Hard Light Productions Forums
Off-Topic Discussion => General Discussion => Topic started by: jr2 on May 28, 2007, 11:45:55 pm
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Umm, BTW, I was wondering, how fast does a beam of light/radio wave travel if fired forwards from an object moving quite fast? (eg, .55c?) Normal speed, or 1.55c?
Exactly at c, of course*. In every inertial frame, too. But let's not turn this into a science debate (unless Black Wolf agrees to that); you can ask that question in own thread and I'll provide more physics... ;7
*"of course" here can be derived from two physical principles; the first being the generally accepted assumption that laws of physics must be same to everyone regardless of their inertial co-ordinates, and the second being the fact that the speed of light is a constant at vacuum.
Those two things combined will produce the special theory of relativity, which states that light's vacuum speed is constant to all observers.
I don't get it. If you jumped off of a spacecraft traveling at 40,000 mph, and your forward velocity was 5 mph, then your total velocity would be 40,005 mph. Why is light different?
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i dont think light knows what time is. even if you manage to get up to the speed of light it will still be traveling at the speed of light (because for you time is paused). its not that lights relative to you its that youre relative to time (and lighs not).
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Oh... I meant the light beam itself. Obviously, it travels at 1.00c But, it is being fired forwards from a ship traveling at 0.55c So how fast is the beam traveling, based on how long it will take to reach a predetermined destination?
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the lights traveling at 1c. if it were a bullet with a muzzel velocity of 1000 m/s and youre traveling at 10000 m/s a second, that bullet will travel at 11000 m/s. but those rules dont apply to light. we like to think in terms of distance per time. but sence time means nothing to light, its always traveling at 1.
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Hmm, why not?
EDIT: BTW, is e=mc2 a real math equation? ie, sqrt(e/m)=c?
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the absence of mass maybe
and thats the conversion of matter to energy
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See my EDIT above... now how about this:
e/c2=m
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and that would be conversion of energy to mass (the inverse of e=mc^2, assuming the math is right)
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Okay.
The most basic thing we can assume about the universe is that the laws of nature are same to all observers, regardless of their state of motion.
The speed of light (actually speed of all electromagnetic wave motion) arises from the structure of empty space. More specifically, in Maxwell's equations it is shown that the speed of light depends only about the permeability and permittivity of the vacuum. Also, since there is no universal base co-ordinates to reference in a vacuum, that indeed means that everyone will observe the speed of light in vacuum to be constant, c, since vacuum itself will appear exactly the same to everyone passing through it - you can't reference to nothingness!
Now, when a situation like what you described occurs - an observer (A) sends a light beam (or a photon) forwards while moving at velocity v in relation to another observer (B) - we can from the previous deduction simply say that both observers will see that the photon moves at the constant speed of light, c. This is a fact, and all that follows has variable interpretations and requires a bit deeper analysis to understand.
Because there is a speed difference, yet both must observe the speed of light to be constant, we can deduct some interesting things. Mathematically, you can derive the so-called Lorenz-contractions for distance and time for both observers, based on the speed difference. It all gets a bit hairy when it's written with a computer so I won't bother to start with (I'll do a copy-paste later if it's necessary). The basic idea is that when relative velocity increases, the observers start seeing things different from each other. If both were stationary, they would see all distances similarly, and time would pass at similar rate for both observers. However, if there's a large speed difference between observers, the following (and some) happens:
-when a stationary observer observes a moving target which has a clock on it's surface, he will observe that the clock is running slower than his own clock. Note that this applies to both observers - they both see the other's time is running slower than their own. It is a bit difficult to explain, but there's no paradoxes there in the end.
-same applies to the length on the direction of velocity. A stationary observer will note that a fast-moving observers' one-metre long scale looks somewhat shorter. This can similarly be inverted, since both observers will consider themselves static observers and the other one to be on the move.
Now what happens when, say, there's a velocity difference of 0.5c between observers and the other sends a photon forwards?
Observer A will measure that in one second, the photon moves about 300,000 kilometres from it's starting point. In other words, typical velocity of light, c.
Observer B will measure the same speed for the photon, but now you need to remember that from A's point of view, B's measure sticks are shorter and seconds take longer. That means that when the observer A sees that B's clock has passed one second, about 300,000,000 of B's one-metre long measure sticks will fit between B and the photon. So A can see that B also measures the speed of light to be constant.
...I've never been especially good at explaining the theory of relativity. It all gets more clear once you derive the Lorenz-contractions a couple of times based on the proven assumption that every observer measures speed of light as constant. There are many ways to explain special relativity, but I prefer first explaining why light will appear to move at constant speed regardless of the speed you're moving at (in relation to other objects and observers) and then explaining a bit what it means and what the interpretations are.
the lights traveling at 1c. if it were a bullet with a muzzel velocity of 1000 m/s and youre traveling at 10000 m/s a second, that bullet will travel at 11000 m/s. but those rules dont apply to light. we like to think in terms of distance per time. but sence time means nothing to light, its always traveling at 1.
