14 replies to this topic

[chubtoad]

This thread will serve as an introduction and summary of relativity.

Edited by chubtoad, 23 July 2005 - 09:20 AM.

[chubtoad]

http://science.howst...relativity2.htm

Frames of Reference

Einstein's special theory of relativity is based on the idea of reference frames. A reference frame is simply "where a person (or other observer) happens to be standing". You, at this moment, are probably sitting at your computer. That is your current reference frame. You feel like you are stationary, even though you know the earth is revolving on its axis and orbiting around the sun. Here is an important fact about reference frames: There is no such thing as an absolute frame of reference in our universe. By saying absolute, what is actually meant is that there is no place in the universe that is completely stationary. This statement says that since everything is moving, all motion is relative. Think about it - the earth itself is moving, so even though you are standing still, you are in motion. You are moving through both space and time at all times. Because there is no place or object in the universe that is stationary, there is no single place or object on which to base all other motion. Therefore, if John runs toward Hunter, it could be correctly viewed two ways. From Hunter's perspective, John is moving towards Hunter. From John's perspective, Hunter is moving towards John. Both John and Hunter have the right to observe the action from their respective frames of reference. All motion is relative to your frame of reference. Another example: If you throw a ball, the ball has the right to view itself as being at rest relative to you. The ball can view you as moving away from it, even though you view the ball as moving away from you. Keep in mind that even though you are not moving with respect to the earth's surface, you are moving with the earth

Edited by chubtoad, 23 July 2005 - 09:18 AM.

[chubtoad]

http://www.pinkmonke...35/p3535501.asp

The postulates of Special Relativity

Postulate I

The Principle of Relativity holds good for the whole of Physics, i.e. the laws of Physics should be invariant under transformations from one to another inertial frame in relative uniform translational motion with respect to each other.

Postulate II

The Speed of light in any direction in vacuum in any inertial frame of reference is the same universal constant C = 3*10^8 m/s.

Edited by chubtoad, 23 July 2005 - 09:17 AM.

[chubtoad]

Time dilation
http://www.thebigvie...raphformula.gif
http://www.fourmilab...p/timedial.html
http://physics.about...t1/a/110703.htm

Rest Frame Time Elapsed
per Day on Ship
v/c Days Years
0.0 1.00 0.003
0.1 1.01 0.003
0.2 1.02 0.003
0.3 1.05 0.003
0.4 1.09 0.003
0.5 1.15 0.003
0.6 1.25 0.003
0.7 1.40 0.004
0.8 1.67 0.005
0.9 2.29 0.006
0.95 3.20 0.009
0.97 4.11 0.011
0.99 7.09 0.019
0.995 10.01 0.027
0.999 22.37 0.061
0.9999 70.71 0.194
0.99999 223.61 0.613
0.999999 707.11 1.937
0.9999999 2236.07 6.126
0.99999999 7071.07 19.373
0.999999999 22360.68 61.262
0.9999999999 70710.68 193.728
0.99999999999 223606.79 612.621
0.999999999999 707114.60 1937.300
0.9999999999999 2235720.41 6125.261
0.99999999999999 7073895.38 19380.535
0.999999999999999 22369621.33 61286.634

Edited by chubtoad, 23 July 2005 - 09:17 AM.

[chubtoad]

http://www.fourmilab...ip/lorentz.html
http://www.fourmilab.../gr_lorentz.gif
http://home.usit.net...en/tlgtcon4.gif

Lorentz Contraction

Here's a table that gives the observed length for velocities of various fractions of the speed of light.





Velocity / Length
0 1.000
0.1 0.995
0.2 0.980
0.3 0.954
0.4 0.917
0.5 0.866
0.6 0.800
0.7 0.714
0.8 0.600
0.9 0.436
0.95 0.312
0.97 0.243
0.99 0.141
0.995 0.100
0.999 0.045
0.9999 0.014

Edited by chubtoad, 11 November 2003 - 06:57 AM.

[chubtoad]

http://www.starlight...ialation_sm.gif

Equations Compared to classical view.

[chubtoad]

http://www-groups.dc...relativity.html
History General relativity

Edited by chubtoad, 23 July 2005 - 09:15 AM.

[chubtoad]

http://www.physics.f...y/Spacetime.gif

The Light Cone/Spacetime

Edited by chubtoad, 11 November 2003 - 08:01 PM.

