/sci/ - Science & Math

which one

>>2144662

How many are there?

>>2144667
Well, it's relative

>>2144675

>>2144658
Poor Einstein. You see the disappointment in his face.

obvious samefagging

>>2144675
>>2144667
>>2144662
>>2144658
obvious samefag is horrendous. good idea but still. especially with the glee.jpeg

Seriously though. I don't understand it.

>>2144662
>>2144667
>>2144675
>>2144679
>>2144686
>>2144687
>>2144698
>>2144701

samefag

>>2144698

No, no, that wasn't me. I just want to understand it.

>>2144658
All inertial reference frames are cool. Light moves at the same speed no matter which reference frame you're in.

>>2144724

Elaborate?

OP, please delete your thread, because you're a dick who's now going to join in with calling all the posts in this thread a samefag (including this one)

you have no life. you are a virgin who has nothing better to do than troll /sci/. just go and make a religion thread and be done with it.

This picture holds the answer you need.

Stare at it.

CAN YOU FEEL YOUR BRAIN GROWING!?

>>2144742

I just want to fucking understand the theory of relativity! D:

>>2144658
When you see somebody standing a long distance away from you, they seem very small. You might think, therefore, that they you might appear as a giant to them... but instead, you look just as small from their point of view. In fact, it's impossible for either of you to determine whether you're a long way from him, or he's a long way from you just based on how large you appear.

That's relativity.

Galileo commented that when you're flying in an airplane at 400 miles per hours and accidentally drop your packet of peanuts it doesn't fly backwards and shatter the skull of the flight attendant. In fact, if you close your eyes and there's no turbulence, it's easy to imagine you aren't moving at all.

That's relativity.

>>2144758
>Galileo
>Airplanes
WAT

>>2144758

Thanks, but I don't understand the second one.

>>2144735
Everything else is just math, I'm not typing out derivations, even though they're not too complex, at least for special relativity. General is much more a pain in the ass.

>>2144782

Aw, shit. Well, thanks for trying.

-Galileo states the principle of relativity: the laws of physics have the same form in all inertial reference frames (that is, observers moving at a constant relative velocity cannot distinguish which one is moving and which one is at rest, so saying one is moving or one is at rest is meaningless).

-Newton show's how the principle of relativity is consistent with Newton's laws.

-Maxwell et al develop the laws of electromagnetism, culminating in Maxwell's equations predicting that light is a form of electromagnetic radiation.

-Maxwell's equations do not seem to be consistent with the principle of relativity, and hence there appears to be a favoured frame of reference, called the ether, where Maxwell's laws hold.

(con't)

>>2144772
When moving, everything you are carrying is also moving at exactly the same speed. The same is true of an airplane, a train, a car, or (and this was Galileo's real example) a ship. When you're on a ship and you drop something... from your point of view it falls straight down. From the point of view of somebody watching the boat from the shore, the path of that falling object traces an arc identical to if the same object had been thrown from the same height at the ship's speed.

Both viewpoints are identical, and equally true. How things appear is -relative- to the observer.

-Maxwell's equations predict that electromagnetic waves travel at a fixed speed c. The idea was, if this true for one observer (that is, if observer A measures the speed of an electromagnetic wave (which herein I'll call light) to be c, then another observer, observer B, traveling at a speed v relative to A in the direction of the light beam should see light travel at a speed c-v, contradicting Maxell's equations. Hence Maxwell's equations do not preserve relativity.

-As the Earth orbits the sun, its speed through the ether presumably changes. So by measuring the variations in the speed of light, experimenters should be able to determine earth's speed through the ether.

-Such an experiment was performed, yielding a negative result. Either the earth, in its manifold changes in speed and direction and it orbits the sun, which orbits the galaxy, etc. is constantly at rest w/ respect to the ether, or else there is not ether.

(con't)

no, but this guy can

http://www.youtube.com/watch?v=nNgzqpKZwhE&feature=BF&list=PL095393D5B42B2266&index=22

-How can this be? As we have shown, it seems that Maxwell's equations are fundamentally inconsistent w/ the principle of relativity. Some people took this as a sign that Maxwell's equations were wrong, but the attempts to modify Maxwell's equations never worked out.

-Einstein made the the bold suggestion that it was our views of space and time which were wrong, not Maxwell. He said that, if observer A measures the speed of light to be c, maybe observer B will also measure the speed of light to be c, regardless of relative velocity! THE SPEED OF LIGHT IS CONSTANT. This can only be true if our ideas about measuring length and time fail at high velocities. Special relativity modifies space and time in order for light to travel at a fixed speed in every reference frame. In the process, time dilation and length contraction were discovered, as well as the idea that space and time are part of a single, spacetime continuum.

-Newton's laws, like F=ma, are only consistent with the principle of relativity under the only ideas of space and time, so they need to be changed to accommodate special relativity. This leads to the prediction that mass increases with speed, and that E = mc^2.

Hope this helps, feel free to ask questions.

>>2144679
>>2144675
>>2144667
>>2144662
>>2144658

I actually heard comedy drums. classic.

>>2144900

Jeez. I didn't understand anything. But you don't have to explain it again.

>>2144904

OP here. I am just here to understand the theory of relativity. I am not involved in any samefagging.

>>2144913
I'm willing to go through it point by point. Would you be interested?

>>2144959

Yeah, but I'm a 17 year old girl, I mean, this is all pretty complicated.

>>2144963
It's appears complicated when you don't understand it, simple as soon as you do. It doesn't require extensive knowledge of physics to understand.

>>2144985
This anon is right.

Despite being the backbone of physics- relativity doesn't really require much physics to get a working knowledge of.

>>2144985

Enlighten me.

>>2144963
What, you're 17 and can't figure this out after this much assistance? Shaaaame.

>>2145013

I'm sorry! I was never good at physics. And the fact that Enlgish isn't my first language makes it harder.

>>2145008
Step-by-step.
"Galileo states the principle of relativity: the laws of physics have the same form in all inertial reference frames (that is, observers moving at a constant relative velocity cannot distinguish which one is moving and which one is at rest, so saying one is moving or one is at rest is meaningless)."

How much of this do you understand (BTW my english isn't strong either, so if it doesn't make sense it might be me, not you!)

>>2145043

Ok, I understand that.

>>2145055
So all was fine and dandy, until a physicist named maxwell came along. In the 19th century, physicists were concerned with deducing the laws of electricity and magnetism. Maxwell finished off the job, and discovered a very fascinating and very important result: light, which before had been a mysterious substance, was actually a wave of the electromagnetic field.

You don't have to understand what this means, but what you do have to understand is this: according to the equations which Maxwell deduced, if something emits light, it travels at a speed c (~3*10^8 m/s). PERIOD. That means, if Maxwell's equations are correct, light must always travel at the speed of light in any direction, regardless of how the thing that produced the light is moving.

Does that make sense?

>>2145150

Yeah, I understand.

The theory pretty much says this:

'There is no absolute perspective, since we live in a universe where everything is constantly moving.'

For example, if there were three men in space- two moving and one still, the one still is only still because relative to us, he's the distance between us isn't changing. The man standing still is actually the only one moving relative to the two men- who are "still" because, relative to that other man, they "moving" at the same rate and in the same direction.
If us, the observers, were having a changing distance relative to the three men, they all appear to be moving, relative to us.

Because of this, there is no definition of what's "still" and what's "moving". Everything is relative to each other.

I think this book may help

ITS A LIE
ONLY THE BIBLE IS TRUTH

>>2145171
This presents a problem for the principle of relativity. Suppose we have two observers, A and B. Suppose A just finished deducing Maxwell's equations, showing that the speed of light is constant, etc. Now, suppose A shines a flashlight in some direction. At the same time, B is traveling relative to A at a speed v (say, half the speed of light) in the same direction as the light beam.

From B's perspective, at what speed is the light traveling at? Well, obviously it has to be c - v, or half the speed of light. But this is a problem, because from B's perspective, Maxwell's equations are wrong. So the principle of relativity is violated.

As a result, if you're in a spaceship with no windows, and you wanted to find out at what speed you were traveling at, then all you had to do is shine some light and measure its speed: the deviation from the speed of light is your speed. No more relativity, or so it seems.

Good so far?

http://www.youtube.com/watch?v=V7vpw4AH8QQ

>>2145245

Yeah, I get it.

>>2145245
HEATHEN!!!! you are so fucking dumb bro. point out to me EXACTLY where that is in the bible eh? nowhere you say? FUCK YOU, PRAISE JESUS

>>2145245

makes no sense, because if what you say is true, then it doesn't matter whether you measure light's speed or not because it's always constant.

Whether you'll be in the ship or not, it'll always measure c. So how will you know how fast you're going without looking out the window again?

