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Thread: Einstein's Relativity

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    Local Pedant Contributor lazserus's Avatar
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    Arrow Einstein's Relativity

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    Many people think the concept of Einstein's relativity theory is incomprehensible to the layman. This is far from the truth. Naturally, certain aspects of General Relativity are much more difficult to grasp, but the overall concept is not beyond layman understanding. I am attempting to explain the overall concept of relativity so that anyone can grasp it. I'll start with a few questions about the subject.

    Relativity theory was first proposed by Galileo. The theory is that the laws of physics apply to all equally, there are no special circumstances. This was significant for the Renaissance period because of what disciplines of physics were known. Einstein adopted Galilean relativity and simply applied it to contemporary technology and knowledge by creating Special Relativity. Don't be fooled by the term "special" because it wasn't that the theory was actually different or even special. What Einstein did was associate Galilean relativity with known physics of the time. The major difference was that Einstein introduced a new constant of measurement: the speed of light. The speed of light was well established before Einstein published his special relativity paper; he just put the constant speed of light as a reference of measurement. This may be getting confusing, but just know that all Einstein did with his paper on Special Relativity was upgrade Galileo's theory so that it matched the times. So truly, Galileo's theory of relativity is still used today, but we tend to associate it with Einstain. Again, relativity theory is that the laws of physics apply to all within a relative frame of reference.

    A perfect application would be: You're standing still and I'm sprinting toward you. You could say I am running at 5 miles an hour relative to your position. Though I'm running, I could say you're moving 5 miles an hour toward me. The point is, we are both right! It's relative motion! As observers, we both measure motion identically. Special relativity explained!

    Special relativity is explained above. It simply covers that the laws of physics apply to all observers regardless of velocity. However, Einstein later introduced General Relativity. GR focused on the specifics of velocities equivalent to the speed of light and gravity. This is where things get a little complicated and even wacky.

    According to General Relativity (GR), massive objects distort space and time. Even objects as insignificant as basketballs bend the space around themselves. Granted, objects of such insignificant stature are irrelevant to this question, it's important to know. When we look at the larger scale, such as our solar system, we get a better picture of GR. General Relativity, with all its proven applications, is actually very obscure. Einstein proposed that the universe is flat, much like a disc. Planetary orbits are actually straight paths, but they mimic circular (or elliptical) orbits in a curved space. This is not a difficult concept to grasp. If you were to take a piece of paper and draw a straight line from one end to another, then fold the page so that the ends connected, you would create a simplified model of Einstain's universe. The paper represents the universe while the line is the path any body would take. This is an Einstein geodesic.

    The fun comes when dealing with time dilation. According to Einstein, all massive objects not only bend space around them, but influence time. This is a theory that anyone can experiment with. If you took two clocks and placed one at a high altitude and another at a lower, you'd notice a different in time after a few weeks. Granted the time difference would be in the thousands of seconds, it would still be sginificant. Imagine that at a grander scale, such as astronauts (cosmonauts) in high orbit arouind the earth for long periods of time. Not only does gravity influence time, but velocity as well. The thoery states that if you travel at close to the speed of light you will age slower. Hence, the Twin Paradox.

    That about covers the basics. Naturally there are many questions about the theories, so ask away.
    Last edited by lazserus; Jan 31st, 2007 at 11:04 PM.

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    Dead Meat
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    A few Questions.

    Thanks for that great summary Laz. I read that Einstein wasn't the first to postulate this formula E=MCSq. If so then why is he the main reference?

    Getting to my questions.

    1. If a photon has no mass then how can gravity affect its path?

    2. Can Gravity exist to an object travelling at the speed of light towards it. I mean on one axis directly at it. If one travels (if possible) at the speed of light towards a black hole nothing will happen as it is impossible to go any faster?

    3. Have we records of black holes colliding?

    Last was a bit off topic but just threw it in there to see if we had and if so is there any records of what happened?

    Thanks

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    Cart-mod 2.0 Global Moderator Cartesiantheater's Avatar
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    Quote Originally Posted by Agent Tellman View Post

    1. If a photon has no mass then how can gravity affect its path?
    Because the space around the photon is bent by gravitational fields. It isn't gravity pulling on the photons- it's gravity warping the space that the photons travel through.

