပ္ပုံဟာ-လက္ရွိျမန္ မာျပည္သူျပည္သားေတြအလုိရွိေနတဲ့ဒီမုိကေရစီအခြင့္အေရးေတြေပးတဲ့ဖြဲ ့စည္းပုံျဖစ္ တဲ့အတြက္-အဲ့ဒီဖြဲ ့စည္းပုံကုိျပန္ေတာင္းၾကဘုိ ့တုိက္တြန္းေနပါတယ္။
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ထူးဆန္းတာက-ေဒၚစုသည္-သူ ့ဖခင္ေရးဆြဲခဲ့သည့္ ၄၇ခုဒီမုိကေ၇စီဖြဲ ့စည္းပုံကုိတခါ မွေျပာတာမၾကားရပါ။ ျမန္မာနိဳင္ငံ၏ဒိမုိကေရစီခ်န္ပီယံျဖစ္သူ ၀န္ၾကီးခ်ဳပ္ဦးနဳ ၏ဒိမုိကေရစီတည္ေဆာက္ေပးခဲ့ပုံကုိလည္းတခါမွေျပာတာမၾကားရပါ။
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သူတဦးတည္းက-အခုမွျမန္မာနိဳင္ငံကုိဒီမုိကေရစီစနစ္သြက္သြင္းေပးမဲ့-သူရဲေကာင္း ပုံစံလုပ္ေနပါတယ္။ ဤကိစၥကုိျပည္သူေတြျပန္ဆန္းစစ္ၾကဘုိ ့လုိေနပါျပီ။
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တကယ္ ျပည္သူေတြအားလုံးတုိက္ပြဲ၀င္ၾကရမွာက-ဦးဇင္းေရးထားတဲ့-စစ္မွန္တဲ ့ဖြဲ့စည္းပု့ံဆုိတာကုိျပန္ရေအာင္တုိက္ပြဲ၀င္ၾကရမွာျဖစ္ပါတယ္။
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-အဲ့ဒိစစ္မွန္တဲ့ဖြဲ ့စည္းပုံဆုိတာ-၄၇ခုဖြဲ့စည္းပုံ- ဗုိလ္ခ်ဳပ္ေအာင္ဆန္းဦးေဆာင္ေရး ဆြဲေပးသြားတဲ့ဖြဲ ့စည္းပုံသာျဖစ္တဲ့အတြက္-ထုိဖြဲ ့စည္းပုံကုိျပန္ေတာင္းၾကဘုိ ့-
ထုိ ့ေနာက္မွ-ေခတ္ႏွင့္အညီျဖစ္လာေအာင္-လုိတာေတြကုိျပဳျပင္ေပးဘုိ ့သာ လုိပါသည္ဦးဇင္း။

အဲ့ဒါမွမဟုတ္လုိ ့-အခုလုိအင္အယ္ဒီေတြလုပ္ေနပုံကုိဘဲေစါင့္ၾကည့္ရမယ္ဆုိရင္ေတာ့့ - အခ်ိန္ကုန္လူပန္း-(ဂ်ပ္ေအးသူ ့အေမရုိက္)၀င္ကမၻာလမ္းမဆုံးသာ-ျဖစ္ေနၾကမွာပါဥိးဇင္း။
ေလးစားစြာျဖင့္
ဗုိလ္ေအာင္ဒင္ (ဥကၠဌ-ပါလီမန္ဒီမုိကေရစီပါတီ-ပီဒီပီ) PDP
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Posted by sayanyein at 1:46 PM 1 comment:

Thursday, June 29, 2017

30 june 2017. What is time dilation? What is length contraction? What is Mass increment ?

30 june 2017.
What is time dilation?
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In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more.

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GETTING A GRIP ON GRAVITY Einstein's general theory of relativity explains gravity as a distortion of space (or more precisely, spacetime) caused by the presence of matter or energy. A massive object generates a gravitational field by warping the geometry of the surrounding spacetime.Oct 4, 2015
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Length contraction is the phenomenon of a decrease in length of an object as measured by an observer who is traveling at any non-zero velocity relative to the object.

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Tuesday, June 27, 2017

28 june 2017.In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.

28 june 2017.
https://en.wikipedia.org/wiki/Special_relativity



Albert Einstein around 1905, the year his "Annus Mirabilis papers" – which included Zur Elektrodynamik bewegter Körper, the paper founding special relativity – were published.