>>2145298

Anyway...

>>2145300

Oh, come on! I was understaing everything and now you come and you fuck things up.

>>2145280
Physicists weren't too worried about this. "Well, so much for the principle of relativity" was the basic idea. They called the frame of reference at which light travels at the speed c (that is, when Maxwell's equations hold up) "ether". So in our previous example, Observer A would be at rest with respect to the ether, because light moves at the predicted speed in accordance to Maxwell's equations. Observer B was moving at half the speed of light with respect to the ether, which he could determine experimentally by measuring the speed of light in his frame of reference.

Likewise, 19th century physicists tried to do the same thing: measure the speed of the earth through the ether. (con't next post)

>>2145339

Ok.

>>2145300
As I said, the speed of light would be constant (so it seems) only in one particular reference frame. Other people would measure a different value for the speed of light...as we shall see, this is not correct, but this was what was assumed, because to assume otherwise would have grave repercussions on our common-sense understanding of the world.

con't from >>2145339
So physicists tried to measure Earth's speed through the ether...tried and failed. All experiments seemed to suggest that earth was stationary with respect to the ether, no matter the time of the year (experiments were conducted year-round)...which makes no sense, because the earth is orbiting the sun (so its speed is constantly changing), and the sun is moving in the galaxy, etc. To think that, by chance, all these motions would cancel each other out would be preposterous. So physicists had a mess on their hands.

Good so far?

>>2145383

Yeah, I understand.

>>2145394
Great.

So what could be the problem. Well, some people thought, perhaps Maxwell`s equations were the problem. Perhaps they are, in fact, wrong. And people tried to modify Maxwell's equations, but none of the modifications worked, and ultimately people were resigned to admit that Maxwell's equations were right.

Here was Einstein's idea, one of the hallmarks of human thought (although he had a bit of help): perhaps both Maxwell's equations AND the principle of relativity were correct. That would explain why no one could measure the Earth's speed through the ether...there was no ether! Maxwell's equations were right in every reference frame.

"How can that be possible," you might ask. "If A measures the speed of light to be 3*10^8 m/s, and B is moving at half that speed in the same direction, the only way for the laws of physics to be correct in both reference frames is for B to measure the speed of light to be 3*10^8 m/s as well, even if he's heading in the direction of the beam of light. But that's preposterous!". Indeed, it does seem so. But it's correct. More to be explained next post, but good so far?

>>2145454

I guess, but I don't understand how that is correct.

>>2144658
nothing could tavel faster than the speed of light.

Strange things happen when you get close the speed of light.

Strange things happen when you get close to gravitational feilds.


That's all i could tell you now. To describe what really happens takes a lot of mathematics

>>2145467
It does seem impossible. It seems impossible to everyone who first hears it, and so I'll try to explain why it might be plausible.

A lot of people falsely assume that this bizarre behavior is due to some weird property of light...but it's something more fundamental, as i'll try to explain now.

If A, instead of shining a beam of light, were to throw a rock at, say, 10 m/s. And suppose B were to travel in the direction of the rock at 5m/s. How fast will the rock travel from B's perspective? Classically, the answer is 10 - 5 = 5m/s. According to Einstein, the answer is 5m/s + a bit. This extra 'bit' is incredibly tiny, much too small for any one of us to notice in everyday life. If the rock were traveling at 100m/s, this "bit" would be even bigger, but still much too small to notice. But, as the rock speeds up faster and faster, the difference between what we expect classically and what happens according to Einstein becomes greater and greater, until finally, if the rock were traveling at the speed of light, even B would see it traveling at the speed of light.

Einstein had to assume this was true if the principle of relativity were to agree with Maxwell's equations, which experiment said they did. More on this next post, but so far so good?

>>2145482
or that?
http://www.youtube.com/watch?v=V7vpw4AH8QQ

>>2145498

Yeah, go on.

>>2145519

Still, this may not seem satisfactory. After all, it just seems "right" that speeds should just add. Let's see how we first derived the idea that speeds add, and see what assumptions we made along the way.

Again, consider A and B, with B moving at a speed v relative to A. Suppose both are looking at some object traveling (say, a rock). In some time interval <math>\delta t<\math>, suppose that the rock travels a distance of <math>\delta x<\math>. Evidently, B won't see the rock travel the same distance. So what distance, <math>\delta x'<\math>, will B see the rock travel? Our immediate assumption is that <math>\delta x' = \delta x - v \delta t <\math>. Why? Because the distance the rock travels w/ respect to B (<math>\delta x'<\math>) + the distance B travels w/ respect to A (<math>v \delta t<\math>) should equal the distance the rock travels with respect to A (<math>\delta x<\math>). But there's a problem with this reasoning (more next post)

>>2145540
Damn, I don't seem to be able to LATEX...hang on, trying some things out.

<math>a</math>
<span class="math">a[\math][/spoiler]

<span class="math">a<span class="math">
a[/spoiler][/spoiler]

<span class="math">\delta x<span class="math"> asdasd \delta x

\delta x asdasd \delta x[/spoiler][/spoiler]

mind just exploded

>>2145540

Ok, I think I understand, but these <math>'s are making it confusing.

>>2145572
Understood, I'm trying to fix it lol.

Does anyone know LATEX by any chance? I'll do some more trial and error in the mean time...

<span class="math">\Delta x[/spoiler] asdasda

Realtivity:

Energy and mass are the same thing. If you remove some yet unknown thing from mass, it becomes energy. If you add that thing to energy it becomes mass.

With a proper understanding of that, you can explain a lot of shit about the universe because it is made up of forms of energy and mass.

Again, consider A and B, with B moving at a speed v relative to A. Suppose both are looking at some object traveling (say, a rock). In some time interval <span class="math"> \Delta t <span class="math">, suppose that the rock travels a distance of \Delta x . Evidently, B won't see the rock travel the same distance. So what distance, \Delta x' , will B see the rock travel? Our immediate assumption is that \Delta x' = \Delta x - v \Delta t . Why? Because the distance the rock travels w/ respect to B ( \Delta x' ) + the distance B travels w/ respect to A ( v \Delta t ) should equal the distance the rock travels with respect to A ( \Delta x ).[/spoiler][/spoiler]

Again, consider A and B, with B moving at a speed v relative to A. Suppose both are looking at some object traveling (say, a rock). In some time interval <span class="math"> \Delta t [/spoiler], suppose that the rock travels a distance of <span class="math"> \Delta x [/spoiler]. Evidently, B won't see the rock travel the same distance. So what distance, <span class="math"> \Delta x' [/spoiler], will B see the rock travel? Our immediate assumption is that <span class="math"> \Delta x' = \Delta x - v \Delta t [/spoiler]. Why? Because the distance the rock travels w/ respect to B (<span class="math"> \Delta x' [/spoiler]) + the distance B travels w/ respect to A (<span class="math"> v \Delta t [/spoiler]) should equal the distance the rock travels with respect to A (<span class="math"> \Delta x <span class="math">).[/spoiler][/spoiler]

>>2145572
So, replacing this >>2145600 into >>2145540, do things make sense?

>>2145591

Yes, I understand.

>>2145608
Alright, well the problem is that this violates Einstein's postulate: that the speed of light is the same no matter how fast you're moving (and that two observers moving relative to one another will measure the speed of a light beam to be the same). Why?
Well take the equation <span class="math"> \Delta x' = \Delta x - v \Delta t [/spoiler]. We used a rock in that example, but we could have used anything, like, say, light. Dividing both sides of the equation by <span class="math"> \Delta t [/spoiler] gives: <span class="math"> \Delta x' / \Delta t = \Delta x / \Delta t - v [/spoiler]. But <span class="math"> \Delta x' / \Delta t [/spoiler] is just the speed of light as measured by B (speed = distance divided by time), so this says the B will measure light to travel at a different speed than A.

>>2145629

Ok, I think I undrstand.

>>2145629
Where did we go wrong? We must have gone wrong somewhere if Einstein was right. So what incorrect assumption did we make?

When we said that <span class="math"> \Delta x' = \Delta x - v \Delta t [/spoiler], we assumed that both A and B measure length the same way. <span class="math"> \Delta x' = \Delta x [/spoiler] is how much farther the light beam travels w/ respect to B from A's perspective, but maybe B will measure this length differently. And when we divided both sides of the equation by time to get the speed of light in both reference frames, we assumed that they both measure time the same way.

So we are force to accept that length and time are measured differently by different observers. It is possible to calculate how they change, but that requires me drawing some diagrams and shit, and I'm tired as fuck...if you're on /sci/ tomorrow, you can give me a shout and I'll draw some stuff. Alternately, you can email me if you want.