    Here's a link.
    Quote Originally Posted by link
    We also knew that photons are affected by gravitational fields not because photons have mass, but because gravitational fields (in particular, strong gravitational fields) change the shape of space-time. The photons are responding to the curvature in space-time, not directly to the gravitational field.
    "I was put on trial twice near Y2K for acting like Jesus and claiming to be the Messiah. Its not everyday that a man parks a Chariot of Fire in front of a tomb and stands against the US government with a bow and razor tipped arrows over his shoulder. I wore a suit of armor and was protected by an invisible bubble and my sharp tongue was more than the judicial system could handle."Jake
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    Local Pedant Contributor lazserus's Avatar
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    Quote Originally Posted by Agent Tellman View Post
    Thanks for that great summary Laz. I read that Einstein wasn't the first to postulate this formula E=MCSq. If so then why is he the main reference?
    I haven't heard of anyone actually postulating E=mc^2 specifically, but you may be thinking of Poincaré. Poincaré was working on something very similar to, but independently of Einstein.

    From Wikipedia:
    Poincaré introduced the modern principle of relativity and was the first to present the Lorentz transformations in their modern symmetrical form. Poincaré discovered the remaining relativistic velocity transformations and recorded them in a letter to Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, the final step in the formulation of the theory of special relativity.
    Quote Originally Posted by Agent Tellman View Post
    1. If a photon has no mass then how can gravity affect its path?
    Using the reference CT provided, also recall the notebook paper analogy. Say the straight line represents a photon and the paper space. Then, you could take a tennis ball and let it represent a massive stellar object. If you fold the paper around the tennis ball, the photon is still traveling in a straight line, but now in curved space.

    Quote Originally Posted by Agent Tellman View Post
    2. Can Gravity exist to an object travelling at the speed of light towards it. I mean on one axis directly at it. If one travels (if possible) at the speed of light towards a black hole nothing will happen as it is impossible to go any faster?
    I'm not exactly sure of what you're asking here. Could you rephrase the question?

    Quote Originally Posted by Agent Tellman View Post
    3. Have we records of black holes colliding?
    Absolutely. There is an article here. Also, you can look at some images of the processes.

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    star gazer..... Contributor Protostar's Avatar
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    #1 Where can I go live at the speed of light and slow down my aging process?
    #2 I wonder if anti-matter effects gravity?
    #3 the all knowing question everyone wants answered: if all of our planets line up in the galactic plane <precission of equnox> will the gravity of each planet effect each other?

    Photon light is interesting as the astronauts couldn't sleep as the photon's shot pass them and kept them awake <in the sea of tranquility>. So they saw it under their eyelids! That's strange.

    Do not fear death so much, but rather the inadequate life.

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    Laz's Test Bunny Contributor Sammy56's Avatar
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    Quote Originally Posted by Protostar
    #1 Where can I go live at the speed of light and slow down my aging process?
    Technically, you wouldn't slow down your own personal aging process. You would still feel like you lived a normal amount of years, assuming no kind of accident. It's just possible that everyone else's aging process would be "speeded up" by the fact that time is going slower for you and faster for them.

    Quote Originally Posted by Protostar
    #2 I wonder if anti-matter effects gravity?
    I'm not sure on that one...

    Quote Originally Posted by Protostar
    #3 the all knowing question everyone wants answered: if all of our planets line up in the galactic plane <precission of equnox> will the gravity of each planet effect each other?
    I think I can answer this one. No. Although all matter in the universe pulls on every other particle of matter in the universe, gravity drops off quickly when distance is increased. That's why the moon, being so close, affects us dramatically. However, the rest of the planets are too far away for them to have noticeable gravitational effects and, although a planetary alignment would be cool, the planets would not interfere with us gravitationally.
    "As far as the stars are from Earth is the distance of your wonderfulness."

    "For there is nothing either good or bad but thinking makes it so..." ~Shakespeare

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    ראה Contributor Raptor Witness's Avatar
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    Laz, I'm so impressed. You are too good for the AO forum of misfits and harbor steals.