Actually, the relativistic addition of velocities can be applied to bullets as well. In such low speeds, however, the result would be something like 10999.99999999998 m/s so it doesn't really pay to calculate the difference... usually. But it's there nevertheless. Obviously, in shooter's reference frame the bullet would be moving at constant 1000 m/s assuming it's a vacuum. :cool:
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i wonder how hard it would be to program a game with relativity physics :D
as if newtonian was hard enough :D
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Well at least online games wouldn't be so severely affected by lag... :lol:
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a game using relativistic physics would be imposable for multi-player, because everyone would be in a different time scale.
the thing to remember about relativity is that space and time change as you move, time moves slower the faster you go.
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Quick, someone modify IW2 to have relativistic physics! :nervous:
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I'm sure you could program a game to have relative physics... it would be easier in turn-based games where, depending on movement speeds, that your "tick" (turn) is slightly faster or slower. I think it would be very hard for the game engine to be able to calculate relative physics upon all objects in the game and match them so it is actual gameplay. Never say it's impossible ever. It may not be possible now but that's saying nothing for years from now...
There's a picture floating around somewhere of a person showing off a "home computer" invisioned in the early 1950s, saying the tech to make it won't be available until at least 2003 (iirc). Well, we beat his entire thing by 1990, and then look at the computers from 4 years ago.
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maybe with a physx card... :nervous:
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Those are actually junk. The PCI slot simply doesn't have the bandwidth to receive and send all the physics calculations required. Now what could do it is a card on a PCI-e x4/x8/x16 slot--there would be enough bandwidth to do it all. I would say a SLI/xFire config could probably do this quite efficently.
Here are all games using the Havok physics engine...
* Age of Empires III
* Age of Empires III: The Warchiefs
* Alan Wake
* Amped 3
* Armed and Dangerous
* Astro Boy
* Auto Assault
* Backyard Wrestling: Don't Try This at Home
* Backyard Wrestling 2: There Goes The Neighborhood
* Brute Force
* Crackdown
* Crash Nitro Kart
* Company of Heroes
* Condemned: Criminal Origins
* Counter-Strike: Source
* Darkwatch
* Dawn of Mana
* Dead Rising
* Destroy All Humans!
* Destroy All Humans! 2
* Deus Ex: Invisible War
* The Elder Scrolls IV: Oblivion
* Evil Dead: Regeneration
* Fable 2
* F.E.A.R.
* Freelancer
* From Russia with Love
* Full Spectrum Warrior
* Half-Life 2
* Halo 2
* Just Cause
* The Lord of the Rings Online: Shadows of Angmar
* The Matrix: Path of Neo
* Max Payne 2: The Fall of Max Payne
* Medal of Honor: Pacific Assault
* Mercenaries: Playground of Destruction
* The Outfit
* Painkiller
* Pariah
* Perfect Dark Zero
* Pitfall: The Lost Expedition
* Psi-Ops: The Mindgate Conspiracy
* Red Steel
* The Punisher
* Robot Arena 2: Design and Destroy
* Robotech: Invasion
* Saints Row
* Second Life
* Sonic Heroes
* Sonic the Hedgehog (2006 next-generation game)
* Starsky and Hutch
* SWAT 4
* Thief: Deadly Shadows
* Tom Clancy's Ghost Recon 2
* Tom Clancy's Ghost Recon: Advanced Warfighter
* Tom Clancy's Splinter Cell: Chaos Theory
* Tom Clancy's Splinter Cell: Double Agent
* Torque: Savage Roads
* Tribes: Vengeance
* Uru: Ages Beyond Myst
* WWE Crush Hour
And here are PhysX:
* Auto Assault (patch)
* Bet on Soldier: Blood Sport
* Bet on Soldier: Blood Of Sahara
* CellFactor: Revolution
* City of Heroes/City of Villains (patch)
* Dark Physics (Consumer Development Tool)
* Gothic 3
* Gunship Apocalypse
* Kuma\War 2
* History Channel's ShootOut! The Game
* Infernal
* Joint Task Force
* RoboBlitz
* Stoked Rider: Alaska Alien
* Tom Clancy's Ghost Recon Advanced Warfighter
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Detroy all humans :wtf: Seems a waste of processor power if you ask me :doubt:
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ok, look it's as simple as this, how are you going to simulate a time scale for person A which is 10000 times faster than person B were all events in both person A and person B's locality seem to be moveing at the same rate? untill you have the ability to actualy modify time, or at the very least te perception of it, it will be imposable to make a game engine with relitivistic physics and more than one player. none of you have any idea how complex or simple relitivistic calculations are, you are just assumeing they are the most mind blowingly hard to calculate things ever because you don't know anything about them, in reality most of the math in relitivity is only slightly more computationaly expensive than a very complete newtonian model.
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Should it really matter when most space shooter ships travel at only a few percent of c, at most? A relativistic sim of FreeSpace, for example, wouldn't matter for ships going at 80 m/s. Even in WC with speeds of (supposedly) 500+ km/s, that isn't very fast relative to c.