At any rate, here's special relativity compressed: Einstein realizes that in order for the principle of relativity to be consistent with light, light must be measured the same by all observers. If this is true, out ideas about space (as in length measurement) and time must be different than previously thought. Special relativity says how exactly space and time are different.

>>2145665
In the second paragraph, I meant <span class="math"> \Delta x' = \Delta x - v \Delta t [/spoiler]

>>2145665

Ohh, don't worry about it, you've already gone through enough explaining all of this, thank you so much. :D

>>2145677
Haha really it's no problem, I'd be happy to go over it some more. Seriously, if you're on /sci/ and are brimming with questions, just ask :)

>>2145684

Thanks :) Maybe I will, but I'm gonna go to sleep now, night!

>>2145665
>>2145629
>>2145498

MOOOAAAR

>>2145684
Thanks Mr. Anon, disregard any sarcasm. That really helped me understand. Night

When you do something cool and nice, time is fucking fast.
When you do something stupid and boring, time is fucking slow.
It's RELATIVE to what you do, hence the coined name "Theory of Relativity".

Or maybe it has something with family... I may be wrong here.

One of its theory basically states that space isn't an empty void but a very huge piece cloth (space) holding huge fucking marbles (any huge elemental object) that contorts and bend the space (cloth) around it at least thats my uderstanding.

Justicing for great bump. because this is one of the few times /sci/ did its job and explained science

>scontrai left!

>>2147507
Yeah this was a relatively good thread

>>2147531
yup, thought so too

I can't believe I posted this thread last night and it's still alive.

bump, wake up man and give us the ruler and clock diagram

all this shit will make sense once you see the ruler and clock diagram

>>2147602

He should be here somewhere...

>>2147807
So this thread is still alive...nice. I'm in the process of diagramming and stuff, just hold on.

>>2147828

Yeah!

Okay, so the usual way special relativity is taught is with thought experiments. These are very elegant, very clear...but I'm thinking of trying a different approach, which I believe is more powerful. At the very least, it offers a different way of looking at special relativity (imo, a better way of looking at SR). So, seeing as >>2147835 appears to be the only one hear, I'll let you decide...so you want the usual way, or a diferent way?

>>2147859

Different way.

Lorentz group, generators, etc?

Alright then, let's recapitulate:
-Einstein showed that the only way for the principle of relativity to be consistent with Electricity n' Magnetism/ Light is for Light to always travel at the same speed <span class="math">c[/spoiler], regardless of how fast observers are moving relative to each other.
-This can only be true if some of our assumptions about space and time are wrong. We require these assumptions to be modified, and that's what we'll do here: show how space and time change between observers.

if you want to learn in depth about this go here

For a deep understanding go here

"http://www.learner.org/vod/vod_window.html?pid=611"

For a simple understanding go here

http://en.wikipedia.org/wiki/Theory_of_relativity

>>2147883

Ok, go on,

First, let's define a few terms. An event is something which occurs in a specific place and time. Under this definition, World War 1 wasn't an event, because it happened in many distinct places (all over Europe) and over a large span of time (four years if my history is correct). The assassination of Franz Ferdinand was an event, because it happened in one particular location and time (more or less; his death probably took a few seconds, but you get the point).

A coordinate system is a way of describing an event. If a pencil hits the ground next to you, you can describe the location of this event by its position relative to you. Its position relative to me would be very different, yet it is the same event. We just have different ways of describing it.

>>2147897

Mhm.

taking a break from /n/, thought i'd swing by. let me try and drop some stoner logic in here.

pour glass of milk.
put some ice cream in bowl.
drink milk. it's cold
eat ice cream. it's cold
drink milk again. now it's warm.
your mouth was colder than milk due to ice cream

The usual way of describing an event is to use Cartesian coordinates (ie specify an event by its x, y, and z position).

For a moment, let's look at things classically. How will an event appear to two observers moving relative to each other?

Suppose that observer O is at rest, and that observer O' is moving at speed v in the x-direction. We'll make some simplifying assumptions: as in the picture, we'll say that the two coordinate systems coincide at time t = 0. (The reason I'm not drawing the lines overlapping is because you wouldn't be able to see the two lines! But presume they're overlapping).

At some later time, the situation looks like this.

>>2147926

Yeah, go on.

Now suppose there's some event, like a pencil making contact with a table. To observer O, the event can be specified by x, y, z, and t, where x, y, and z give the position of the event, and t gives the time of the event (all from O's perspective). Now the question is, what are x', y', z', and t'?

>>2147936

I'm not sure I understand what x' and y' are.

>>2147947
forgot pic

>>2147954


Ok, go on.

>>2147953
If I say that something happens 5m from me, someone else might say that it happened 3m from her, because she's closer. x would be 5m, and x' (the position from the other observer's vantage point) would be 3m. Does that make sense?

>>2147967

Yeah.

Question: Didn't they experimentally prove that the s peed of light changes at high velocities? I remember reading something about light speeding up if it's reflected between 2 moving mirrors at very high velocities or something? Was I trolled or have I completely misunderstood what you said? If I were to sum up your posts with one sentence, it'd be: Light always travels at c (3x10^8 m/s) NO MATTER WHAT.

Inb4 I completely misunderstood.

Well, this should be simple enough. Looking at the diagram, it appears that
<span class="math">x' = x - vt
y' = y
z' = z
t' = t[/spoiler]
The last step is justified on the grounds that both observers should measure time the same way.

>>2147990
Should be
<span class="math"> x' = x - vt[/spoiler]
<span class="math">y' = y[/spoiler]
<span class="math">z' = z[/spoiler]
<span class="math">t' = t[/spoiler]

>>2147988
You were trolled I think. Light always travels at c...although there have been weird experiments where light has travelled much faster than c, and where light has stood still. I don't know what's up with that, but it apparently doesn't affect relativity.

>>2147990

Yeah, ok.

read part of this thread, not op, so do relative speeds basically go like this?

>>2148006
wait, no fucked that up, nvm i cant graph apparently

>>2148002
Light slows down when passed through any thing but vacuum. Slowest was 160 meters per seconds, I *thought*.

Now, the equations given about are called the Galilean transformations. But they're wrong! If they were right, then necessarily observers moving relative to one another would measure light to travel at different speeds. Why?

Let x be the position of a light beam at time t. We have
<span class="math">x' = x - vt[/spoiler]
<span class="math">\Delta x' = \Delta x - v \Delta t[/spoiler]
<span class="math">\Delta x' / \Delta t' = \Delta x' / \Delta t = \Delta x / \Delta t - v[/spoiler]
But <span class="math">\Delta x / \Delta t[/spoiler] is the speed of light as measured by O, and <span class="math">\Delta x' / \Delta t'[/spoiler] is the speed of light as measured by O'. And these are not the same! Ergo, the Galilean transformations are incorrect.

We will now derive the correct transformation laws.

>>2148040
Very thankful for your edification, Anon.

Sincerely,
Anon

>>2148011
In that case the light isn't actually slowed down. If light travels inside a material, like glass, the photons will travel at the speed of light until they hit an atom. When they hit the atom, the photon gets absorbed, and released a bit later. The overall effect is for light to travel more slowly, but at any point it's traveling at the speed of light.

>>2148040

Ok, I understand.

Since the Galilean transformations do not obey the law that the speed of light is a universal constant, Einstein derived a new prescription for describing the same event in different (non-accelerating) frames of reference. Because Einstein derived them, we call them the Lorentz transformations...yeah.

We will assume that the Lorentz transformations take the form
<span class="math">x' = Ax + Bt[/spoiler]
<span class="math">y' = y[/spoiler]
<span class="math">z' = z[/spoiler]
<span class="math">t' = Cx + Dt[/spoiler].

>>2148072

Ok, but I'm not sure I understand.

>>2148072
Our goal is to solve for A, B, C, and D. If you're wondering why the Lorentz transformations take this form, I can justify it later...let me first solve for A, B, C, D.

We will do this by considering four separate cases where we know how the transformations will behave.

Case 1: Observer in (x,y) sees origin of (x',y') moving along the x-axis at speed v. We know that
<span class="math">x = vt[/spoiler], <span class="math"> x' = 0[/spoiler]. Therefore
<span class="math">0 = Avt + Bt, B = -vt [/spoiler].

>>2148081
Does >>2148093 make you understand? If not, stop me know and I'll explain.

>>2148096

No, no, you lost me.

>>2148103
Can you be more specific about what you don't understand? Is it the A, B, C, and D? Or the Lorentz transformations in general?

>>2148120

The Lorentz transformations in general.

>>2148132
Okay, do you see why the regular transformations
<span class="math">x' = x-vt[/spoiler] etc. don't work?

>>2148139

Yes.

>>2148149
So, the question remains: what ARE the correct equations to replace the Galilean transformations?