Contents





In physics, special relativity (SR, also known as the special theory of relativity or STR) is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time.
In Albert Einstein's original pedagogical treatment, it is based on two postulates:

  1. The laws of physics are invariant (i.e. identical) in all inertial systems (non-accelerating frames of reference).
  2. The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.
It was originally proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies".[1]
The inconsistency of Newtonian mechanics with Maxwell's equations of electromagnetism and the lack of experimental confirmation for a hypothesized luminiferous aether led to the development of special relativity, which corrects mechanics to handle situations involving motions at a significant fraction of the speed of light (known as relativistic velocities).
As of today, special relativity is the most accurate model of motion at any speed when gravitational effects are negligible.
Even so, the Newtonian mechanics model is still useful (due to its simplicity and high accuracy) as an approximation at small velocities relative to the speed of light.

Not until Einstein developed general relativity, to incorporate general (or accelerated) frames of reference and gravity, was the phrase "special relativity" employed.
A translation that has often been used is "restricted relativity"; "special" really means "special case".[2]

Special relativity implies a wide range of consequences, which have been experimentally verified,[3] including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit and relativity of simultaneity.
It has replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Combined with other laws of physics, the two postulates of special relativity predict the equivalence of mass and energy, as expressed in the mass–energy equivalence formula E = mc2, where c is the speed of light in a vacuum.[4][5]

A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations. Time and space cannot be defined separately from each other.
Rather space and time are interwoven into a single continuum known as spacetime.
Events that occur at the same time for one observer can occur at different times for another.

The theory is "special" in that it only applies in the special case where the curvature of spacetime due to gravity is negligible.
[6]
[7] In order to include gravity, Einstein formulated general relativity in 1915.
Special relativity, contrary to some outdated descriptions, is capable of handling accelerations as well as accelerated frames of reference.[8][9]

As Galilean relativity is now considered an approximation of special relativity that is valid for low speeds, special relativity is considered an approximation of general relativity that is valid for weak gravitational fields, i.e. at a sufficiently small scale and in conditions of free fall.
Whereas general relativity incorporates noneuclidean geometry in order to represent gravitational effects as the geometric curvature of spacetime, special relativity is restricted to the flat spacetime known as Minkowski space.
A locally Lorentz-invariant frame that abides by special relativity can be defined at sufficiently small scales, even in curved spacetime.

Galileo Galilei had already postulated that there is no absolute and well-defined state of rest (no privileged reference frames), a principle now called Galileo's principle of relativity. Einstein extended this principle so that it accounted for the constant speed of light,[10] a phenomenon that had been recently observed in the Michelson–Morley experiment.
He also postulated that it holds for all the laws of physics, including both the laws of mechanics and of electrodynamics.[11]



Contents

  • 1 Postulates
  • 2 Lack of an absolute reference frame
  • 3 Reference frames, coordinates, and the Lorentz transformation
  • 4 Consequences derived from the Lorentz transformation
    • 4.1 Relativity of simultaneity
    • 4.2 Time dilation
    • 4.3 Length contraction
    • 4.4 Composition of velocities
  • 5 Other consequences
    • 5.1 Thomas rotation
    • 5.2 Equivalence of mass and energy
    • 5.3 How far can one travel from the Earth?
  • 6 Causality and prohibition of motion faster than light
  • 7 Geometry of spacetime
    • 7.1 Comparison between flat Euclidean space and Minkowski space
    • 7.2 3D spacetime
    • 7.3 4D spacetime
  • 8 Physics in spacetime
    • 8.1 Transformations of physical quantities between reference frames
    • 8.2 Metric
    • 8.3 Relativistic kinematics and invariance
    • 8.4 Relativistic dynamics and invariance
  • 9 Relativity and unifying electromagnetism
  • 10 Status
  • 11 Detractors
  • 12 Theories of relativity and quantum mechanics
  • 13 See also
  • 14 References
    • 14.1 Textbooks
    • 14.2 Journal articles
  • 15 External links
    • 15.1 Original works
    • 15.2 Special relativity for a general audience (no mathematical knowledge required)
    • 15.3 Special relativity explained (using simple or more advanced mathematics)
    • 15.4 Visualization









