What's the problem with Euclidean geometry for astronomical phenomena?How can time dilation be symmetric?What is the proper way to explain the twin paradox?Calculating angles for tetrahedral molecular geometryWhere do I start with Non-Euclidean Geometry?Euclidean Geometry in Classical Thought - Realization or Representation?Geodesics in KerrHow does the density of states for black-body radiation change with geometry?Non-Euclidean geometry of a rotating cylinderWhy was pseudo-Euclidean geometry not enough for general relativity?Geometry with differential angles
How to accelerate progress in mathematical research
More than three domains hosted on the same IP address
Why has Marx's "Das Kapital" been translated to "Capital" in English and not "The Capital"
How can I hint that my character isn't real?
Let A,B,C be sets. If A△B=A△C, does this imply that B=C?
How to make a pipe-divided tuple?
Why is Sojdlg123aljg a common password?
Why are UK MPs allowed to abstain (but it counts as a no)?
Do you need to burn fuel between gravity assists?
Are fast interviews red flags?
How to best explain that you are taking pictures in a space for practice reasons?
Why did Tony's Arc Reactor do this?
Where on Earth is it easiest to survive in the wilderness?
At what point does a land become controlled?
Project Euler problem #112
Template default argument loses its reference type
Why is it that I have to play this note on the piano as A sharp?
I multiply the source, you (probably) multiply the output!
How do I write a vertically-stacked definition of a sequence?
Should I tip on the Amtrak train?
How do German speakers decide what should be on the left side of the verb?
Is Sanskrit really the mother of all languages?
How can electricity be positive when electrons are negative?
Statistical closeness implies computational indistinguishability
What's the problem with Euclidean geometry for astronomical phenomena?
How can time dilation be symmetric?What is the proper way to explain the twin paradox?Calculating angles for tetrahedral molecular geometryWhere do I start with Non-Euclidean Geometry?Euclidean Geometry in Classical Thought - Realization or Representation?Geodesics in KerrHow does the density of states for black-body radiation change with geometry?Non-Euclidean geometry of a rotating cylinderWhy was pseudo-Euclidean geometry not enough for general relativity?Geometry with differential angles
.everyoneloves__top-leaderboard:empty,.everyoneloves__mid-leaderboard:empty,.everyoneloves__bot-mid-leaderboard:empty margin-bottom:0;
$begingroup$
This passage from John Pierce, An Introduction to Information Theory:
"also note that while Euclidean geometry is a mathematical theory
which serves surveyors and navigators admirably in their practical
concerns, there is reason to believe that Euclidean geometry is not
quite accurate in describing astronomical phenomena"
got me wondering. What makes Euclidean geometry inaccurate for this purpose?
The book is neither about geometry, nor about astronomy, so this issue remains unexplained.
general-relativity geometry
edited 8 hours ago
ACuriousMind♦
75.8k18 gold badges139 silver badges355 bronze badges
asked 8 hours ago
Quora FeansQuora Feans
2191 gold badge3 silver badges11 bronze badges
$endgroup$
add a comment |
$begingroup$
This passage from John Pierce, An Introduction to Information Theory:
"also note that while Euclidean geometry is a mathematical theory
which serves surveyors and navigators admirably in their practical
concerns, there is reason to believe that Euclidean geometry is not
quite accurate in describing astronomical phenomena"
got me wondering. What makes Euclidean geometry inaccurate for this purpose?
The book is neither about geometry, nor about astronomy, so this issue remains unexplained.
general-relativity geometry
edited 8 hours ago
ACuriousMind♦
75.8k18 gold badges139 silver badges355 bronze badges
asked 8 hours ago
Quora FeansQuora Feans
2191 gold badge3 silver badges11 bronze badges
$endgroup$
add a comment |
$begingroup$
This passage from John Pierce, An Introduction to Information Theory:
"also note that while Euclidean geometry is a mathematical theory
which serves surveyors and navigators admirably in their practical
concerns, there is reason to believe that Euclidean geometry is not
quite accurate in describing astronomical phenomena"
got me wondering. What makes Euclidean geometry inaccurate for this purpose?