We can, as Einstein did, solve for them algebraically. However, we will first assume that the equations adopt the form written above, with all the A, B, C's etc. THESE ARE UNKOWNS. We are trying to find out what their values are. Originally, A = 1, B = v, C = 0, and D =1. We will now solve for the correct values. Does that make sense?

>>2148168

Yeah, ok.

>>2148174
Recommended music for relativity: http://www.youtube.com/watch?v=VqANh4QnNxA

So, does >>2148093 make sense? I'm trying to, by considering a few cases where we know the relationships between x' and x etc., to solve for the values of A, B, etc.

How is special relativity useful for anything (or provable)?

I "understand" (not really) how general relativity is useful for GPS systems and how it was proven trough experiments and observations, but what about special relativity, what did it do for us?

>>2148191

I don't get it...

>>2148192
Well, general relativity needs special relativity, so if GR is useful, then SR is necessarily useful.

Second, typically elementary particles travel fast enough for relativistic effects become important. For instance, in gold atoms electrons travel at something like half the speed of light, maybe faster. So our understanding of matter requires SR. Molecular electronics, I think, is sensitive for SR to become important, and Molecular electronics will be the source of modern technology in the future.

But anyway, even if it wasn't useful, why does that make it not worth studying? Does something have to have applications to merit attention? Relativity is a beautiful theory, and changes our concepts of space and time...doesn't that make it worth learning?

>>2148203
Is it the algebra or the idea?

>>2148192
SR is the standard, it has been proven correct countless times. Tons of electronics use SR, it is used for anything dealing with magnetic/electric fields.

>>2148216

x=vt, x=0. Therefore
0=Avt+Bt B=−vt.

That. I don't understand how you figure that out.

But I have to go shower, I will be back in like 30 minutes.

>>2148246
Our "event" is the position of O' 's origin at time t. Obviously, x' = 0, because that's the definition of the origin. And because O' is moving at a speed of v away from O in the x direction, x = vt.

Now, we can plug this into the equation x' = Ax + Bt. Substituting x' = 0 and x = vt, we get 0 = Avt + Bt, and thus B = -Av.

I'll post the rest of the algebra so that you can read it while you're in the shower.

>>2148192
>Thinks special relativity hasn't been proven

it's special alright

Note that now <span class="math">x' = Ax + Bt = Ax -Avt = A(x-vt)[/spoiler] because B = -Av

Case 2: We'll consider the situation the other way around. The observer in the (x',y') frame sees the origin of (x,y) move along the x' axis at a speed of -v. Then, using the same logic as before,
<span class="math">x=0, x'=-vt'[/spoiler]

Wait.

So at CERN, for example, when they accelerate two particles to collide at near light speed velocity...wait what the shit.

If the first particle is accelerated at 60% of the speed of light and the second at 60% too, will the relative speed the particles approach eachother at the spped of light, 100%? Or 60%? Or 60% + something% which would be something other than 60%+60% because at relativistic speeds we need to calculate it differently blah blah.

So if they somehow managed to accelerate particle A at the speed of light and particle B at the speed of light, the two particles would collide at the same speed as if particle A was at the speed of light and particle B wasn't moving? fuckcuntdicks

They can measure this shit can they?

Plugging this into the equation
<span class="math"> x' = A(x-vt)[/spoiler], we get
<span class="math">-vt' = A(0-vt)[/spoiler]. But
<span class="math">t' = Cx + Dt = Dt[/spoiler] (because x = 0). Plugging this into the last equation, we get
<span class="math">-vDt = -Avt, D = A [/spoiler].

>>2148322

And yes I know their particles can't reach the actual speed of light.

Case 3: A light pulse is sent out from the origin at t = 0. Now, by the constancy of the speed of light, x = ct and x' = ct'. Note that
<span class="math">t' = Cx + Dt = Cx + At[/spoiler] because D = A. Now,
<span class="math">x' =A(x-v)[/spoiler]. So
<span class="math">x' = ct' = c(Cx + At) = c(Cct + At) = A(ct - vt)[/spoiler]
Canceling the Act 's from both sides, we get
<span class="math">C = -Av/c^2[/spoiler]

>>2148322

From an observation point somewhere in between particle A and Particle B...

Particle A is approaching at 0.6c. Particle B is approaching from the opposite direction at 0.6c.

From the perspective of particle A, particle B is approaching at some velocity < c. And vice versa.

I'd just guess somewhere in the mid to upper 90% C.

>>2148322
1) The relative speeds wouldn't 60% or 60% + 60%. It would end up being very close to the speed of light.

2) As you said, A and B can't be at the speed of light, but let's suppose that they're close to the speed of light. So when they collide, they're relative velocities will still be smaller than the speed of light, but a bit higher than before. If you think that this "bit higher" is a negligible amount, think again. The mass of a particle is
<span class="math">m = m_0/sqrt{1 - v^2/c^2}[/spoiler]. Small changes in the speed when the particle is going close to the speed of light make enourmous changes in the mass, and hence the energy of the collision

Now finally, Case 4: Light is emitted along the y-axis in the (x,y) frame at t = 0. Evidently, in the (x',y') frame the light will have components in the x' and y' axes.

We know that x = 0, and y = ct. We also know that
<span class="math"> x'^2 + y'^2 = c^2 t'^2[/spoiler].

Classy gentlemen stick to classical mechanics

Probability of finding an electron? time dilation? NOPE.

Why? Well the pulse will travel in the x'-y' plane, and the distance it will travel after time = t' will be <span class="math">\sqrt{x'^2 + y'^2}[/spoiler] by the Pythagorean theorem. This equals ct'.

Note that, using C = -Av/c^2, we can rewrite the equtaion <span class="math">t' = Cx + At = A(t - vx/c^2)[/spoiler].

Plugging in shit, we get
<span class="math">x'^2 + y'^2 = (A(x-vt))^2 + y^2 = A^2 (0 - vt)^2 + (ct)^2 = c^2 t'^2 = c^2 A^2 (t - v0/c^2)^2 [/spoiler].

Solving for A, we get
<span class="math">A = 1/ \sqrt{1 - v^2/c^2}[/spoiler]

But we already solved for B, C, and D in terms of A, so we know them all! So finally, substituting A, ..., D into the Lorentz transformation, we get:
<span class="math">x' = (x-vt)/ \sqrt {1 - v^2/c^2}[/spoiler]
<span class="math">y' = y[/spoiler]
<span class="math">z' = z[/spoiler]
<span class="math">t' = (t - vx/c^2) / \sqrt {1 - v^2/c^2}[/spoiler].

TADA! We now have the Lorentz transformations, the backbone of Special relativity. Everything can be deduced from these equations, such as time dilation, length contraction, the structure of causality, etc. I will do this in due time, but not now.
If you're interested in learning more, keep this thread alive, and whenever I'm on /sci/ again (probably tomorrow) I'll continue where I left off. If you have questions, ask them here and I'll get back to you when I can.

>>2148421

Thanks again!

>>2148387
HA Einstein is disapoint

>>2148427
No problemo... are you the OP?

>>2148443

Yeah.

Riemannian geometry everywhere

To the guy who's actually taking his time to teach us stuff:

Good job, You're what makes /sci/ worth browsing.

>>2148472

I know, right?

wat
Why did you assume that x' = Ax + Bt...couldn't x' = Ax^2 + Bt or something

and why y' = y and not Ey + Ft or something

>>2144772

PHYSICS IS THE SAME EVERYWHERE, REGARDLESS OF WHERE YOU ARE IN THE UNIVERSE.

That's broken down. Quite a lot, actually.

Can we get this thread archived, or are too many people concerned with religion vs atheism and who's degree is better?

>>2148633

How do you do that?

>>2148644
>implying I know
Noob at 4chan :(

>>2148647
http_://_4chanarchive_.org/brchive/main.php?mode=submit
remove the _s

>>2148647

Damn it.

>>2148647
>>2148644
Go to 4chan archive org >request interface and enter the thread number and board.

>The guy who was doing the relativity stuff before
You, sir, are awesome!

Thanks for your request.
It has been added to our database and the thread will be archived as soon as enough request for that thread have been made.
This thread has been requested 3 times now.

What is the thread id?

>>2148686
The number in the URL of the thread, alternatively it's the post number of the OP which would be
>>2144658
:)

>>2148694

Thanks. Four times, now.

Bumping. We need more requests.

Bamp.

Bump.

>>2148952

Thanks!

everyone loves you, relativity guy.

I saw this happen

Bumping some more.

>>2149061

Sadly he's not here now :( But he said he'll be back tomorrow. We have to archive this.

tried to archive, couldn't do the captcha. this is bullshit.

>>2149110

Sure man, we have 6 now :3 ONE MORE!