    It must grieve your brain to have to pay us any attention, at all.
    "In the last days perilous times will come, for men shall have a form of godliness, but denying the power thereof." 2 Tim 3

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    Lucky survivor Seasoned Member The Space Pope's Avatar
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    Quote Originally Posted by Raptor Witness View Post
    Laz, I'm so impressed. You are too good for the AO forum of misfits and harbor steals.

    It must grieve your brain to have to pay us any attention, at all.
    I agree that Laz is great, but maybe he enjoys the misfits of AO. I know I do; it just wouldn't be the same without Bill, uki, GGTMK, CT, Jake, you, or any of the other countless crazies on here.

    *NOTE: I use "crazies" affectionately
    When they kick at your front door
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    With your hands on your head
    Or on the trigger of your gun

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    Cart-mod 2.0 Global Moderator Cartesiantheater's Avatar
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    Quote Originally Posted by Sammy56 View Post
    Technically, you wouldn't slow down your own personal aging process. You would still feel like you lived a normal amount of years, assuming no kind of accident. It's just possible that everyone else's aging process would be "speeded up" by the fact that time is going slower for you and faster for them.
    Well, I may be wrong, but as you approach the speed of light, time should approach zero, should it not? (however, since you cannot ever reach the speed of light... hehe... we have a LIMIT...)

    Thinking of it as a 2-D relationship, with space the y-axis and time the x-axis, as you move more through space (increase the y-axis) then you should move less through time (this is assuming that all objects ALWAYS are moving through SPACETIME at the speed of light- although for us, we are moving through TIME much more than through SPACE [of course, the two are connected- this is just an illustration from the book mentioned below- and I really should say our VELOCITY through time is much faster than that of space- obviously...]; as you accelerate, you move more through space and less through time [that is, you move a a velocity through space, which SUBTRACTS some from your velocity through time, because your total speed can never pass c)

    *btw, this comes from an example in Brian Greene's The Elegant Universe.
    I hope I haven't misrepresented it...
    "I was put on trial twice near Y2K for acting like Jesus and claiming to be the Messiah. Its not everyday that a man parks a Chariot of Fire in front of a tomb and stands against the US government with a bow and razor tipped arrows over his shoulder. I wore a suit of armor and was protected by an invisible bubble and my sharp tongue was more than the judicial system could handle."Jake
    "The toilet is more than a throne. It is a sacred chamber."-Anton LaVey, High Priest of Satanism

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    Dead Meat
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    Cool Thread

    Thanks for those answers and links Laz. Great Stuff.

    My question is that if your momentum was C and you were heading straight for a large object with a large gravitation pull would you not feel anything as you could npt accelerate any faster. Hence gravity has no effect on you on a direct axis. If you were slightly off direct axis then gravity would only effect you on a perpendicular axis. Difficult to explain if this doesn't make sense so happy to let someone else add to this if they feel they know what I am trying to say.

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    Cart-mod 2.0 Global Moderator Cartesiantheater's Avatar
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    Quote Originally Posted by Agent Tellman View Post
    Thanks for those answers and links Laz. Great Stuff.

    My question is that if your momentum was C and you were heading straight for a large object with a large gravitation pull would you not feel anything as you could npt accelerate any faster. Hence gravity has no effect on you on a direct axis. If you were slightly off direct axis then gravity would only effect you on a perpendicular axis. Difficult to explain if this doesn't make sense so happy to let someone else add to this if they feel they know what I am trying to say.
    Maybe I'm not quite understanding your question, but it's easier for me to think of it like this:

    First, the "natural" motion of objects would be to move in a straight line.

    Second, for me, it's easier to think of gravity as nothing but the warping of space and time, rather then the Newtonian concept of gravity pulling on all objects. And in that way, if you view an object moving at c as just going straight, but due to a gravitational field the space it is moving in is curved toward the massive object, then the object will be "pulled" toward the massive object simply because it moves in a "straight" line, but the space it is moving in is curved.