Special relativity
The world line: a diagrammatic representation of spacetime
  • Principle of relativity
  • Theory of relativity
Foundations[show]
Consequences[show]
Spacetime[show]
Dynamics[show]
  • History
  • Precursors
[show]
People[show]
Alternative formulations
of special relativity


Posted by sayanyein at 3:12 PM No comments:

General relativity is considered the most beautiful of all existing physical theories.[3]

28 JUNE 2017.
https://en.wikipedia.org/wiki/General_relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915[2] and the current description of gravitation in modern physics.
General relativity is considered the most beautiful of all existing physical theories.[3]
General relativity generalizes special relativity and Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time, or spacetime.
In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present.
The relation is specified by the Einstein field equations, a system of partial differential equations.

Some predictions of general relativity differ significantly from those of classical physics, especially concerning the passage of time, the geometry of space, the motion of bodies in free fall, and the propagation of light. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational redshift of light, and the gravitational time delay.
The predictions of general relativity have been confirmed in all observations and experiments to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory that is consistent with experimental data.
However, unanswered questions remain, the most fundamental being how general relativity can be reconciled with the laws of quantum physics to produce a complete and self-consistent theory of quantum gravity.

Einstein's theory has important astrophysical implications.
For example, it implies the existence of black holes—regions of space in which space and time are distorted in such a way that nothing, not even light, can escape—as an end-state for massive stars.
There is ample evidence that the intense radiation emitted by certain kinds of astronomical objects is due to black holes; for example, microquasars and active galactic nuclei result from the presence of stellar black holes and supermassive black holes, respectively.
The bending of light by gravity can lead to the phenomenon of gravitational lensing, in which multiple images of the same distant astronomical object are visible in the sky.
General relativity also predicts the existence of gravitational waves, which have since been observed directly by physics collaboration LIGO.
In addition, general relativity is the basis of current cosmological models of a consistently expanding universe.

Contents

  • 1 History
  • 2 From classical mechanics to general relativity
    • 2.1 Geometry of Newtonian gravity
    • 2.2 Relativistic generalization
    • 2.3 Einstein's equations
    • 2.4 Alternatives to general relativity
  • 3 Definition and basic applications
    • 3.1 Definition and basic properties
    • 3.2 Model-building
  • 4 Consequences of Einstein's theory
    • 4.1 Gravitational time dilation and frequency shift
    • 4.2 Light deflection and gravitational time delay
    • 4.3 Gravitational waves
    • 4.4 Orbital effects and the relativity of direction
  • 5 Astrophysical applications
    • 5.1 Gravitational lensing
    • 5.2 Gravitational wave astronomy
    • 5.3 Black holes and other compact objects
    • 5.4 Cosmology
    • 5.5 Time travel
  • 6 Advanced concepts
    • 6.1 Causal structure and global geometry
    • 6.2 Horizons
    • 6.3 Singularities
    • 6.4 Evolution equations
    • 6.5 Global and quasi-local quantities
  • 7 Relationship with quantum theory
    • 7.1 Quantum field theory in curved spacetime
    • 7.2 Quantum gravity
  • 8 Current status
  • 9 See also
  • 10 Notes
  • 11 References
  • 12 Further reading
      • 12.1 Popular books
      • 12.2 Beginning undergraduate textbooks
      • 12.3 Advanced undergraduate textbooks
      • 12.4 Graduate-level textbooks
    • 13 External links

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    History

    Relativistic generalization

    Light cone
    As intriguing as geometric Newtonian gravity may be, its basis, classical mechanics, is merely a limiting case of (special) relativistic mechanics.[23]
    In the language of symmetry: where gravity can be neglected, physics is Lorentz invariant as in special relativity rather than Galilei invariant as in classical mechanics.
    (The defining symmetry of special relativity is the Poincaré group, which includes translations, rotations and boosts.)
    The differences between the two become significant when dealing with speeds approaching the speed of light, and with high-energy phenomena.[24]

    With Lorentz symmetry, additional structures come into play. They are defined by the set of light cones (see image).
    The light-cones define a causal structure: for each event A, there is a set of events that can, in principle, either influence or be influenced by A via signals or interactions that do not need to travel faster than light (such as event B in the image), and a set of events for which such an influence is impossible (such as event C in the image).
    These sets are observer-independent.[25]
    In conjunction with the world-lines of freely falling particles, the light-cones can be used to reconstruct the space–time's semi-Riemannian metric, at least up to a positive scalar factor. In mathematical terms, this defines a conformal structure[26] or conformal geometry.