OPEN ARE THE DOUBLE DOORS OF THE HORIZON

OK Imma gonna try this too. (Not samefag)

We agree that the problem is that the speed of light is constant.

Suppose you're measuring the speed of light by having one guy stand on a mountain, and another guy stands on a nearby mountain. One guy flashes light at the other, and they figure out how long it takes to travel between mountains.

If you don't care for this, suppose you're flashing lasers at the moon or whatever. Same difference.

So the two gentlemen (since Gauss actually attempted this experiment, let's have one of them be Gauss) flash light at each other and measure how long it takes light to travel between mountains a known distance apart. They arrive at 3x10^8 m/s.

And here's the trick: suppose that, instead of standing still, one of both of our two gentlemen is running at any arbitrary speed twoard the other one.

If they were throwing a baseball, their velocity would be added to the velocity of the ball and the ball would reach the other mountain in a shorter time. But the speed you are moving makes no impact on how fast light travels. It is always a constant.

This is weird because if the SPEED LIGHT GOES BETWEEN MOUNTAINS doesn't change it must be that THE DISTANCE BETWEEN MOUNTAINS seems to change.

Again if the speed of light is a constant when the speed of the thrower changes, then the distance between mountains ISN'T constant. And the time it takes to go between mountain changes, too, depending on who's looking.

If the distance between mountains isn't constant, Einstein asked, what is?

>>2149239
Maxwell's equations implied a constant:

x^2 +(ct)^2

where 'x' is the distance between mountains and 't' is the time. When you hold THIS constant, no matter what speed the events are being obsevered at, you arrive at the famous 'time dilitation' which makes time go slower to moving objects--and, yes, you do live slightly longer if you are running. You also get 'length contraction' that tells you the distance between mountains SHORTENS when the two gentlemen's experiment is observed from a moving platform.

These two things explain how distances and elapsed times warp in order to keep the speed of light constant.

But there is an even more elegant way of looking at it.

>>2149259

Go on!

>>2149259
The constant

x^2 + (ct)^2

implies that spacial dimensions and time hold the same footing. Yes, we live in three dimensions, but those dimensions change if you're not including time as a fourth component. Instead of measuring the distance between mountains by subtracting one gentlemen's x, y, and z position in space from the other--one must measure the difference in x, y,z and z positions AS WELL AS TIME. When you do this you can keep their distance in 'spacetime' constant.

Suppose now that you are watching our two gentlemen's experiment from a moving platform. Normally you'd find the distance between them by finding the difference in their x, y, and z directions--call this the vector D, the distance between them. Relativity says that the magnitude of the distance between them is

D^2 = x^2 + y^2 + z^2

...and it says that this quantity is not a constant if you are watching the experiment while moving. If you add TIME to the distance between them,

D'=(x,y,z,ct)

Now their distance is

D'^2 = x^2 + y^2 + z^2 + (ct)^2

and once you hold time on the same footing as space, D'^2 is now constant.

What about the vector D'=(x,y,z,ct) itself? It turns out that moving acts like a ROTATION in this space. If you are moving fast, the vecotr rotates more in the time direction. You get length contraction because if the vector is composed more and more of time, its projection in the three spatial dimensions must get shorter.

This is called a 'Minkowski transformation', and it's the most elegant way of thinking about it. But it needs pictures, so google!

>>2149306

Well, thank you!

>>2149239
>>2149259
>>2149306
why is the speed of light constant?

is this a law or was it determined somehow?

>>2149335
I was a bit liberal with the facts but I think the old 'flash light between mountains' argument is still the clearest.

Interested readers will want to check out 'Relativity Visualized'. Also, there's some movies showing what relativity looks like at:

http://www.anu.edu.au/physics/Searle/

>>2149372
It's probably not!

Light changes speed when it goes through a medium (which is why it bends in water). You can also play around with the difference between 'group velocity' and 'phase velocity' to make it seem like light is moving faster than 'c':

http://www.nature.com/nature/journal/v406/n6793/full/406277a0.html

As far as the speed IN VACUUM, it's constant in the presently observable universe, but may have been different in earlier times:

http://www.springerlink.com/content/h8v714325165521j/

>>2149372
That c is constant in a vacuum was determined experimentally.

Most of relativity stems from the assumptions that the speed of light in a vacuum is constant for all non-accelerating reference frames.

>>2149259
>x^2 +(ct)^2

>>2149445
shit you're right

(ct)^2 - x^2

it's not a rotation but an hyperbolic rotation. happy?

>>2149454
Much better.

fun fact:
the magnetic force is just the electrical force with relativity applied, try the derivations and see for yourself

Imagine yourself floating next to someone outside one of those space satellite things they are always fucking fixing and shit.

You look at your friend, you guys look like you are staying still to each other. You are really both orbiting the earth going 23,000mph relative to our earth space/time.

>>2149548
>>2149548

Ok not 23,000 but pretty fast


I just close my eyes and think of how fast the earth is spinning, yet it looks so still from my spaceship.

I really need to be in a room with people like anons here.

>>2149454
And it's not just nitpicking; the sign does matter. If it were x^2 + (ct)^2 then we would be living in a world where all you'd have to do is pull a 180-degree turn, and you'd be traveling backwards through time. Alas, this is not possible in our universe.

However, the nice thing is that you can still use almost all the geometrical rules from the space with distance given by <span class="math">\sqrt{(\Delta w)^2 + (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2}[/spoiler]; all you have to do is replace all the w's with ict (or alternatively, replace the w's with ct and the x's etc. with ix). This includes the rules of trigonometry, but one finds that if you want to do a rotation in the tx plane, the allowed angles are imaginary numbers. And since 2pi isn't on the imaginary axis, rotations in the tx, ty, and tz planes never take you full circle like the ones in the xy, xz and yz planes do.

OP here. Thank you all for posting :)

>ilovethisthreadsomuch.jpg

Just read through the whole thing, took me at least a half hour. I'm just a shitty community college student, but I want to be like you guys. This board is a collection of some unbelievably smart people.

Bumping this thread in case people didn't read it, and so it's alive when relativity guy comes back

>>2149760
No, this board is full of average, if not below, high school students, college students that think they know what they are talking about but really don't, trolls, thousands of them and some helpful guys like the one in this thread and a handful of grad students. Except for the last two categories, I really wouldn't count them as smart. When /sci/ was new things were different but then summer happened...

OP here, waiting for relativity guy.

Great job on archiving this. The people at the archive were probably thinking /sci/ was nothing more than troll physics.

Also: put this on Conservapedia.

Bump.

It's all relative, man. That's just your opinion. Etc.

The first time I had relativity formaly taught to me was in my first year university. I think they should introduce the ideas way earlier. You could make a unit in high school, shit even middle schoo,l about relativity if you just simplify it and strip enough of the math away. It's too cool and too fundamental a theory to have to wait that long.

>>2151964

I know, right?

I had my physics teacher explain some of it to me last year, but without the math. It was pretty complicated.

>>2144658
Why do you want to learn it? It is is just a theory.

sad bump, waiting for relativity guy

>>2152644

Because I don't understand it.

>>2154614
http://www.youtube.com/watch?v=BAurgxtOdxY&feature=BF&list=PLCCD6C043FEC59772&index=1

Learn it like a grad student

I'm guessing it has already been said but basically Einstein was like:
Maxwell's equations give you the value for the speed of light but there is no dependence on frame of reference. I wonder if fundamentally light is the same speed independent of frame (versus the idea that Maxwell's equations need modification).

The rest is coordinate transforms...

>mfw this thread was archived
In all sincerity I'm actually touched and impressed by this. I'm glad people are taking an interest in how the world works. Sorry about not being here earlier!

So, anyone here wanted to learn some relativity?

Well, too bad, imma post anyways.

First, and important point I forgot to address last time. When deriving the Lorentz transformation, we assumed that it followed the form
<span class="math">x' = Ax + Bt[/spoiler]
<span class="math">y' = y[/spoiler]
and so on. But why couldn't <span class="math">x'[/spoiler] be a quadratic equation of x's and t's, something like <span class="math">x' = Ax^2 + Bx + Ct[/spoiler]. And why did y' = y?

Well, if the Lorentz equations weren't linear (as in, the highest power term has exponent one), then it's easy to show that something moving at constant velocity in one frame would accelerate in another.

>>2154737

OP here! Welcome back!

Likewise, a very elegant argument can be made supporting the assumption <span class="math">y' = y[/spoiler].

Suppose that <span class="math">y'[/spoiler] is moving relative to <span class="math">y[/spoiler] as in the picture (fig. 1).

Looking at it from the other side of the paper, we see fig. 2. By the principle of relativity, fig. 2 is equivalent to fig. 3 (only relative speed matters). Therefore, fig. 3 is equivalent to fig. 1. But fig. 3 is just fig. 1 with y' and y interchanged. This can only be true in general if y' = y.