    So gravity affects you if the space you are moving through is curved by the objects mass, and in this way the light really isn't accelerating any faster relative to anything. It is moving in a straight line, but the space it's moving in is curved... of course, I could be wrong...I really don't have an understanding of Einstein's explanation of gravity...

    Now, again, I don't think that answers your question...(I don't understand this "axis" part of it...) but hey... I tried. : ) In time laz will sign on... hehe...he's quite knowledgeable on... everything...
    "I was put on trial twice near Y2K for acting like Jesus and claiming to be the Messiah. Its not everyday that a man parks a Chariot of Fire in front of a tomb and stands against the US government with a bow and razor tipped arrows over his shoulder. I wore a suit of armor and was protected by an invisible bubble and my sharp tongue was more than the judicial system could handle."Jake
    "The toilet is more than a throne. It is a sacred chamber."-Anton LaVey, High Priest of Satanism

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    ראה Contributor Raptor Witness's Avatar
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    Quote Originally Posted by The Space Pope View Post
    I agree that Laz is great, but maybe he enjoys the misfits of AO. I know I do; it just wouldn't be the same without Bill, uki, GGTMK, CT, Jake, you, or any of the other countless crazies on here.

    *NOTE: I use "crazies" affectionately
    Nuts and snakes,that's what we have here. The snakes are watching the nuts and the nuts are =[stomping] on the snakes.
    "In the last days perilous times will come, for men shall have a form of godliness, but denying the power thereof." 2 Tim 3

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    Local Pedant Contributor lazserus's Avatar
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    Quote Originally Posted by Protostar View Post
    #1 Where can I go live at the speed of light and slow down my aging process?
    You don't actually need to be traveling at a relativistic velocity in order to slow your aging down. The longer you spend in motion away from massive objects (planets, planetoids, stars, etc.) the slower you will age. Planets with less gravity, such as Mars, would affect aging differently that on Earth. The best analogy is using the clock on the water tower. If you took two atomic clocks, placing one on top of a tall water tower and the other at sea level and left them there for a month, you could return and notice that the times on the two were different. The one closer to the earth will be ahead of the one on the tower because gravity has a stronger influence closer to the center of the Earth.

    Quote Originally Posted by Sammy56 View Post
    Technically, you wouldn't slow down your own personal aging process. You would still feel like you lived a normal amount of years, assuming no kind of accident. It's just possible that everyone else's aging process would be "speeded up" by the fact that time is going slower for you and faster for them.
    It's the other way around. All clocks, including the biological clock actually slows at relativistic velocities. As CT mentioned, the closer to c an object reaches the closer to time equals zero.

    Quote Originally Posted by Protostar View Post
    #2 I wonder if anti-matter effects gravity?
    Yes, anti-matter warps space-time just as ordinary matter does and has gravitational consequences. Anti-matter is nothing more than ordinary matter with reversed spin and charge. The anti-matter equivelent of an electron is a positron.

    Quote Originally Posted by Protostar View Post
    #3 the all knowing question everyone wants answered: if all of our planets line up in the galactic plane <precission of equnox> will the gravity of each planet effect each other?
    A similar alignment has happened recently and no mayhem was caused. A lot of people are concerned that if a galactic alignment happened gravity would be streamlined and cause a variety of natural disasters. That's highly improbable. Like Sammy said, gravity affects every object but only is significantly powerful when closer to massive objects. Gravity is the weakest of all the forces.

    Quote Originally Posted by Agent Tellman View Post
    Thanks for those answers and links Laz. Great Stuff.

    My question is that if your momentum was C and you were heading straight for a large object with a large gravitation pull would you not feel anything as you could npt accelerate any faster. Hence gravity has no effect on you on a direct axis. If you were slightly off direct axis then gravity would only effect you on a perpendicular axis. Difficult to explain if this doesn't make sense so happy to let someone else add to this if they feel they know what I am trying to say.
    Simple answer would be to say no. Since you are already traveling at a relativistic velocity you would not notice a head-on approach. However, if you were to change your trajectory in the slightest the massive object's gravity well accelerate you and you could lose relativistic momentum, thus your velocity decreases. Make it known that decceleration is a fictional term. Any change in an object's velocity is called acceleration.