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@Herra: Hmm, missing my point, but your explaination helps me understand the point you thought I was after. :)
My wondering is:
Let's say you have a photon detector at point y, 1 ly away from point x. You have a spacecraft travelling at .55c, and when it passes through point x traveling in a straight line towards point y, it fires a photon beam forwards at point y. How much time will pass at the detector site before the photon detector at point y registers the beam that the spacecraft fired? 1 year? Or 3/4 of a year?
ie, when the spacecraft shows up and says, we fired that beam two years ago, will the detector site say we detected it 1.25 years ago?
EDIT: Of course, time would be skewed for a person traveling at .55c, right? darn this is confusing...
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1 au (light year, right?)
Wrong :p
1 AU is 1 Astronomic Unit = 150*106 km = average Sun-Earth distance.
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Bah. What is the light year official name/abbreviation?
EDIT: ly (http://en.wikipedia.org/wiki/Light_year) ... Of course :rolleyes:
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Let's say you have a photon detector at point y, 1 au ly (light year, right?) away from point x. You have a spacecraft travelling at .55c, and when it passes through point x traveling in a straight line towards point y, it fires a photon beam forwards at point y. How much time will pass at the detector site before the photon detector at point y registers the beam that the spacecraft fired? 1 year? Or 3/4 of a year?
ie, when the spacecraft shows up and says, we fired that beam two years ago, will the detector site say we detected it 1.25 years ago?
EDIT: Of course, time would be skewed for a person traveling at .55c, right? darn this is confusing...
An observer at X would see the photon precicely one year after the ship passed point Y. Of course, that would be a simultaneous event in X's reference frame... :drevil:
But, for simplicity's sake, let's make the ship move at 0.5c since half is a nice round number (more so than 0.55 anyway).
X and Y are at the same reference frame, so time passes at same speed for both (but the concept of simultaneity is still different for distant points). Anyway, let's say they are a light year apart.
At t=0, a ship traveling at 0.5c passes point Y, vith velocity towards X, and fires a single photon towards Y.
This photon arrives at X exactly at t=1a (a=annum=year). The ship will arrive at X at t=2a.
On ship time (let's mark it with capital T), the photon is fired at T=0 as well. But the ship will arrive at (or pass) the point X at about ship time T=1.73a. They could rightfully claim that they fired the photon 1.73... years ago.
They would also claim that since they were moving at 0.5c, the distance between X and Y was not light year, but only about 0.865 ly, since they were able to pass it in less than two years at speed 0.5c...
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This photon arrives at X exactly at t=1a (a=annum=year). The ship will arrive at X at t=2a.
I'm not catching how this is so. It was fired from a moving object. Along the path, it would be detected (if possible) traveling at 1c, I can get that, but shouldn't the speed of the beam be affected by its source? Why not?
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Because the only thing that affects the speed of light is the properties of the vacuum, and the vacuum appears exactly the same to all observers... Light propagates through the vacuum, and the emitter's velocity doesn't affect the photon's velocity once it's in "free space".
It's kinda the same way like if you were staying still on calm air. Every sound will seem to be moving at constant speed to you. If a train approaches you, the velocity of the sound it makes doesn't depend on the train's velocity, it will move in the air. As long as you remain still, the air is to sound just like vacuum is to light in space.
In space, though, things get a bit different, but essentially you could think that everyone moving at constant velocity has their own reference frame, which is analogous to having calm air around them. The analogy is not perfect, but will do for now.
Think about it this way - what if the ship that emits the photon doesn't move, but you do? Both approaches are perfectly valid when there is no universal reference frame to which you could compare velocities. You can only compare velocities in relation to other things.
However, the initial velocity does indeed affect the light; it just doesn't affect it's velocity. It goes straight into the energy (or rather, momentum) of the photon.
The initial velocity gives photon a boost (or leech) of energy, which means that the photon will have a different energy depending on the relative velocity between the emitter and the observer.
In short, if the emitter and the observer are at rest in relation to each other, the observer will observe the photons to have the expected energy and thus wave length. For example, let's say that there's a laser that emits exactly 500 nm photons (green light). We know that the device emits this wave length.
But if the emitter is moving fast towards the observer, the observer will measure the photon's energy to be more than expected, because the velocity of the emitter adds energy to individual photons... but since this energy cannot affect the photon's velocity due to it's constant nature, it goes to the wave length/frequency of the photon.
This is the source of blue shift and red shift that is talked of in cosmology. Objects that approach us fast (like Andromeda galaxy) have their light shifted towards the blue (higher energy) end of electromagnetic spectrum, whereas objects that are moving away have a red shift measurable.
At extreme velocities, the time dilation will also kick in and make things even more complex, though... the fast moving emitter's time will slow down in observer's perspective, which will affect the functionality of the laser - it will work "slower", so to say, which means that in it's own reference frame it'll keep producing photons that have steady frequency, but to outside observer the photons would appear to have lower frequency due to time dilation.
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Interesting... I'll have to think about that for awhile.. Thx :)
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This photon arrives at X exactly at t=1a (a=annum=year). The ship will arrive at X at t=2a.
I'm not catching how this is so. It was fired from a moving object. Along the path, it would be detected (if possible) traveling at 1c, I can get that, but shouldn't the speed of the beam be affected by its source? Why not?