>>2154762
:)

Alright, now that that's out of the way, a few more details and then we can get to the really interesting parts.

First, we define <span class="math">\gamma = 1/ \sqrt{1-v^2/c^2}[/spoiler] for convenience.

So, the lorentz equations are
<span class="math">x' = \gamma (x-vt)[/spoiler]
<span class="math">y' = y[/spoiler]
<span class="math">z' = z[/spoiler]
<span class="math">t' = \gamma (t - vx/c^2)[/spoiler].

So, we have x', y', z', and t' in terms of x, y, z, and t. Can we have it the other way around? That is, can we have x, y, z, and t written in terms of x', y', z', and t'?

Well, one way would be to do a bunch of algebra to solve for it. Alternatively, a little bit of thinking can be done. From (x',..., t')'s vantage point, (x, ..., t) is moving away at a velocity of <span class="math">-v[/spoiler] in the x-direction. So, we can just replace all the v's with -v's and get
<span class="math"> x = \gamma (x' + vt')[/spoiler]
<span class="math"> y = y'[/spoiler]
<span class="math">z = z'[/spoiler]
<span class="math">t = \gamma (t' + vx'/c^2) [/spoiler]

An important consequence of this is that what we deduce for one frame (say, time dilation) can also apply for another frame without have the principle of relativity be violated.

ALRIGHT, now we can start getting some results from these bad boys. We begin with the most famous result of special relativity, time dilation.

Consider a clock at rest in the (x', ..., t') system. Now, a clock can be anything which, in theory, can be used to tell time. Examples: wrist watch, swinging pendulum, cell division, spread of cancer, speed of a person's thinking, etc.

Imagine two events <span class="math">E_1[/spoiler] and <span class="math">E_2[/spoiler], both occurring at same point in the (x', ..., t') frame. (examples: time between clicks on a watch).

We can describe these events by
<span class="math">E_1: x_0 ', t_1 '[/spoiler] and <span class="math">E_2: x_0 ', t_2 '[/spoiler].

WIN WIND THIS THREAD IS O WIN!

(we ignored the y's and the z's because they're not important).

The interval <span class="math">\Delta \tau = t_2 ' - t_1 '[/spoiler], the time interval between events in the rest frame, is called the proper time.

What's the time interval in the (x,...,t) frame? Just apply the Lorentz transformations!

<span class="math"> t_1 = \gamma (t_1 ' +vx_0 '/c^2)[/spoiler]

<span class="math"> t_2 = \gamma (t_2 ' +vx_0 '/c^2)[/spoiler]

Subtracting to get <span class="math">\Delta t[/spoiler], the time interval in the (x,...,t) frame, we have
<span class="math">\Delta t = t_2 = \gamma (t_2 ' +vx_0 '/c^2) - t_1 = \gamma (t_1 ' +vx_0 '/c^2) = \Delta \tau / \sqrt {1 - v^2/c^2}[/spoiler].

Because <span class="math">\gamma > 1[/spoiler], the time interval in the non-rest frame is greater than the time interval in the rest frame. Moving clocks run slower! This is the effect of time dilation.

*I meant <span class="math"> \Delta t = t_2 - t_1 [/spoiler]

Incidentally, something I forgot: Notice how is an object's speed is greater than c, <span class="math">\gamma[/spoiler] becomes imaginary and it seems impossible for the object to have a reference frame. This serves as a good first indication that objects can't exceed the speed of light, although this isn't be any means the strongest argument.

Time dilation also supports this claim. If an object were to move faster than light, then its time would be .. imaginary? Again, doesn't seem to make sense.

At any rate, time dilation has been well documented experimentally. Particles whose decay-rates are ordinarily millions of a second can last for a few seconds if they are accelerated to near light speeds (aka in a particle accelerator).

Time dilation presents an interesting paradox: Say an observer, who we will call A, sees another observer, who we will call B, moving to the left at speed v. Because A sees B moving, A should see B's clock slow down due to the time dilation.

However, from B's perspective A is moving. So B should see A's clock slow down. But this seems to contradict the principle of relativity! Why?

>>2154941

:O WHY?

Well, the two observers could do a race of sorts. Starting their watches at zero, they can do a race to see who's clock reaches 1 minute first. At first glance, it seems that if from A's perspective A is at rest, then B's clock with be slow and so A will win. But from B's perspective, she will be at rest and A's clock will be slow, so B will win. But they can't both win, so can the winner will determine who's really at rest, and hence there will exist absolute motion as opposed to relative motion .

PS ignore the horrific grammar, I'm typing/deleting/retyping fast and can't be bothered to proof read.

The resolution of this paradox is tricky, so we will do an example with numbers. Suppose B is moving relative to A with a speed of 0.8c along the x-axis. When they pass each other, they will start their stopwatches. They decide before-hand that B will call or text A as soon as her watch reads 1 minute. A will then compare the time he receives the text to his stopwatch and determine the winner.

(Note that <span class="math">\gamma = 1/ \sqrt{1-0.8^2} = 5/3[/spoiler])

Because of time dilation, when B's watch reaches 1 minute, A's watch reaches 1.67 minutes. Is this when A receives a text? NO! it takes time for the text, which is transferred by radio waves moving at the speed of light, to reach him. They are separated by 0.8c * 1 minute = 0.8 lightminutes (lmin).

>>2155030
forgot pic

It takes 0.8 minutes for the text to reach A, so he only receives the text at t = 2.47 minutes. But A's not stupid: he accounts for the travel time of the text, and sees that his watch did indeed read 1.67 minutes when she sent his text. With a smug grin, he thinks he's the winner: he's the one really at rest.

(If people are not following something
>implying people are reading this
just stop me!)

DAMN! Huge math error: The distance between them should read 0.8c * 1.67 min = 1.33 lightminutes!
Then A recieves the text at t = 3 minutes.

>>2155077

OP here, monitoring this thread.

So, what's happening in B's frame?

Well, they start of when both their watches read t = 0.
When her watch reads 1 minutes, his watch reads <span class="math">1min/ \gamma = 0.6min[/spoiler]. They are separated by 0.8 lightminutes. B sends the text.

>>2155094
FORGOT PIC

Now here's the important part: from B's perspective, A is moving away from the text-message signal! So it takes quite a bit longer to reach him than if he were at rest. How long? That's easy to calculate: it's just
<span class="math">d/(c-v) = 0.8lightmin/0.2c = 4 min[/spoiler], where d = is the distance between them when the signal is sent. So when the signal reaches him (from B's perspective), B's watch reads 4 + 1 = 5 minutes.

What about A's watch? Well it reads, by time dilation ... 3 minutes! THAT'S EXACTLY WHAT WE GOT WITH FROM A's PERSPECTIVE! So either way, the text gets read at the same time by A. And of course, when he recieves the text he'll assume he's at rest when he accounts for the travel time of the signal, and hence he'll believe that B time dilated even if he's time dilated.

So there's no way to determine who's clock is actually slower, so the question is meaningless: both statements are correct and consistent with each other.

>>2155123

Well that's amazing.

"Well," you might say, "clearly the issue is that their separated when they compare their watches. What if B changed directions and then they compared watches?"

If that happens, then the game is up. Special relativity only works for observers moving at a relative CONSTANT velocity to each other. If B has to change directions, then she will necessarily accelerate and so special relativity can no longer apply.

Why does special relativity only work for constant velocities? Well, imaging you're in a car that's going in circles. Everything seems to fly to one side of the car. So it's difficult to make the claim that you're actually at rest, when it's very easy to see that you're accelerating.

>>2155141
***"...what if B changes direction and heads back to A and compares watches"

Now, on to length contraction. As it turns out, if an object is moving (w/ respect to someone), it will appear to shrink in the direction of motion. We will demonstrate that now:

Imagine a ruler is at rest in the (x',...,t') frame, lying on the x/x' axis. The length of the stick as measured in the (x',...,t') frame is called the proper length, and denoted <span class="math">l_0[/spoiler]. (In general, the "proper" system is the system at which whatever we're talking about is at rest)

We can measure the length of the stick in the (x,...,t) frame, which we'll call <span class="math">l[/spoiler], by taking the difference of the positions of its endpoints. (look at the pic for a reference)

So <span class="math">l = x_2 - x_1[/spoiler]. evidently, <span class="math">l_0 = x_2 ' - x_1 '[/spoiler].

Using the algebra in the pic, we get that <span class="math">l = l_0 \sqrt{1-v^2/c^2}[/spoiler]. Because <span class="math">\sqrt{1-v^2/c^2} < 1[/spoiler], the ruler appears shorter in the frames in which it is moving. That's the length contraction!