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    Dead Meat
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    So Laz, Does all gravitational bodies have a blind spot so to speak when it comes to gravity effect? A direct approach to a gravitation point at the speed of light produces no discernible effect.

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    Survivalist! Skynet12's Avatar
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    I think were' going too complex with this...
    I come and go but as long as CT is on here, there needs be an antichrist to oppose his wonder ;) x

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    Local Pedant Contributor lazserus's Avatar
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    Quote Originally Posted by Agent Tellman View Post
    So Laz, Does all gravitational bodies have a blind spot so to speak when it comes to gravity effect? A direct approach to a gravitation point at the speed of light produces no discernible effect.
    There are no "blind spots". It's just that when you're approaching something at relativistic velocities you're already traveling as fast as possible, so no other force can speed you up. If you were traveling away from something the story would be different.

    Quote Originally Posted by Skynet12 View Post
    I think were' going too complex with this...
    I don't think so. It's all within the bounds of relativity.

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    Cart-mod 2.0 Global Moderator Cartesiantheater's Avatar
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    A Bit On General Relativity: Is There Any Reason to Postulate a New Geometry For Space-Time?

    I was going to make a new thread on this, but I figured there are enough special threads. This should be posted here.


    In the discussion about the speed of light in special relativity, the fact that general relativity supposes that our universe is not based upon Euclidean geometry came up. This got me thinking, and then reading*. Einstein's general relativity involves a new kind of geometry in which space (and time) curve and warp. Why did he do that?


    Okay, as we all know, Einstein explained the reason that inertial mass always equals gravitational mass (i.e. the mass you measure on a scale equals the mass you would calculate from F = ma if you know the force and acceleration on a body). Prior to Einstein you could only assume that this equivalence was a coincidence of nature. Einstein's argument began by giving the following example:



    Suppose there is a guy in a closed off room floating somewhere in the deep regions of space, far enough away from every object that there is no gravity. He is basically floating in the middle of the room, because there is no gravitational attraction moving him anywhere. If he pulls his wallet out and lets it go, it will just float right next to him. If he gives it a little push, it will move in the direction he pushed it until it hits the wall. This is all possible because the man is in an inertial reference frame- i.e. Newton's laws accurately describe what happens in his room.

    Now, let's say outside the room, unbeknownst to the man, there is a rope attached to a giant hook on the 'ceiling.' Then some 'being' starts pulling on the rope with a constant force, and so the room, from anyone watching on the outside, would be constantly accelerating in the direction being pulled.

    However, inside the room, the man will suddenly feel himself being pulled down to the 'floor' of the room. If he now takes off his watch and lets it go, instead of just floating like his wallet did before, it will 'fall' straight down to the ground. The man is completely justified, therefore, in assuming that he is now in a gravitational field, and all objects in the room will 'fall' down just like his watch does.


    The point is that being uniformly accelerated "feels" exactly like being in a gravitational field. This led Einstein to the famous "equivalence principle," which states that a uniform acceleration and a gravitational field amount to the same thing, more or less.




    But why should this mean that space-time is "warped?" How does Einstein get from "uniform acceleration and gravitation are indistinguishable" to "space-time bends?"
    Hopefully this post will shed some light on that. I can't explain it in any real detail, but I can repeat an example that shows why Euclidean geometry had to be thrown out the window as a geometrical theory of our universe.


    Here is the example, a though experiment Einstein devised:





    Let's say there is a very large circular disk, rotating at some fast rate. On this disk, very near the center is a small circle drawn. Further, assume there are two observers: one in the middle of the giant disk, and one on the outside. The observer on the outside is in an inertial frame. Here is what the disk looks like:



    A little circle painted on the center of the big circle.




    Now, imagine the whole thing rotating really fast. If you are clever, you will notice that points on the outside of the circle are moving at a greater speed than points further inside the circle. That is because in order to remain attached to the circle, those outside points have to cover more ground in the same amount of time as points closer to the middle of the circle do. (This is pretty obvious if you've ever watched a CD or record spin, or if you've ever been hit in the head by a stick- it hurts a lot more to be hit by the edge of a stick moving in an arching path than to move in close and instead get hit by, say, the handle, as the edge of the stick moves past you.)


