Special relativity

Discussion of theories involving time as a dimension, time travel, relativity, branes, and so on, usually applying to the "real" universe which we live in.

Special relativity

Postby PWrong » Fri May 14, 2004 5:46 am

I'm going to try to explain Einstein's theory of special relativity properly, based on Brian Greene's explanation in the Elegant Universe. I'm also going to try to avoid mentioning the fourth dimension, because it's important that people stop confusing our fourth spacial dimension with time and gravity, and stop treating relativity like some kind of religious thing. Please correct me if I get anything wrong or I don't explain something properly.

I'll start with the properties of light. Light always moves at the same speed to every observer, regardless of your frame of reference. This is not how ordinary matter works. If someone throws a ball at you at 20 m/s and you run away from them at 5 m/s, the ball will appear to be moving towards you at only 15 m/s. This is just common sense.

Now if they fire a laser at you at light-speed, and you fly away in a spaceship at half the speed of light, you would expect the laser to follow you at half the speed of light. But it doesn't. It still moves towards you at exactly the speed of light, whether you're running away or running towards it. This has some clear contradictions to it, but bear with me for a while.

Here's some other important ideas in relativity

1. When you're on a train with the windows boarded up, no noise, and no bumps on the track, you have no idea what speed you're going. You could be motionless or you could be going at half the speed of light. The inside of the train is always the same regardless of its speed.

2. When you move away from someone, it looks like they're moving away from you. Similarly, they think you are moving away from them. In fact, both are correct.

Now this is the tricky bit. Imagine a "light clock", where a photon bounces up and down between two parallel mirrors. When the photon hits the top, the clock "ticks" and when it hits the bottom, it "tocks". Let's say that one tick counts as one second. Here's a diagram: (sorry about the dots, I need them to stop the diagram from falling apart :wink:)

Path of photon relative to clock:
______
..../\.....
.....|.....
.....|.....
.....o.....
.....|.....
.....|.....
__\/___

Now what happens if we slide the light clock across the table at a high speed?

Path of moving clock:

.______.....>>>>...______.....>>>>...______
....................................................................
..................................o................................
....................................................................
....................................................................
....................................................................
.....o........................................................o....
.______.....>>>>...______.....>>>>...______

Now when we trace the path of the photon relative to the observer, we get a zigzagging pattern. The Pythagoras theorum tells us that this path is longer than the path of the photon in the stationary clock.

Path of photon relative to an observer:
...............o..............o
............./...\.........../..
........._/.......\......_/...
........./|......._\/..../|...
......./..............\../......
.....o.................o.......
(The lines in the middle are supposed to be arrows, by the way)


Now we know that
a) Light travels at the same speed relative to the observer as it does relative to the clock.
b) The clock is always the same on the inside, whether moving or not, so the distance the photon travels should be the same as in the stationary clock.

So we have the following problem:
To the obsever, the photon is moving a greater distance than inside the clock, but at the same speed.

Now speed = distance / time, and we are increasing the distance.
So to keep the speed of the photon constant, we have to slow down time inside the moving clock.

This is the fundamental result of special relativity, and it applies to every object, not just light clocks.
Time always slows down for an object in motion.

Sorry if I've got anything wrong, please tell me if you've studied relativity before and I've left something out. I find that when I read an explanation of relativity, I understand it perfectly for about 5 minutes. Then I forget some important detail from the explanation, inconsistencies start cropping up, and I have to read it again. :( It's an exhausting topic to understand.
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Postby Aale de Winkel » Fri May 14, 2004 12:08 pm

Yes you grasped the concept of Time Dilation, which is simular to the Lorentz Contraction, references are:
http://scienceworld.wolfram.com/physics ... ivity.html
http://scienceworld.wolfram.com/physics ... ation.html
http://scienceworld.wolfram.com/physics ... ction.html
this exists at all speeds however regularly not noticeable due to the fact the β = v/c <<<< 1
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Postby elpenmaster » Sat May 15, 2004 5:04 am

i think that the reason light travels at the same speed is that when it leaves something, it does so with a quantum jump. thus when it leaves the matter, the matter is still
just a guess :wink:
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Postby Aale de Winkel » Sat May 15, 2004 8:01 pm

Light travels only in vacuum with the speed of light, when lightenter something it also slows down, this allows for prisms maging rainbows. Thus give rise to the paricle / wave dualism.
so there is no factor of light leaving something with a quantum jump or such things. It is true that gamma quanta are created by particle collision, or other particle processes. These things are the reason that light exists, Not the reson that the speed of light in vacuum is a constant in all directions at any speed. This is simply a fact of the currently known universe!
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Re: Special relativity

Postby Euclid » Sun May 16, 2004 4:40 am

PWrong wrote:Now speed = distance / time, and we are increasing the distance.
So to keep the speed of the photon constant, we have to slow down time inside the moving clock.