The book is neither about geometry, nor about astronomy, so this issue remains unexplained.
general-relativity geometry
edited 8 hours ago
ACuriousMind♦
75.8k18 gold badges139 silver badges355 bronze badges
asked 8 hours ago
Quora FeansQuora Feans
2191 gold badge3 silver badges11 bronze badges
$endgroup$
This passage from John Pierce, An Introduction to Information Theory:
"also note that while Euclidean geometry is a mathematical theory
which serves surveyors and navigators admirably in their practical
concerns, there is reason to believe that Euclidean geometry is not
quite accurate in describing astronomical phenomena"
got me wondering. What makes Euclidean geometry inaccurate for this purpose?
The book is neither about geometry, nor about astronomy, so this issue remains unexplained.
general-relativity geometry
general-relativity geometry
edited 8 hours ago
ACuriousMind♦
75.8k18 gold badges139 silver badges355 bronze badges
asked 8 hours ago
Quora FeansQuora Feans
2191 gold badge3 silver badges11 bronze badges
edited 8 hours ago
ACuriousMind♦
75.8k18 gold badges139 silver badges355 bronze badges
asked 8 hours ago
Quora FeansQuora Feans
2191 gold badge3 silver badges11 bronze badges
edited 8 hours ago
ACuriousMind♦
75.8k18 gold badges139 silver badges355 bronze badges
edited 8 hours ago
ACuriousMind♦
75.8k18 gold badges139 silver badges355 bronze badges
edited 8 hours ago
ACuriousMind♦
75.8k18 gold badges139 silver badges355 bronze badges
75.8k18 gold badges139 silver badges355 bronze badges
asked 8 hours ago
Quora FeansQuora Feans
2191 gold badge3 silver badges11 bronze badges
asked 8 hours ago
Quora FeansQuora Feans
2191 gold badge3 silver badges11 bronze badges
asked 8 hours ago
Quora FeansQuora Feans
2191 gold badge3 silver badges11 bronze badges
2191 gold badge3 silver badges11 bronze badges
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
On the scale of most astronomical phenomena, general relativity (GR) is the relevant theory.
There are many aspects in which this theory is incompatible with Euclidean geometry. An illustrative and often used analogy is that Euclidean geometry is already inaccurate for a being confined to the surface of a sphere - if you draw a triangle on a sphere, its interior angles do not in general sum up to 180°. What makes GR a bit strange still is that it posits that it is not space alone that participates in such curved geometry, but spacetime.
That is, general relativity does not assume that space(time) is flat, and it even intermingles space and time so that different observers that move relative to each other will neither agree on whether two arbitrary events are synchronous nor whether they happen at the same place.
The specific physical effects this has are too varied to discuss them here at length and have already been extensively discussed on this site, see e.g. How can time dilation be symmetric?, What is the proper way to explain the twin paradox? and many other questions in the general-relativity tag.
answered 8 hours ago
ACuriousMind♦ACuriousMind
75.8k18 gold badges139 silver badges355 bronze badges
$endgroup$
add a comment |
Your Answer
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "151"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/4.0/"u003ecc by-sa 4.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f500567%2fwhats-the-problem-with-euclidean-geometry-for-astronomical-phenomena%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
On the scale of most astronomical phenomena, general relativity (GR) is the relevant theory.
There are many aspects in which this theory is incompatible with Euclidean geometry. An illustrative and often used analogy is that Euclidean geometry is already inaccurate for a being confined to the surface of a sphere - if you draw a triangle on a sphere, its interior angles do not in general sum up to 180°. What makes GR a bit strange still is that it posits that it is not space alone that participates in such curved geometry, but spacetime.
That is, general relativity does not assume that space(time) is flat, and it even intermingles space and time so that different observers that move relative to each other will neither agree on whether two arbitrary events are synchronous nor whether they happen at the same place.