Both will measure the speed of light as the same.
Therefore if they measure different times, they will also measure different distances.
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I'm not really a math genios or anithing but I believe that the speed of light can be beaten or rather it will be beaten sometime in the distant future. Why? Simply because it is a barrier which we must overcome. And if history has tought us anithing is that whenever we hit a brick wall which we consider to be inpenetrable we find a way to brake it down or go around it.
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Herr Doktor, bring on the heavy artillery; derive the transformation equations. Doing that myself was the only way to start understanding what is actually going on. No analogy will help in here.
The whole basis of Special Relativity rests on two assumptions:
1. The speed of light is constant (in the vacuum and does not depend on the motion of the reference frame as long as it is not accelerating). If you don't believe it, feel free to make your own measurements as this is an experimental result. It should be possible to repeat it with college level equipment. But before going any further, it might be good to read the situation before the Special Relativity, as the Physics had a huge unexplainable problems at hand before Einstein published his papers.
A common problem with Special Relativity is that it is many times seen like a separate block of Physics with no overlapping with Electromagnetics and Mechanics, when the opposite is true.
2. All coordinate systems are equal. There is no global reference coordinate system, only local coordinate systems.
When these principles are applied on the modified Galilean transformation equations, the resulting set of equations give the relativistic transformation equations. The nice thing about this is that you can do it yourself, as only college level understanding of Maths is needed and then some background in Physics.
Then General Relativity is something else. Can't wait to get to the Energy-momentum and Stress-tensors (what a name!)... and the choice of metrics to whatever suits the problem best. Boy those guys surely thought a lot hundred years ago. Sad thing that Schwarzschild died in the trenches during WWI - he, afterall, send the paper that solved Einstein's field equations for the first time during the time he actually was in the trenches.
Speaking of muddy waters in Physics, I would vote Lagrange Invariant / Optical Invariant / Etendue the most misunderstood conservation law of Physics ever.
Mika
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no, you can get the jist of it without having to integrate sets of 3d diferential equations. it's simple the faster you go the slower your time moves, so a beam of light will seem to go the same speed no mater how fast you move because even if you are going at .5c your time is running half as fast, so the remaining .5c of the beam will to you be moveing at c not .5c. that's the "not very accurate but good enough to give you the jist of how it works without haveing to make you learn ubbermath" version. it is as you would expect a lot more complex than that, because space becomes warped as well and neither the time nor space warp is a simple linear scaler of speed, but unless you want to learn advanced calculus that's as good as your going to get.
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I don't get it. If you jumped off of a spacecraft traveling at 40,000 mph, and your forward velocity was 5 mph, then your total velocity would be 40,005 mph. Why is light different?
According to every layman's physics book I've ever read, the answer is "because it is".
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Long Post Ahead!
The mathematics is actually really simple. The most complex thing to do is handle some square roots and second exponents but otherwise it's just dividing, multiplying, adding and substracting... you don't even need to use calculus (or differential mathematics, whatever you want to call it), basic algebra will do.
Anyway, as it was asked, the easiest way to derive equations for time dilation and Fitzgerald-Lorenz-contraction is as follows. I think showing how these two are derived is actually more informative in this context, since Lorenz-transformations actually are only useful if you want to know what co-ordinates a certain known point in space and time has in another, moving co-ordinate system. Anyway... Gunnery control, charge photon beam cannons, commence plasma core insertion! Let us begin.
We have a ship with a mirror fixed to it's side some distance from the ship itself, so that it will reflect photons emitted from the ship back towards the ship. The ship travels at, let's say, velocity of v (arbitrary value, assign what you want to it) in relation to an observer. As it passes an arbitrary point (we'll call it A), the ship emits a photon perpendicularly to it's direction of velocity, ie. directly towards the mirror.
In the ship's reference frame, the photon simply travels to the mirror, reflects back and is observed back in the ship.
However, in the reference frame of an observer, the photon will move substantially more - this is a grossly exaggerated drawing and in fact the ship here would exceed the speed of light, but this will do for now. Observe:
(http://img120.imageshack.us/img120/7154/relativeth4.gif)
On the upper level, there's how the situation appears to the ship itself, and on the lower level it shows how it looks like to the observer.
Note how there's two right-angled triangles there in the image? Let's concentrate on the first one of them - the one which has it's sides marked by points A, B and the point where the photon hits the mirror.
Now, the distance between B and the hit point is the distance the photon has travelled in ship's co-ordinates. Let's mark this length with d'.
On the other hand, in the observer's reference frame the photon has moved from point A to the mirror hitpoint. Since this is also the distance that the photon has traveled (in observer's co-ordinates), we'll mark this length as d without the '-mark. For convenience, we'll mark everything that happens in ship's reference frame with that mark and everything that happens in observer's frame without it.
Because we can assume that speed of light must be same for both observers - those inside the ship and the one outside, static in this case - we can form two simple equations. Since velocity is the distance divided by the time it took to travel that distance,
c = d / t and c = d'/t'
and subsequently,
d = c t
d' = c t'.