This is the fundamental result of special relativity, and it applies to every object, not just light clocks.
Time always slows down for an object in motion.


I would say this is where the dimensional arguments come in. For light to remain the same speed, does it "go somewhere" in the sense of a shortcut? Could that somewhere be another dimension. If you are a being in Spaceland, can't you go from point A in Flatland to point B faster by taking the space route? I am talking of a constrained path, not straightline distance.
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Re: Special relativity

Postby Keiji » Sun May 16, 2004 7:46 am

Euclid wrote:If you are a being in Spaceland, can't you go from point A in Flatland to point B faster by taking the space route? I am talking of a constrained path, not straightline distance.


Only if space is curved.
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Postby Aale de Winkel » Sun May 16, 2004 8:56 am

No guys, there is no extra dimension involved here, it simply means that space is (Lorentz-) contracted at the speed of light or in fact any speeds though at our speeds we don't notice.

(I havn't the faintest wheter this means instanteneous travel to anywhere at the speed of light, Never heard this mentioning, according to starttrek this happens at warp 10 but with LC at warp 1 already???) (it has been over 20 years back since I studied these things!)
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Re: Special relativity

Postby Euclid » Sun May 16, 2004 5:36 pm

bobxp wrote:
Euclid wrote:If you are a being in Spaceland, can't you go from point A in Flatland to point B faster by taking the space route? I am talking of a constrained path, not straightline distance.


Only if space is curved.


What I meant was that for A Square to leave his study and go to the market, he has to get out of his house and make his way around all objects in his path. His friend the sphere simply lifts up into Spaceland and takes the direct route.

The constraint on the speed of light might have something to do with the physics of the fourth (or higher) dimensions. The fact that "other rules might apply" is often overlooked in these discussions.
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Special?

Postby mghtymoop » Thu Jun 10, 2004 1:56 am

that wasn't special relativity, that was general relativity, special relativity is a just a little bit more complicated and is not generally thrown around in books aimed at the general public.
and as for time not being the fourth dimension, you string theory nazi's are starting to drive me nuts, what we percieve as time is the 3d representation of motion through a 4th spatial dimension, therefore what we are within the fourth spacial dimension is a temporal streak extending from the moment of our creation to the moment of our end, therefore given that what we see as the passage of time is simply the motion between points of displacment in the 4th dimension the fourth dimension is in fact time itself, einstien showed this to be true, yet no-one has yet given any reason to beleive in string theory, is anyone out there willing to discuss conventional 4d physics or it everyone obseesed with a 10d spacial form where time is completely unrelated
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Re: Special?

Postby Euclid » Thu Jun 10, 2004 12:58 pm

mghtymoop wrote:<snip> you string theory nazi's are starting to drive me nuts <snip> yet no-one has yet given any reason to beleive in string theory, is anyone out there willing to discuss conventional 4d physics or it everyone obseesed with a 10d spacial form where time is completely unrelated


String theory nazis? <sigh>

"believe in string theory"? <bigger sigh> String theory is not a religion. There is no obsession with multiple dimensions. String theory has shown, already, to be a unifying theory. The problem is that the proof will require a greater technology than we currently have. The super hadron collider, when finished, may reveal a great deal. Just like when Einstein developed relativity theory, it was not until later that much of what he theorized was proved. Get out of religion and into science.
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String Nazis

Postby mghtymoop » Fri Jun 11, 2004 3:36 am

String theory is a very pretty mathmatical construct, pure and simple. However it is my no means even close to science. Science is the doing of objecting experiments using directly testable hypotheses. where technology or more commonly funding is lacking indirect testing may be allowed but you would have a lot more trouble getting it published and your article would spend the rest of it's life getting picked to bits by undergraduates who would love to use it to practice their critique writing skills. you can prove a lot of things on paper that are very much different in the real world and i firmly consider string theory to be one of these. the great unifying theory is still yet to be found because i don't believe string theory will ever be it, besides it's founders leave a bit to be desired, if you had even bothered to look into their past exploits and scientific backgrounds that is.
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Re: String Nazis