>>2155196
pic

Alright, now for the final result of the night, and perhaps the most bizarre: the relativity of simultaneity. We can exploit this to reveal how the speed of light is connected to causality, but I'll do this later today after some sleep.

Suppose observer A (now a black female because of affirmative action) is at rest in between two walls equally space from her, as in the pic. There is another observer, B, moving relative to her, who can see her as well.

She shines simultaneously two light rays, each directed at one of the walls. Evidently from her perspective, they hit the walls at the same time.

What happens from B's perspective? Well, from his perspective, everything's moving to the right at a speed v ... including the walls! So one wall is rushing towards the light, while the other wall is rushing away from the light. Therefore, the light will hit one wall first...the light doesn't hit the walls simultaneously anymore!

Therefore, it is meaningless to say something is absolutely simultaneous, because another observer might see them happening at very different times. You can use the Lorentz transformations to calculate the exact time difference between the events.

Well, that's it for now. If people are interested, I'll continue tomorrow. In the meantime, feel free to leave questions/comments/and especially feedback!

'Night OP!

>>2155282

Sleep well, relativity guy! Thank you!

>>2155271

While that's all fine for illustration purposes, it is wrong.

>Therefore, it is meaningless to say something is absolutely simultaneous, because another observer might see them happening at very different times.

This is specifically very wrong. The limitations of your sensory organs to observe 2 simultanious events that for some reason do not appear simultaneous, doesn't mean they were not simultanious.

Einstien used examples like this that he knew were fallcies to illustrate a point. And these are crtisized because they lead to conlusions like yours that are wrong.

This thread is awesome! hope relativity-guy will be back soon:D

Bump.

>>2155326
Er ... wat? "Simultaneous" can only refer to to a specific frame of refrerence. For a moving observer, two specific points in spacetime, need not to be on an equal proper-time plane and are therefore not "simultaneous", regardless on how our eyes perceive them.


Or am I mixing things up here?

>mfw this thread is still alive

special:
you cant tell wether you are moving in a straight line or standing still.
the speed of light is the same in all reference frames.
relativity is some mathematics that makes this possible, by fucking with length and time.
also makes sure you cannot go faster than the speed of light.

general:
gravity is not strictly a property of matter ,but the fact that space responds to the precence of matter. (analogous to balls on a rubber sheet)
more math to make this possible.
it is fascinating that GR is consistant

tl;dr
mathematical trickery that makes good predictions

Let's examine some consequences of the relativity of simultaneity, the first one related to conservation laws.

As we know even from classical physics, there exist quantities that are conserved, such as energy, charge, momentum, etc. We will use energy as an example, but this applies to all conservation laws.

The Law of Conservation of Energy states that the total energy of the universe is constant. However, energy can change form and place. As a rock is falling to the earth, it loses potential energy while gaining kinetic energy. During collisions kinetic energy is usually transferred to sound energy and heat, which are just other forms of kinetic energy. An object radiating light will cool down.

Let's ask the following question: can energy disappear in one location and reappear in another?

Classically, the answer appears to be yes: so long as the amount of energy that disappears is equal to the amount of energy that appears, the law of conservation of energy is not violated. An example of this is provided in the pic: the rock losses potential energy, while the water's temperature increases.

However, special relativity does NOT allow this.

Suppose the situation in the pic were to happen. To an observer moving relative to the rock/water setup, the energy exchange would NOT be simultaneous: for example, at first the rock would lose potential energy, and later the water would gain the missing energy. So for a brief time, energy would not be conserved. But this would violate the Law of Conservation of energy, because at one point the total energy of the universe would be lower than usual. But by the principle of relativity, the laws of physics must remain the same to all observers, and if one observer sees the conservation of energy being violated, then game's up.

Hence, if energy is exchanged, it must be done locally (ie the thing that gains energy must be at the same place as the thing that loses energy).

The Special Theory can be understood by anyone who passed high-school algebra. Find an English translation of Einstein's theory and read it.

>>2155326
Oh, I forgot to comment on this.

Your post doesn't make sense. The relativity of simultaneity isn't an optical effect or anything. As in the example provided, the light really does reach one wall before the other, and this is entirely a result of the constancy of the speed of light.

Besides, an argument that observer B isn't seeing the situation right (saying that the two events are simultaneous but B just "isn't seeing it right") can also be applied to A (saying that the two events are not simultaneous but A just "isn't seeing it right").

Space-like and Time-like intervals

Suppose we have two events in the (x,...,t) system: Event A w/ coordinates <span class="math">(x_A, t_A)[/spoiler] and <span class="math">(x_B, t_B)[/spoiler]. The distance L between the two events is <span class="math">L=x_B - x_A[/spoiler] and the time T between the two event is <span class="math">T=t_B - t_A[/spoiler]. We'll assume both L and T are positive, without loss of generality. So, what is the distance and time between the events in the (x',...,t') system? (that is, in a system moving to the right at speed v along the x-axis)

***...and Event B w/ coordinates <span class="math">(x_B, t_B)[/spoiler]

All we need to do is apply the Lorentz transformations.

<span class="math">x_A ' = \gamma (x_A - vt_A)[/spoiler]
<span class="math">x_B ' = \gamma (x_B - vt_B)[/spoiler]
<span class="math">L' = x_B ' - x_A ' = \gamma (L - vT)[/spoiler] and

<span class="math">t_A ' = \gamma (t_A - vx_A / c^2)[/spoiler]
<span class="math">t_B ' = \gamma (t_B - vx_B / c^2)[/spoiler]
<span class="math">T' = t_B ' - t_A ' = \gamma (T - vL/c^2)[/spoiler].

Notice that, if v is less than c, if L > cT, L' is always positive, while T' can be positive or negative (or zero).

This makes some sense intuitively. Imagine that we have two lightbulbs atop two pylons on a highway. Event A is the first lightbulb on the first pylon turning on, and Event B is the second lightbulb turning on. The highway is the (x,...,t) frame, while the (x',...,t') frame is the frame of a car passing on the highway. If the car cannot exceed the speed of light, and if the two cones are separated by a distance greater than cT, then it will be impossible for the driver to drive fast enough for the second cone when it flashes to be behind where the first cone flashed. However, by the simultaneity of relativity, as we discusses before, it seems reasonable that the time order of the events change.

This sort of interval is known as space-like.

If, however, L < cT, the situation is reversed: T' will always be positive, while L can be positive or negative or zero. That is, it is impossible to pick a reference frame where the order of the events changes.

I'm here :)

This is called a time-like interval.

Why is this important? Consider a cause-and-effect relationship, like the sound generated by your vocal cords causing my ear drums to vibrate. If causality is to be preserved, we demand that cause precede effect. To think otherwise would be very taxing on the imagination.

Now here's the deal: if the two events (the vocal chords generating the sound and my ear drums responding) are separated by a distance greater than cT, where T is the time delay between the events (caused by the finite speed of sound), then it is possible to find a frame of reference frame where the time delay is negative (ie they happen the OTHER WAY AROUND; my ear drum vibrates, and then your vocal chords shake). But then causality will be violated; effect precedes cause.

>>2159330
Nice! Stop me if I'm not making sense.

However, this can be avoided only if the two events are seperated by less than cT. How can we interpret cT? It is the time it takes light (or something moving as fast to reach it) to make it from the cause to the effect.

This is why we say things can't travel faster than the speed of light: if some signal (anything than can affect something else) could travel faster than light speed (we can imagine that sound waves traveled faster than c), then L > cT and causality would be violated. Signals and information must travel at or less than the speed of light.

This can be represented graphically by a light cone, as in the pic. The first event (the cause) is on the origin. time is graphed on the vertical axis and x on the horizontal axis.The lines represent the how a light beam would travel, and the space between them is know as a light cone. Note that the steeper the line, the slower the thing travels.

Events within the future light cone can be affected by the origin, while events on the outside cannot. Likewise, events outside the past light cone cannot have influenced the origin, and events inside the past lightcone could have influenced the event at the origin.

Anyways, this more-or-less covers the space-time aspects of relativity. There's still dynamics left (E = mc^2, mass increasing, and so on) but I have to get back to my homework...I'll cover it tomorrow if people are interested!

OP, do you know calculus?

>>2159476

I'm not sure what that is, but I don't think so.

What solid real life evidence is there for the constancy of light velocity?

Atom decay, how do we KNOW that their longer lifespan is due to time slowing down and not just the stability (or whathever else, I don't know) change that occurs because of their velocity?

I'm not here to say "I don't believe in SR", I'm just curious what real life proof of SR we have. I know there's some, sure.

>>2159533
It's a branch of math that would have made the other parts of relativity nicer, but we can do without it. Sorry for being here not long, but I got homework to do.