    Okay, so now the real test: the two observers will measure the radii and circumference of each circle, and see if both of them give the ration of π. If they both give this value, than we can safely assume that the laws of Euclidean geometry hold. If either one of them do not, then we can only assume that the laws of Euclidean geometry hold for the frame in which the ration of π is measured, and we cannot assume that the laws of Euclidean geometry hold for both reference frames.



    Alright, so the outside observer measured the length of both radii and both circumferences. He then divided the two, and got, as he predicted, the value π. Obviously, because he was measuring circles. So it can be reasoned that the outside observer's space-time is consistent with Euclidean geometry.

    Now, then the circle starts rotating uniformly, and the man on the circle begins measuring. He measures the radius of the small circle, and then the circumference of the small circle. Remember that the velocity of points inside the small circle are much smaller than the velocity of the points on the edge of the big circle, so his measurement of the radius and circumference are each respectfully the same as the measurements found by the outside observer. The observer on the circle then computes the ratio, and correctly calculates the number π for the small circle.

    Then he begins to measure the radius of the big circle, starting from the inside and working his way out with his measuring rod, one ruler length at a time. Note that there is no velocity in the direction of the radius- the disk is spinning, not zipping along horizontally- all of the velocity is directed in a circle. Because of this, there are no relativistic affects on his ruler in the direction of the ruler's length (the ruler's length remains constant), so he again measures the exact same length for the large radius as the outside observer did.

    He then begins to measure the circumference of the large disk. Here is where things get interesting. According to special relativity, objects moving at near the speed of light will have their lengths contracted (shortened) in the direction of motion. Since the man is now measuring along the same direction that the circle is spinning (the circumference), according to special relativity his ruler should be contracted. If he is measuring the same circle with a shorter measuring rod, then he will correctly measure the circle to have a larger circumference than the outside observer did.


    But if he measured the SAME distance for the radius, but a DIFFERENT distance for circumference, then how can he get the same ratio that the outside observer did? The answer is that he CAN'T. 4/20 ≠ 4/25. It's basic math. Therefore, the observer on the disk will NOT get π as the ratio of circumference to radius. Therefore we can reasonably conclude that the space-time of the observer on the disk is NOT consistent with Euclidean geometry.



    He would need different geometrical laws to describe space-time in his reference frame.

    And in order to describe the entire situation (both observers), we would need geometrical laws that behave like Euclidean geometry in inertial frames, but behave differently in accelerated frames.





    And now if we combine this new result with the first part of this post, the equivalence of uniform acceleration and gravitation, we could derive a geometry that behaves like Euclidean geometry in inertial frames (and free fall frames), but behaves differently in both accelerated frames and in gravitational fields.



    That is the very basic foundation of where this idea of "space-time curving" comes from. It turns out that the spatial geometry that was derived that matches measurements turns out to involve space-time that bends. Just like the two dimensional surface on a sphere is "bent" compared to the two dimensional surface of a plane. (Draw a small triangle on earth and the total degrees of all the angles will be 180. Draw a triangle that covers several miles and you will see that the total angles will NOT be 180. This is the same basic concept, but instead of two dimensional surfaces were are talking about 4 dimensional space-time.) Space-time is "bent" in general relativity because that is the type of geometry that would allow for some frames to make measurements that seem consistent with Euclidean geometry and other frames to make measurements that seem inconsistent with Euclidean geometry. Again, keep in mind the example of the "bending" of the surface of a sphere versus the flat surface of a plane.




    * source used:

    The Evolution of Physics: From early concepts to relativity and quanta.
    Albert Einstein and Leopold Infeld. pg 226-228
    "I was put on trial twice near Y2K for acting like Jesus and claiming to be the Messiah. Its not everyday that a man parks a Chariot of Fire in front of a tomb and stands against the US government with a bow and razor tipped arrows over his shoulder. I wore a suit of armor and was protected by an invisible bubble and my sharp tongue was more than the judicial system could handle."Jake
    "The toilet is more than a throne. It is a sacred chamber."-Anton LaVey, High Priest of Satanism

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