Understanding through Discussion

QuickSearch

 Messages Thread Titles This Thread

 Welcome! You are not logged in. [ Login ] EvC Forum active members: 64 (9071 total)
 309 online now: jar, nwr, ringo, Tanypteryx, WookieeB (5 members, 304 visitors) Newest Member: FossilDiscovery Upcoming Birthdays: Percy Post Volume: Total: 893,084 Year: 4,196/6,534 Month: 410/900 Week: 116/150 Day: 9/38 Hour: 1/0

EvC Forum Science Forums Big Bang and Cosmology

# Geometry of Spacetime

Thread  Details

Author Topic:   Geometry of Spacetime
nwr
Member
Posts: 5968
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 2.9

 (1)
 Message 3 of 41 (701434) 06-18-2013 11:57 PM Reply to: Message 1 by Iblis06-18-2013 10:11 PM

 a² + b² = c²

With the Pythagorean formula, we measure distance in two dimensions as . The equivalent for three dimensions is to measure distance as

Once we add in a time dimension, that becomes

This assumes that we have scaled things so that , the velocity of light, is 1.

That's pretty much the metric that is the basis for relativity.

Edited by nwr, : No reason given.

Fundamentalism - the anti-American, anti-Christian branch of American Christianity

 This message is a reply to: Message 1 by Iblis, posted 06-18-2013 10:11 PM Iblis has taken no action

 Replies to this message: Message 4 by Coyote, posted 06-19-2013 12:02 AM nwr has replied

nwr
Member
Posts: 5968
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 2.9

 Message 5 of 41 (701438) 06-19-2013 12:50 AM Reply to: Message 4 by Coyote06-19-2013 12:02 AM

 Why do you + x, y, and z but –t? Why not +t?

It's connected to the fact that there's a minus in the wave equation:

Light (electromagnetic fields) satisfy the wave equation.

 And how do you know?

I'll admit that my relativity is a bit rusty.

Fundamentalism - the anti-American, anti-Christian branch of American Christianity

 This message is a reply to: Message 4 by Coyote, posted 06-19-2013 12:02 AM Coyote has taken no action

nwr
Member
Posts: 5968
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 2.9

 Message 16 of 41 (701535) 06-20-2013 3:28 PM Reply to: Message 15 by New Cat's Eye06-20-2013 12:05 PM

 The way I understand it, the only way for the time component of your path to be at a true 90 degrees would be if you were not moving.

And the way I see it, is that in space-time there is no such thing as "true 90 degrees" between a time-like direction and a space-like direction. It is all relative to the observers frame.

Fundamentalism - the anti-American, anti-Christian branch of American Christianity

 This message is a reply to: Message 15 by New Cat's Eye, posted 06-20-2013 12:05 PM New Cat's Eye has replied

 Replies to this message: Message 17 by New Cat's Eye, posted 06-20-2013 4:10 PM nwr has replied

nwr
Member
Posts: 5968
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 2.9

 Message 18 of 41 (701543) 06-20-2013 7:34 PM Reply to: Message 17 by New Cat's Eye06-20-2013 4:10 PM

 But if you have a particle that is at rest (in whatever reference frame), then aren't the time-like and space-like directions at 90 degrees?

I'm not sure if that even makes sense.

Take ordinary 2-dimensional space. If we stretch out the x-axis, say rescale it so that what was one unit of length becomes 2 units, then angles change -- assuming that we don't also stretch out the y-axis. So, in some sense, the magnitude of angles is an artifact of how we measure them.

In the case of spatial directions, we normally require rotational symmetry. And if we require rotational symmetry, we cannot stretch out the x-axis without also stretching out the y-axis.

As far as I know, we cannot rotate things from a space-like direction to a time-like direction. So we don't have something like rotational symmetry to normalize our way of measuring. So I think that unavoidably leaves measurements of angles between space-like and time-like directions to be dependent on our arbitrarily chosen standards.

Fundamentalism - the anti-American, anti-Christian branch of American Christianity

 This message is a reply to: Message 17 by New Cat's Eye, posted 06-20-2013 4:10 PM New Cat's Eye has taken no action

 Replies to this message: Message 19 by NoNukes, posted 06-21-2013 1:22 AM nwr has seen this message

nwr
Member
Posts: 5968
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 2.9

 Message 25 of 41 (701947) 06-28-2013 9:03 AM Reply to: Message 24 by Iblis06-28-2013 12:14 AM

Re: Anybody?
Some of this is basic calculus, and some of it comes from the mathematical model that Einstein used in special relativity.

Einstein's intuition told him that the velocity of light should be the same for all observers, and the Michelson-Morley experiment seemed to confirm that. But that was incompatible with the traditional Newtonian/Euclidean view of space, which saw time and distance as independent. So the problem was one of finding a new metric which connected time and space in such a way that the velocity of light could be the same for all observers.

It worked very well. It accurately predicted motion in particle accelerators. One could deduce which seemed to accurately account for the energy seen in radioactive materials, and which was confirmed by nuclear physics.

And yes, many people at that time thought it counter-intuitive. But science is a pragmatic enterprise, and it is hard to beat "it works very well."

Fundamentalism - the anti-American, anti-Christian branch of American Christianity

 This message is a reply to: Message 24 by Iblis, posted 06-28-2013 12:14 AM Iblis has taken no action

 Date format: mm-dd-yyyy Timezone: ET (US)
 Newer Topic | Older Topic Jump to:Board Administration     The Public Record     Announcements     Proposed New Topics     Suggestions and Questions Science Forums     The Bible: Accuracy and Inerrancy     Big Bang and Cosmology     Dates and Dating     Education and Creation/Evolution     Biological Evolution     Geology and the Great Flood     Human Origins and Evolution     Intelligent Design     Is It Science?     Creation/Evolution Miscellany     Origin of Life Social and Religious Issues     Bible Study     Comparative Religions     Social Issues and Creation/Evolution     Faith and Belief     Theological Creationism and ID Side Orders     Coffee House     The Great Debate     Free For All     Post of the Month     Links and Information     Creation/Evolution In The News     The Book Nook     Columnist     In Memoriam     Practice Makes Perfect Archives     Topic Proposals Archive     Showcase Retired Forums     Short Subjects (No new topics or messages)     Welcome visitors

Copyright 2001-2018 by EvC Forum, All Rights Reserved

™ Version 4.1
Innovative software from Qwixotic © 2022