>>2159555
The first was the Michelson-Morley experiment, which showed that as the earth moves around its orbit, the speed of light as measured by someone on the surface doesn't vary. I'm sure there are more modern versions of the experiment, but I couldn't tell you much about them.

>>2159576

Oh, no, thank you for being here for so long!
And about calculus, all I know is that my brother is studying engineering, and he's in the first year of university and has calculus, so no, I don't think I ever learned about it.

Relativity Guy, you are awesome and thank you so much for posting. Out of curiousity, what are you pursuing as a major/career?

And if I can make a request, I wonder if you'd be interested (at some point) in discussing black holes, since they are pretty much the most extreme case possible for relativist effects. Plus black holes are downright cool things to begin with. :)

This whole concept about "speed of light limit" seems like nonsense to me. Why would there be a universal speed limit? Moreover, what's 'static', when everything in the universe is moving? And there are many unexplained paradoxes about this whole speed of light thing. It's always constant no matter what reference you're in? It needs to be explained. For example...

Lets say we have 2 objects, call them object A and object B. Object B projects light in the direction west. We'll call the speed of light 'c'. Now, at the same time, we have object B going the same direction When it reaches half the speed of light (relative to object A), it also shoots a beam of light, in that same direction (west). Now, from object A's point of view, object B's light should be going c+(1/2) * c. But it doesn't? That's a gap half the speed of light.

>>2159775

Basically I'm saying "my light moves faster than your light".
Nothing can go faster than the speed of light, sure. But what about light itself? If I shoot a beam of light while going in the same direction, my beam of light should be c + (insert my speed here).

>>2159733

THIS.

>>2159775

have you ever TAKEN a relativity class???

>>2159793

The whole "the faster you go, the slower time goes" also has paradoxes in of themself. Here's that paradox I've yet to have explained to me.

Suppose we have object A, B, and C. We will take object A's perspective, it will always remain static. Object B is going science-knows-how-fast, and relative to us, it's going twice as slow. Relative to B, C is going twice as slow. That means 1 second to C would be 2 seconds to B and 4 seconds to us. But what about the opposite?

If we took C's perspective this time. Now, B goes twice as slow and A goes four times as slow, because relative to us being object C, everything around us is moving and we're static being C.

That said, all this "time slows down" theorys should just cancel themselves out. So again, I ask- if everything in the universe is moving, what's 'static'? Or simply put, what has the reference frame? Speed of light is void, because it's constant no matter what speed you're going.

Inertial reference frames (having no acceleration) exist only as approximations. Newton's 2nd law applies only to inertial reference frames, therefore, some frame in the problem must be assumed to have a zero acceleration. The ground is usually approximated to be an inertial reference frame when dealing with problems on earth, because its acceleration relative to whatever is moving is negligible. However, to answer your question, nothing is "static." Something must be approximated as inertial for the physics to work.

>>2159793

the velocity addition equation addresses this.

a = velocity of object A
b = velocity of object B

v = (a+b)/(1-(a*b)/c^2)

so let's add two things going at the speed of light. one would at first think it's just 2c. but using this equation, we get:

2c/(1+c^2/c^2) = 2c/2 = c

we've been able to use this to synchronize the GPS system, so as far as we know, Einstein was right.

now let's add two things at, say, 5m/s and 10m/s:

(5+10)/(1-(5*10)/c) ~ (5+10)/1 = 15m/s.

this was just to prove that at non-relativistic speeds Newtonian Mechanics still holds.

>>2159921

What is that assumed 'inertial' object? You guys at /sci/ have alot of faith in the theory of relativity. But when I ask a question like...

Earth is revolving around the sun. In a distant cosmos, a meteor is also moving. The difference in their speeds is enough to slow down time by 50%. In other words, the difference nearly the speed of light. Now, is Earth going 50% slower or the meteor?
Your theory demands that time slows down by half. But if I apply the reference frame reasoning, earth is going half as slow to the meteor and vise versa. basically .5=.5, resulting no difference at all. What's the reasoning behind this?

>>2159980

time dilation is the hardest thing to explain for me. the best way for me to learn was to look at a diagram. it's been several months since I was learning special relativity so I can't explain this very well nor do I want to look it up since I'm studying other physics finals.

I remember Wikipedia's time dilation page having an analogy for it though:

Say Bob and Sally are standing far away from each other. To Bob, Sally looks small. But to Sally, she looks normal-sized and Bob looks small.

don't know how much this helps but it could be a small stepping stone.

>>2160037

I've read it, but it makes NO sense.
Here's some copypasta to show you what I mean...


>At .9 times the speed of light, the factor becomes 2.294157338705618. Finally, the effects of relativity become significant. What does this factor mean though? If you were in a spaceship travelling at .9 times the speed of light:
>1) the ship's mass (and you) would increase by a factor of 2.294
>2) the ship (and you) would contract in the direction of travel by 2.294, meaning a 300 foot ship would shrink to 130.77 feet.
>3) Perhaps the most interesting change is that 1 year to you would seem to be 2.294 years for someone back on Earth.

If you look at point #3, 1 year for the guys on the ship would be about 2 years for the guys at Earth. But this is assuming that Earth is static. From the ship's point of view, Earth is moving, not the ship. Because of this, the Earth is slowing down. But why is time on Earth going faster? It makes no sense.
Once that point is trampled, point 1 and 2 also become void. Again, if the ship would shrink, the world would seem larger for the guys on the ship, right? But if we put ourselves on the ship, the world is moving in respect to us, so the world would look smaller, therefore WE are the ones getting larger.

We can't have both at the same time. Do they get smaller or larger? Does time slow down or speed up? I can't understand any of it.

>>2160115

i agree with this, if time slows down for one object, time seams like it speeds up for everything else to the object. current relativity theories slow down time, not speed it up. it has to speed up somewhere along the lines to make sense. for the guys on the ship, the earth speeds up, but the theory demands that it should slow down

>>2160314
The reason this thread is alive is because Relativity Guy was explaining all this shit. Scroll up to >>2145043 and start from there.

>if time slows down for one object, time seams like it speeds up for everything else to the object

No, if from A's perspective B's clock slows down, then from B's perspective A's clock slows down.

Bump.

This is the only good thread /sci/ has ever had
Thankyou man, your writing was very entertaining and insightful
your english is superb as well

\begin{math} \delta \end{math}

I didn't bother to read any of the shit above, but here's a good explanation for part of relativity in case anyone is still looking for it. Imagine a clock composed of two mirrors facing each other. A photon of light bounces between them a certain number of times per second, once it hits that number, one second has passed. Now imagine these mirrors started moving. For the light to reflect off them, it would have to travel in a diagonal line instead of straight across. Since light can't speed up, but it has to go a longer distance, time must slow down to accommodate it. So, when you go fast (or get near a massive object, but this is a bit confusing), time slows down. BOOM. Relativity.

Hopefully I explained that well enough.

>>2161109
Don't mean to break your bubble, but that's only because this is 2nd year shit and anything 3rd year and above gets totally ignored because grad students are too busy leaving mostly highschool faggots.

>>2161230
Did you seriously think that a 280 post thread on relativity doesn't have a photon clock mentioned? And besides, the real nut to crack in relativity is the constancy of the speed of light.

>>2161262
That post actually made no sense.

>>2161363
>made no sense
tl;dr, /sci/ is mostly 16 year olds and barely educated neckbeards.

he wrote a book so people could understand it. it's only 60-70 pages long. stop being such a lazy ass.

>>2159476
Hey, I think it would be great if you could include the calculus-part when you explain this, because this would be really interesting for the people who do know calculus.
Not OP btw

Bumping.

bumping, why not?

Bump.

does the entire thread get archived? or only the thread up to the point when the archive request went through?

This graph shows the effects of relativity, you are always moving at the speed of light, if you stand still, you are moving through time at the speed of light, but as soon as you start moving the speed moves away from time and part of it is used to make you go through space, meaning you go through time slower. Line A shows someone moving through space at approximately half the speed of light, as you can see this also means he moves through time at half the normal rate. He would not experience time going slower, as his thought are slowed as well, but any outward observers would see him shoot by really fast, but he would look as though he is in slow motion (e.g. facial expression=funny).
This theory has been proven right, two atomic clocks, started at the same time, one stays where it is, the other was flown around the world. the one that was flown round was about 1 nanosecond behind the one that had stayed still, meaning time goes slower the faster you go through space, of course, to make any meaningful change in time (time travel) you would have to travel at speeds far higher than we a re capable of.

WE CAN'T LET THIS THREAD DIE WITHOUT REACHING 300 POSTS. POST NOW!!!11!1!eleven

>>2165413

Don't worry, it won't die!

Bump! 300!

a worthy goal for a great thread

bump

Two more!

never die

Bump.