Postby Euclid » Fri Jun 11, 2004 11:36 am

mghtymoop wrote:String theory is a very pretty mathmatical construct, pure and simple. However it is my no means even close to science. Science is the doing of objecting experiments using directly testable hypotheses. where technology or more commonly funding is lacking indirect testing may be allowed but you would have a lot more trouble getting it published and your article would spend the rest of it's life getting picked to bits by undergraduates who would love to use it to practice their critique writing skills. you can prove a lot of things on paper that are very much different in the real world and i firmly consider string theory to be one of these. the great unifying theory is still yet to be found because i don't believe string theory will ever be it, besides it's founders leave a bit to be desired, if you had even bothered to look into their past exploits and scientific backgrounds that is.


That last phrase is intriguing. Could you help me out a bit by elaborating who the founders of string theory are whose backgrounds are spotty?
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Postby jinydu » Sat Jun 12, 2004 3:12 am

Back to the topic about explaining relativity (at least in my post):

First of all, it is NOT true that general relativity is simpler than special relativity. Exactly the opposite is true. Special relativity (SR) IS a special case of general relativity (GR) (just like 1 + 2 + 3 = 6 is a special case of 1 + 2 + 3 + ... + n = (n*(n+1))/2). Specifically, SR only applies when the gravitational field is zero, while GR applies to gravitational fields of any strength (at least, its supposed to). The equations of SR were taught in my high school class, while the equations of GR were left untouched (because they are much more complicated and involve things such as tensor fields). Remember, Einstein published SR in 1905 but didn't publish GR until 1915.

Now, I think that it is important to emphasize the two postulates of SR:

1) The speed of light in a vaccuum is always measured to have the same value for all observers (this is a prediction of Maxwell's theory. Before Einstein, physicists found this idea unacceptable. This was one of the reasons that they postulated that the universe is filled with an invisible substance, called ether, that provides a medium for electromagnetic waves and gives a universal frame of reference) According to Einstein, however, there is no ether.

2) The laws of physics work equally in all inertial (non-accelerating)reference frames. As a corollary, there is no universal reference frames. Instead, all measurements must be made relative to particular reference frames. If you are on a boat, a person on a nearby island might claim that he is stationary while you are moving forwards. You would claim that you and the boat are stationary, while the island and the entire ocean is moving backwards. According to this second postulate, there is NO experiment that can prove either you or the islander wrong. From the viewpoint of SR, you are both right.

Also, I think you should try to clear up some misconceptions. Sometimes, it is claimed that as you approach the speed of light, time slows down almost to a standstill, length (in the direction of motion) contracts down to zero and your mass rises to infinity. This is quite a confusing way to state the effects of SR. Suppose Person A boards a rocket and fires its engines away from the Earth. No matter how hard he tries to fire the engines, A will NOT observe his clocks slowing down, or his rulers shrinking, or his mass increasing. To him, everything will seem exactly the same as it was when he was on Earth. In fact, from his reference frame, the rocket is stationary while the Earth is moving backwards. The correct statement is that observers on Earth will claim that A's clocks are slowing down, his length is contracting and his mass is increasing. On the other hand, A will claim that it is the observers on Earth who have slowed down clocks, contracted lengths and increased masses. From the viewpoint of SR, both A and the observers on Earth are right. Please reinforce that the sentence "Time slows down" is inaccurate because there is NO universal time to compare your clocks to. Instead, it is only possible to say that your time slows down in someone else's reference frame.
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founders of string theory

Postby mghtymoop » Wed Jun 16, 2004 3:27 pm

start with michio kaku and michael greene, you'll see what i mean, surprised if you didn't already know of the founders given your love of the theorum
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Postby RQ » Fri Jul 09, 2004 2:52 am

I think a guy blasting himself to about 7 miles per second would feel a hell of a lot of more weight. Number one reason why astronauts are lying down when they blast off, so there is less pressure on their body.
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Re: founders of string theory

Postby PWrong » Tue Jul 20, 2004 6:21 pm

mghtymoop wrote:start with michio kaku and michael greene, you'll see what i mean, surprised if you didn't already know of the founders given your love of the theorum


Michael Greene? Do you mean Brian Greene? I read his book. So what's wrong with their past exploits and scientific backgrounds?
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Postby houserichichi » Mon Nov 15, 2004 3:33 am

I know it's late for a reply, but Michael Green was around before Brian Greene I believe (notice no "e" at the end of Mike's surname)....as for exploits I'm also curious... :lol:
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