The specific physical effects this has are too varied to discuss them here at length and have already been extensively discussed on this site, see e.g. How can time dilation be symmetric?, What is the proper way to explain the twin paradox? and many other questions in the general-relativity tag.
answered 8 hours ago
ACuriousMind♦ACuriousMind
75.8k18 gold badges139 silver badges355 bronze badges
$endgroup$
add a comment |
$begingroup$
On the scale of most astronomical phenomena, general relativity (GR) is the relevant theory.
There are many aspects in which this theory is incompatible with Euclidean geometry. An illustrative and often used analogy is that Euclidean geometry is already inaccurate for a being confined to the surface of a sphere - if you draw a triangle on a sphere, its interior angles do not in general sum up to 180°. What makes GR a bit strange still is that it posits that it is not space alone that participates in such curved geometry, but spacetime.
That is, general relativity does not assume that space(time) is flat, and it even intermingles space and time so that different observers that move relative to each other will neither agree on whether two arbitrary events are synchronous nor whether they happen at the same place.
The specific physical effects this has are too varied to discuss them here at length and have already been extensively discussed on this site, see e.g. How can time dilation be symmetric?, What is the proper way to explain the twin paradox? and many other questions in the general-relativity tag.
answered 8 hours ago
ACuriousMind♦ACuriousMind
75.8k18 gold badges139 silver badges355 bronze badges
$endgroup$
add a comment |
$begingroup$
On the scale of most astronomical phenomena, general relativity (GR) is the relevant theory.
There are many aspects in which this theory is incompatible with Euclidean geometry. An illustrative and often used analogy is that Euclidean geometry is already inaccurate for a being confined to the surface of a sphere - if you draw a triangle on a sphere, its interior angles do not in general sum up to 180°. What makes GR a bit strange still is that it posits that it is not space alone that participates in such curved geometry, but spacetime.
That is, general relativity does not assume that space(time) is flat, and it even intermingles space and time so that different observers that move relative to each other will neither agree on whether two arbitrary events are synchronous nor whether they happen at the same place.
The specific physical effects this has are too varied to discuss them here at length and have already been extensively discussed on this site, see e.g. How can time dilation be symmetric?, What is the proper way to explain the twin paradox? and many other questions in the general-relativity tag.
answered 8 hours ago
ACuriousMind♦ACuriousMind
75.8k18 gold badges139 silver badges355 bronze badges
$endgroup$
On the scale of most astronomical phenomena, general relativity (GR) is the relevant theory.
There are many aspects in which this theory is incompatible with Euclidean geometry. An illustrative and often used analogy is that Euclidean geometry is already inaccurate for a being confined to the surface of a sphere - if you draw a triangle on a sphere, its interior angles do not in general sum up to 180°. What makes GR a bit strange still is that it posits that it is not space alone that participates in such curved geometry, but spacetime.
That is, general relativity does not assume that space(time) is flat, and it even intermingles space and time so that different observers that move relative to each other will neither agree on whether two arbitrary events are synchronous nor whether they happen at the same place.
The specific physical effects this has are too varied to discuss them here at length and have already been extensively discussed on this site, see e.g. How can time dilation be symmetric?, What is the proper way to explain the twin paradox? and many other questions in the general-relativity tag.
answered 8 hours ago
ACuriousMind♦ACuriousMind
75.8k18 gold badges139 silver badges355 bronze badges
answered 8 hours ago
ACuriousMind♦ACuriousMind
75.8k18 gold badges139 silver badges355 bronze badges
answered 8 hours ago
ACuriousMind♦ACuriousMind
75.8k18 gold badges139 silver badges355 bronze badges
answered 8 hours ago
ACuriousMind♦ACuriousMind
75.8k18 gold badges139 silver badges355 bronze badges
75.8k18 gold badges139 silver badges355 bronze badges
add a comment |
add a comment |
Thanks for contributing an answer to Physics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f500567%2fwhats-the-problem-with-euclidean-geometry-for-astronomical-phenomena%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