[chubtoad]

Space-Time pictures

http://casa.colorado...sh/sr/lor6f.gif
http://www.valdosta....ages/nsgrid.gif
http://www.astronomy...lutn/grwarp.gif

Edited by chubtoad, 11 November 2003 - 08:01 PM.

[Lazarus Long]

Thank you, thank you, thank you [!]

I have been looking for a concise analysis of Lorentz transformations for some time now and the graphs and formulas you just posted are extremely useful to the novel I have been working on called the "Age of Relativity," which I postulate is the social epoch following the late middle "Age of Information" that I perceive us as going through now.

Secondly, some interesting overlaps of the Relative Referent issue is the treatment of the "Observer" as it overlaps aspects of the philosophical importance of the definition of self, questions of communication between individuals (or self aware identities) in different temporal rates of reference, and a "Singularity" as it must overcome relativity for it to exist in a "Unified Manner" beyond the restrictions of local space/time for such a concept to possess any coherency on a universal scale.

This is why I have said to so many overenthusiastic "believers" in the "Singularity" occurring in the next few decades that I suspect they are being "premature." The issue of Faster Than Light Communications is a hurdle that would require a logical solution before such a possible phenomenon could move very far off world and certainly it becomes a subtle variant for consolidating data processing even at the limits of our Solar System.

I don't want to belabor the point too much as it risks going well beyond the scope of this thread but it is not an answer to the restrictions of faster than light to claim the "Super Intelligence" will figure out a solution or to jump back and forth between the core debates of QM and Relativity. I am extremely glad you started this thread Chubtoad, thank you again.

[chubtoad]

http://images.google...w...-8&oe=UTF-8
http://www.upscale.u.../massenergy.gif

Relativistic mass

[chubtoad]

http://www.upscale.u.../massenergy.gif
Common Relativity Questions

Edited by chubtoad, 23 July 2005 - 09:14 AM.

[chubtoad]

http://hep.ph.liv.ac...mass/img004.gif

Relativistic Momentum

[chubtoad]

http://archive.ncsa....Images/EMC2.gif
http://www.udel.edu/...tm/146nosr5.jpg

Mass Energy Equivalence

Everybody already knows this equation. If you forgot c is a constant about equal to the speed of light about 3.0*10^8 m/s and 3.0*10^5 km/s. The graph would just be a line since it is a linear relationship and c^2 is constant.




Here is energy as a function of velocity

Edited by chubtoad, 12 November 2003 - 04:43 AM.

[Lazarus Long]

Here is a more basic link but it is very valuable as a link to many more links on numerous aspects that are related. It is produced by NASA and the science and resources are impeccable. It is an excellent entry point if you are reading this post and feeling dumbfounded by much of what you scanned to get this far.

http://universe.gsfc.nasa.gov/



The Science
--------------------------------------------------------------------------------


--------------------------------------------------------------------------------

How did the Universe begin?

Does time have a beginning and an end?

Does space have edges?

The questions are clear and simple. They are as old as human curiosity. But the answers have always seemed beyond the reach of science. Until now.

In their attempts to understand how space, time, and matter are connected, Einstein and his successors made three predictions. First, space is expanding from a Big Bang; second, space and time can tie themselves into contorted knots called "black holes" where time actually comes to a halt; third, space itself contains some kind of energy that is pulling the Universe apart. Each of these three predictions seemed so fantastic when it was made that everyone, including Einstein himself, regarded them as unlikely. Incredibly, all three have turned out to be true. Yet Einstein's legacy is one of deep mystery, because his theory is silent on three questions raised by his fantastic predictions:


What powered the Big Bang?
What happens to space, time, and matter at the edge of a black hole?
What is the mysterious dark energy pulling the Universe apart?

To find answers, we must venture beyond Einstein. The answers require new theories, such as the inflationary universe and new insights in high-energy particle theory. Like Einstein's theory, these make fantastic predictions that seem hard to believe: new unseen dimensions and entire universes beyond our own. We must find facts to confront and guide these new theories. Powerful new technologies now make this possible.

Here is where the Beyond Einstein story starts. By exploring the three questions that are Einstein's legacy, we begin the next revolution in understanding our Universe. We chart our way forward using clues from observations and from new ideas connecting the worlds of the very small and the very large.

| Scientific Goals and Missions |