In these equations, t is again the time that passes for the observer, and t' is the time that passes in the ship. Since c must be constant for both, these must be different. Now we just need to determine the difference between d and d', and we can determine the difference between t and t'...
At this point, we get back to the right-angled triangle. We now know the lengths of two edges - one is d and the other is d'. As it stands, we also do know the length of the third side, since we know the ship's velocity v. This third side of the triangle we will mark as dx, since that's convenient and we can say that the ship is moving along X axis of the observer's co-ordinates.
Now then... in observer's co-ordinates, the distance the ship moves between points A and B is obviously
dx = v t
But (this is important!) since the time in ship is different, they will measure the distance between A and B as
dx' = v t'. We'll get back to this later, but for now we need to first define the actual difference between t and t'.
This goes as follows. We now have all three sides of the triangle in our knowledge, in observer's reference frame.
side 1 = d = c t
side 2 = d' = c t'
side 3 = dx = v t
and from the Pythagoran theorem we can deduce that
d = Sqrt ( d'² + dx² )
which we can now solve by inserting the above lengths into this equation:
(c t) = Sqrt ( [c t']² + [v t]² ) || (...)²
(c t)² = (c t')² + (v t)²
c² t² = c² t'² + v² t²
c² t'² = c² t² - v² t²
c² t'² = (c² - v²) t²
t'² = (c² - v²) / c² * t² Sqrt (...)
t' = Sqrt(c² - v²) / c * t
t' = Sqrt( 1 - v²/ c² ) * t
...and there's the equation for time dilation.
Now, back to the distance part - this defines the Fitzgerald-Lorenz-contraction of the axis aligned to the direction of velocity. We know that in the observer's reference frame, the ship moves the distance
dx = v t.
But since for the ship the time passed is different, the same distance will be measured differently by the ship crew. Specifically,
dx' = v t'.
Now, to define the difference between perceived distances, we simply insert the equation of time dilation to the latter one. Like this:
dx' = v Sqrt( 1 - v²/ c² ) * t
We can write this as
dx' = Sqrt( 1 - v²/ c² ) * v t
and since dx = v t, we can insert it into the equation:
dx' = Sqrt( 1 - v²/ c² ) * dx
And there we got the equation for Fizgerald-Lorenz contraction.
In fact, the term Sqrt( 1 - v²/ c² ) is often marked with the greek letter gamma for convenience, since it pops up all the time in calculatiosn that take relativity into account properly. It allows such easy markings as
t' = γ t and
x' = γ x.
Lorenz transformations are actually a way to bind co-ordinate systems with a relative velocity to each other, so that you can insert an XYZT co-ordinate values into the transformation equations and out comes X'Y'Z'T' values for another co-ordinate system, which is moving in relation to the other. They are a bit different from these ones, but basically once you get the idea clear for time dilation and Fitzgerald-Lorenz-contraction, you should have no problem with them. Basically, you first have two co-ordinates with their origos aligned, and the other origo is moving along the other one's X axis at velocity v. With Lorenz co-ordinate transformations you can simply transform one system's co-ordinates into another systems co-ordinates, very much similar to Galilei-transformations allow you to do with objects moving at subrelativistic speeds.
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*applauds* :)
It's funny seeing all of this here, as I was working with special relativity in the final portion of my 600-level E&M II class over the last few weeks of the semester. I did get a bit lost when we started moving into all sorts of wonderfully horrific tensor transformations (Einstein's summation notation may be tidy, but it hides one hell of a long slog of matrix math), but it was amazing to see in the end how Maxwell's equations, energy, momentum, space, and time all boiled down into one neat package. I think the most illuminating 50 minutes of my college experience thus far came when my professor explained an alternate way of looking at the mechanics of special relativity via Euclidean spacetime (it's an artificial construct that's similar to Minkowski spacetime, but with a sign reversal on the time coordinate). All of the usual mental puzzles of special relativity become brilliantly clear when looking at motion in this light. "Paradoxes" like length contraction, time dilation, the "twins" problem...it can all be drawn out in a simple manner as the difference between the slopes of lines. I came out of that lecture almost in awe, and I felt like I'd understood more by being there than I had after taking an entire 300-level course on modern physics. :p
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Sorry to spoil your fun, but then the reality kicks in and some graduated person tells you that Relativity has very limited number of applications in normal Physics, unless you happen to work with something that travels in Space. When you look at it, classical electrodynamics hold their own quite nicely as even Maxwell Equations are an overkill for most of the time. FDTD modelling uses Maxwell Equations as a basis, but most of circuitry stuff has been derived from (or even before!) Maxwell Equations long time ago and is sufficient for electrical engineering. And I'm not even starting about Optics here, suffice to say that I work with photons but I don't need to use relativistic equations at all.
Redshift and blue shift are probably the most common relativistic phenomena, along with exact synchronization problems where the signal speed has to be taken account.
Ahem, maybe I should stop before I kill the interest totally. Wait I already did that. Tomorrow I'll write something about the history before Relativity was introduced, I found that it helped me quite a lot to understand when, how and why relativity became the official truth. Maybe someone else finds it interesting here.