    Special relativity is defined in the absence of gravity, so for practical applications, it is a suitable model whenever gravity can be neglected.
    Bringing gravity into play, and assuming the universality of free fall, an analogous reasoning as in the previous section applies: there are no global inertial frames.
    Instead there are approximate inertial frames moving alongside freely falling particles.
    Translated into the language of spacetime: the straight time-like lines that define a gravity-free inertial frame are deformed to lines that are curved relative to each other, suggesting that the inclusion of gravity necessitates a change in spacetime geometry.[27]

    A priori, it is not clear whether the new local frames in free fall coincide with the reference frames in which the laws of special relativity hold—that theory is based on the propagation of light, and thus on electromagnetism, which could have a different set of preferred frames.
    But using different assumptions about the special-relativistic frames (such as their being earth-fixed, or in free fall), one can derive different predictions for the gravitational redshift, that is, the way in which the frequency of light shifts as the light propagates through a gravitational field (cf. below).
    The actual measurements show that free-falling frames are the ones in which light propagates as it does in special relativity.[28]
    The generalization of this statement, namely that the laws of special relativity hold to good approximation in freely falling (and non-rotating) reference frames, is known as the Einstein equivalence principle, a crucial guiding principle for generalizing special-relativistic physics to include gravity.[29]

    The same experimental data shows that time as measured by clocks in a gravitational field—proper time, to give the technical term—does not follow the rules of special relativity. In the language of spacetime geometry, it is not measured by the Minkowski metric.
    As in the Newtonian case, this is suggestive of a more general geometry. At small scales, all reference frames that are in free fall are equivalent, and approximately Minkowskian.
    Consequently, we are now dealing with a curved generalization of Minkowski space.
    The metric tensor that defines the geometry—in particular, how lengths and angles are measured—is not the Minkowski metric of special relativity, it is a generalization known as a semi- or pseudo-Riemannian metric.
    Furthermore, each Riemannian metric is naturally associated with one particular kind of connection, the Levi-Civita connection, and this is, in fact, the connection that satisfies the equivalence principle and makes space locally Minkowskian (that is, in suitable locally inertial coordinates, the metric is Minkowskian, and its first partial derivatives and the connection coefficients vanish).[30]

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    Singularities

    Main article: Spacetime singularity
    Another general feature of general relativity is the appearance of spacetime boundaries known as singularities.
    Spacetime can be explored by following up on timelike and lightlike geodesics—all possible ways that light and particles in free fall can travel.
    But some solutions of Einstein's equations have "ragged edges"—regions known as spacetime singularities, where the paths of light and falling particles come to an abrupt end, and geometry becomes ill-defined.
    In the more interesting cases, these are "curvature singularities", where geometrical quantities characterizing spacetime curvature, such as the Ricci scalar, take on infinite values.[151]
    Well-known examples of spacetimes with future singularities—where worldlines end—are the Schwarzschild solution, which describes a singularity inside an eternal static black hole,[152] or the Kerr solution with its ring-shaped singularity inside an eternal rotating black hole.[153]
    The Friedmann–Lemaître–Robertson–Walker solutions and other spacetimes describing universes have past singularities on which worldlines begin, namely Big Bang singularities, and some have future singularities (Big Crunch) as well.[154]

    Given that these examples are all highly symmetric—and thus simplified—it is tempting to conclude that the occurrence of singularities is an artifact of idealization.[155]
    The famous singularity theorems, proved using the methods of global geometry, say otherwise: singularities are a generic feature of general relativity, and unavoidable once the collapse of an object with realistic matter properties has proceeded beyond a certain stage[156] and also at the beginning of a wide class of expanding universes.[157]
    However, the theorems say little about the properties of singularities, and much of current research is devoted to characterizing these entities' generic structure (hypothesized e.g. by the BKL conjecture).[158]
    The cosmic censorship hypothesis states that all realistic future singularities (no perfect symmetries, matter with realistic properties) are safely hidden away behind a horizon, and thus invisible to all distant observers.
    While no formal proof yet exists, numerical simulations offer supporting evidence of its validity.[159]
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