Mika
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Redshift and blue shift are probably the most common relativistic phenomena, along with exact synchronization problems where the signal speed has to be taken account.
Well yeah, as far as special relativity is concerned... General relativity then again actually has to be taken into consideration in, for example, precise timing in different gravity fields... like, say, satellite location systems like GPS. If the difference in time passage would not be taken into account, those systems would get serious issues with accumulating errors.
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The speed of light is relative...depending on the medium it's traveling through.
People have managed to reduce it to a speed you could outrun on a bicycle. So there.
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yes light can be slowed down, but there are atomic processes involved. it takes light in the sun thousands of years to reach the surface. but thats because the photon has to be tossed from atom to atom on the way out, shifting energystates along the way, exciting the atom and causing it to want to shed off another photon. im not exactly how it works so i may be completely wrong about how this all works. anyway whatever processes theese photons go through, it will resume going the speed of light once it hits mostly empty space. anyway its not light thats relative its time. people seem to get confused about that.
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The speed of light is relative...depending on the medium it's traveling through.
People have managed to reduce it to a speed you could outrun on a bicycle. So there.
Yeah, that's why we're been talking about the speed of light in a vacuum... and a word of advice - taking the phase velocity of light in medium into discussion is only going to make your few remaining hair more pale than the last rider of Apocalypse.
Because, you know, in medium light becomes a rather complex thing. It's not just photons any more - it's a combination of mechanical vibrations of charged particles in the medium and photons between them, and the average speed of the combination defines the velocity of the wave formation, which defines the phase velocity of the light in the transparent medium. The propagation of mehcanical vibrations (or oscillations) forms virtual particles such as phonons and excitons, which couple with photons to form a combinatory particle called polariton, which, due to it's partially material form, has a small effective mass and therefore cannot travel at c. Basically, the higher the energy of the photon, the more virtual mass it gains when propagating through transparent matter, and the more it's velocity slows... which causes dispersion of colours in simple lenses and prisms. Individual photons on the other hand always do travel at c, though.
Then again, there are some pretty wild stuff done with light and quantum physical experiments such as using the Bose-Einstein condensate as medium. That stuff has some *interesting* characteristics; first of which is the mentioned very low phase velocity of light. Also, apparently it's state of transparency can be altered by changing the energy level of the cloud with a laser - and the knowledge of the photons happening to be inside the cloud at the moment is stored into the cloud. When the modifier laser is released, the light that had been propagating through the cloud when the modifier laser was activated, will simply start from where it left off, with same properties...
Can you say "optical transistor"? ;7
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Hmm, HT, what about their supposed making light travel faster than c? I heard they did that, too, I think it was before they slowed it below c...
EDIT:
www.scienceblog.com/light.html
www.newscientist.com/article.ns?id=dn2796
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IIRC that was also about the phase velocity, which can exceed the speed of light c, but it cannot transmit information, so causality is unbroken... But I don't remember the details.
In other words, c as a constant means that with electromagnetic radiation in vacuum, signal velocity is always exactly c.
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wait how can it not transmit information? if we had two light year long columns of the (sodium or) what ever it was they used to make light move faster and at the end of each column was a mirror, if you shown a light into both of them and had a detector set up to read the return beam wouldn't one go off befor the other?
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what makes light move faster? like a meta-material or somthing? I am lost...
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I'll leave Herra to explain the details because:
1) He enjoys it.
& 2) He's better at it than I am.
However, the salient point is that phase velocity /= velocity of propagation or "group velocity."
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One more time: the greatest signal speed by which information can be transmitted is very close to c, if not c. For this reason, it is assumed that the greatest signal speed is the speed of light in vacuum. If, for some reason someone finds out a signal that goes faster than light in vacuum, the greatest signal speed will become that. But according to the current understanding, if this was to happen, the difference would be very small so it is quite safe to say the maximal achievable speed is c.
In a wave packet what represents an optical pulse (pulse is actually open to interpretation), there are gazillions of different propagating monochromatic waves included. Because each of these waves have always existed and will always exist (by definition of the monochromaticity), the waves add-up destructively in most space, but because we are talking about a pulse, there is also a single location in spacetime where the add-up is constructive, and a peak is formed exactly there.
As you move the observation aperture along the pulse peak, you will see that there are fluctuations propagating in the pulse, and the propagation speed of these fluctuations might exceed c. However, you are only observing the sum of the monochromatic waves at each moment of time. This is perfectly reasonable explanation for me, and according to my understanding it is also the officially correct one. But unfortunately I cannot write it any way better.
But Fourier Maths is great and the above is based on my interpretation on that, so don't skip your lectures there as you might never know where you meet it again (hint: in surprisingly many places)! And quite surprisingly, its justification is that it simply works (for a physicist at least). Then model the same thing with the particle model... and talk about X-rays with the index of refraction below you-know-what. Some wise guy once said that if lambda gets below UV, congratulations, you (are screwed and) have chosen exactly the wrong career ;)
The quantum mechanical teleportation stuff is something beyond me and I cannot comment on those experiments where the two particles supposedly always turn to face each other or something.
By the way Doc, feel free to abrupt this if I'm saying something totally incorrect/incoherent so that I apply self-censoring on it before too many people see it. I usually think more of MTFs and spot sizes than wavepackets.
I digged up some old material regarding relativity, the whole problem in the beginning of 1900's was the aether which got some unphysical properties, as it must have been everywhere and extremely heavy and on the same time have no mass at all. Einstein found a problem by examining Maxwell's equations (I don't bother to repeat it here) and concluded that the speed of light must be c in free space in order to have any sense in anywhere. At that time he was unaware of the experiments conducted by Michelson and Morley, however nowadays the above mentioned experiment is mentioned first as it is an indisputable measurement result and makes sense as such.
So special relativity rests on two assumptions:
1. Speed of light in free space is a constant c.
2. All coordinate systems are equal.
And then all we need is a magnificant idea of mixing time and space together! Einstein himself wrote that the idea dawned to him when he was discussing about the difficulties in Electromagnetic theory with his friend Michele Besso. He only mentioned that that day was specially beautiful spring day for him, he never mentioned anything else about the origins of the idea.
The normal Galilean transformation equations (that you should use in normal life) between coordinate systems along the movement of one axis are:
x' = x-vt
t' = t
Now, mixing time and space together gives:
x' = A_1*x+B_1*t
t' = A_2*t+B_2*x
Here A1, B1, A2 and B2 are the unknown constants to be solved.
Now working with the two basic assumptions of special relativity using two coordinate systems moving along each other at speed v and taking notice that the speed of light should be c when viewed from another coordinate system, and noticing the invariance of light cone in any coordinate system, the transformation equations become:
x ' = (x - vt) / sqrt(1 - v^2/c^2)
t' = (t - vx/c^2) / sqrt( 1 - v^2/c^2)
The details can be found in-depth Physics book and so I skip them :D These are called Lorentz transformation equations, and by using these the time dilatation and the length contraction can be derived in another way.
If anyone is interested, here is a nice site for visualisation of relativistic Optics:
http://www.anu.edu.au/physics/Searle/
Please explain yourself the disformations in the train when it is passing by you.
Mika
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If anyone is interested, here is a nice site for visualisation of relativistic Optics:
http://www.anu.edu.au/physics/Searle/
http://www.anu.edu.au/Physics/Savage/RTR/index.html <-- Real Time Relativity
Get the proggy linked to there; it's cool!
Also, this site was linked to:
http://www.anu.edu.au/Physics/Savage/TEE/site/tee/home.html
Thx for the link(s), Mika! :)
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Sssh, keep it quiet, otherwise they will put it in Freespace SCP.
Mika
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and what would be wrong with that?
muhahahaha!
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Err, the ships in FS don't use FTL... they use sort of a wormhole, you are not actually going FTL, you are traveling through another dimension or somesuch. See here:
(http://img155.imageshack.us/img155/9753/subspacehk9.th.jpg) (http://img155.imageshack.us/my.php?image=subspacehk9.jpg)
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just because freespace has wormholes does not mean that super real physics cant still be used :D
i am kidding of course this engine ouldnt handle it unless some coders have an odd and spontainious desire to add more realism.
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Hmmm, I know what a worm hole is. Or that I suspect that I have an inkling about what it is. The comment was actually related to the sudden changes it the gameplay, which would definately make things a lot more interesting. The sad thing would be that the people who would play it in the internet might complain a lot of things they don't understand. But on the other hand, we would have some huge ships going on, say something like one lightsecond long ship might be a small cruiser. When you are flying at the speed of 0.3 c you might pass it in three seconds.
Your seconds. Now that I thought about it, it is the cruiser that will measure that you'll pass it in three seconds.
To totally mess you up, find problems sets at:
http://cc.oulu.fi/~pmu/jsuht/kurssi07.html
Scroll at the bottom of the page and you can find problem sets from there in English. I always considered them quite humorous, Lightspeeding Ladas and Klingon cruisers with bad aim, galatic welcome is to shoot a deadly beam in front of the incoming spaceship etc etc.
Here is an actual question from a Special Relativity calculations from the University days. I first time saaw it in the department of Physics, University of Oulu (translation is mine):
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Han Solo decides to park his Millenium Falcon (length 30 m, speed 0.8 c) in the garage (length 20 m). Chewbacca is standing next to the door.
a) How long is the Millenium Falcon according to Chewbacca?
b) When Falcon is fully in hangar, Chewbacca closes the door. How long does it take that
Chewbacca realises for his terror that Millenium Falcon crashes to the backside of the hangar?
c) How long is the hangar according to Han Solo? How long is the Millenium Falcon accoding to his observations? [Here we suppose that Solo had misunderstood the Relativity and thought that the hangar only looks shorter.]
d) Is Falcon fully in the hangar when the frontal part of the ship hits the back of the hangar? The cockpit is located 10 m behind the nose of the Falcon.
e) After the crash, Falcon is at rest with respect to the hangar. Chewie says that the 30 m long Falcon was fully in the 20 m long hangar before he closed the door and before the Falcon crashed. How is this possible? According to Han, the crash happened before the door was closed, so the door should not be closed at all! So is the door open or not? Is the Falcon in the hangar or not?
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A small problem for you to think about.
So you all can suppose where this would lead to with n00bs. Consider the following:
"I bloody well shot it before the beam was coming in!"
"How on earth can the mission last for several thousands of years when I was only flying like 5 minutes?!"
"Why everything is so bright in front of the space craft and I cannot see anything from the behind?"
"When the capital ship is accelerating at the jump node and I'm behind it, I only see it decreasing in size and turning more and more red. When I'm in front of it, it's actually turning blue before I die in the crash? Why is that?"
"Why is the capital ship looking twisted and stretched when I fly towards it?"
"Coming next, the Relative Murder Mysteries: who shot the sheriff and when? Stay tuned!"
Need I say more?
Mika
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And also:
"But officer, I can swear that the light was green for me! My flight sensors can confirm that!" :lol:
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That can really be some cool stuff, though. Jumping your attack force in even before the enemy sees it depart, running into a laser blast that you didn't even see, the different mindset you have to have while flying your ship at the speed of light... it could work if people were willing to play a true space simulator and accept that extra level of complexity.
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And then adding accelerations in the game would result in the model that must use General Relativity. Good luck getting that working in real time... not that I would mind if someone could ever pull that one off. That would be one helluva interesting game. Because there is a time delay of where the enemy fighter is in every moment since the light reflected by enemy is travelling towards you, there would be some interesting problems to predict enemies movements also. And when trying to shoot it down, there would be a need to shoot where it doesn't apper to be going, ie. the projectiles and the fighter would be on a course where they would not hit. And then try to make the AI to predict the path. I can already imagine the outcry if that game were ever to materialize.
Mika
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well err....here is another one for you math phisicks whatecer geniouses is warping as in star trek warping posible cuz from what I have seen on a documentary some scientists are treyng to prove it can be done. They said that this way you could travel at the speed of light and faster much faster without all the time passing stuff and infinite mass etc.
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That can really be some cool stuff, though. Jumping your attack force in even before the enemy sees it depart, running into a laser blast that you didn't even see, the different mindset you have to have while flying your ship at the speed of light... it could work if people were willing to play a true space simulator and accept that extra level of complexity.
No, it would suck. It would be totally awesome, but it would also suck. NAFAL ships would arrive at their destinations at almost the speed of light, but systems are light-years apart, so sending an attack force would take years from your end. In-system combat, that's a different matter. The enemy would have at most a couple of minutes' warning, if they saw you warming up your NAFAL drive, and none if they didn't. Combat at relativistic speeds would be impossible for a human. Things, obviously, move way too fast for someone to keep up, not to mention interpret all the distorted images coming their way.
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well err....here is another one for you math phisicks whatecer geniouses is warping as in star trek warping posible cuz from what I have seen on a documentary some scientists are treyng to prove it can be done. They said that this way you could travel at the speed of light and faster much faster without all the time passing stuff and infinite mass etc.
Oh, Jesus Christ.
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Somehow I have a picture of a Trek convention being sort of like the Roman senate in Mel Brook's History of the World Part I:
"**** CAUSALITY!"
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trek conventions are just an excuse for grown men to raid their girlfriends closed to dress up like some gay looking alien and associate with people with the same mental illness.
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Considering that realistic Newtonian Physics model in a space simulator would be too difficult for most of the people i.e. "Why is my ship moving to a direction that I'm not facing?", a Freespace with a General Relativity engine might be far too much for anyone to understand.
So to continue to have fun:
Assuming a warp engine that will accelerate the spacecraft from 0 to 0.1c using a constant 9g acceleration would need about 4 days to achieve that speed - I calculated this with Newtonian stuff; can't be bothered with Relativistic stuff now that I have conveniently forgotten it. But bear in mind that 0.1 c is considered the limit of accuracy for Newtonian Physics. So it might be doable after all, if anyone doesn't find the thought of having to endure 9 g's for four days distrubing. And now, who would? But at that time, the spacecraft would have travelled some 5*10^12 meters.
Not that you could actually turn the ship in any time soon. The turn radius would probably be best described with terms like "huge", "colossal" and "massive". Try and detect those asteroids at Relativistic speeds, suckers. Not that avoiding them would help also.
About warping, I'll believe it when I actually see it happen.
Mika
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hey wait i never said i was a believer in warp as in star trek I just hope sometime in the future we can overcome these kind of barrier with ease. Also I never said it can be proved yet ! But instead i said there were some scientists tryng to prove it can be done. At least on paper. Bu I believe they also said it would reqquire a masive amount of energy much more then we could ever produce acording to some of they calculations. Damn why cant I remember theyr names. It was on a documentary I believ either on Discovery Science or Some other channel like that.
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Popular Science had a mention that NASA was working on a Tractor Beam. ;)
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Popular Science had a mention that NASA was working on a Tractor Beam. ;)
Popular Science also said NASA was working on a way to make your sig smaller, but they ended up moving on to faster-than-light travel citing it as "a less monumental task".
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Imagine how large it would be if BB Tags were not counted towards your char limit. >.> *looks at Goob*.