Simulation of Special Relativity: Lorentz Contraction - OpenGL/GLUT

[jessyjessy4]

brilliant video

[msjessypp]

very interesting thanks

[alexasmithy]

brilliant video

[Lightspectre1]

Sweet video Copycap. Don't sweat the comments; haters gonna hate.

[EccentricInTexas]

Have you ever heard of a Mach-Lorentz thruster? There was supposedly a video about them but I have been unable to find it.

[Copycap]

@EccentricInTexas I think so. Why do you ask?

[EccentricInTexas]

@Copycap Well I don't fully understand the particulars of it how it works.  I do however understand what it would mean if it works.

[Copycap]

@EccentricInTexas I can't find any serious papers regarding that topic, and all I can find about it and related stuff is somehow "esotheric".

[EccentricInTexas]

@Copycap Yeah same here, but I am so hoping it pans out.

[Dextomus]

what sovtware did you use for this?

[Copycap]

@Dextomus Software? Well - I could've done it with Vim and g++ but I think I used the IDE Code::Blocks cause it's easier to work with.

Used Libs: mesa3d implementation of OpenGL and freeglut.

[joseftran]

That's it ??????? What a total waste of time. I could have done the same thing using Microsoft paint and just draw a few sphere's at various intervals. That would have produced the same effect. I bet those equations you use is 10 pages long ! Total waste of time......and what is this suppose to do? I've seen video games that can do this and WAY WAY MORE.

[Copycap]

@joseftran Please, why don't you do it then, draw it in paint and make a video. I'd like to see your video as video response. ;)

And no, those equations are quite simple, just relativistic acceleration and a little use of a scaling matrix. You know the point is, I programmed this with C++ and can adjust the variables as I want to try out things - much better than calculating the objects by hand and drawing the pictures manually.

[joseftran]

@Copycap Have you discovered the 3D video game yet? These days those things are in 3D and you can make a model of this sphere using 3DS max by a single click POP! a sphere appears instantly on the screen. Then you click again and go to the animation functions and you can stretch or bend or WHATEVER you can dream of. You can even turn the shpere into MICKEY MOUSE! I think you're re-inventing the wheel? Good try though.

[Copycap]

@joseftran You missed the point of this video. Did you even read the video description? I try to demonstrate physics and visualize the effect of the lorentz contraction on moved inertial frames. At the end you may just see a sphere that gets compressed here, but the scaling factors (and velocity) are all calculated in realtime by an algorithm that relies on the mathematical model of special relativity.

In a future version of the program I may be able to implement some interesting shaders.

[joseftran]

@Copycap I did but I don't understand why you had to do all that. All you needed to do was animate a sphere getting squashed in 3Ds max which would have taken you about 30 seconds. Also, you could skin the sphere and it would look awsome like the video games. Then you could post it on YouTube and explain what happens to the sphere due to lorentz contraction theory. To me that would be exactly the same and even be more awesome. Put in a few lightning effects too :)

[Copycap]

@joseftran 3Ds max is the most horrible 3D modelling tool I'd ever touched yet, imo. O_o The reason why I didn't use a modelling tool is, because I am a programmer, not a modeller. I want the computer to actually _calculate_ something interesting and show it on screen. It's just boring to stretch a stupid sphere with a modelling tool - and I could't extend it well. With my program, I could add additional effects like light aberration or doppler shift and calculate everyting in realtime.

[joseftran]

@Copycap People have known and calculated the hell out of doppler shifts and light aberration for as far as i can remember. Why do it again? Please state the purpose?

[Copycap]

@joseftran It seems you'll never catch the idea, so I'm asking you to stop commenting here.

[blackcaeser0]

@joseftran Your commentary shows very clearly that you didn't grasp the reason for this video. Since there's a very extensive explanation beneath I assume a lack of ability to understand anything behind your immediate intellectual scope - whose length may be able to prove Planck's is still too big.

[joseftran]

@blackcaeser0 Planck's constant is too big. That's why physicists never get anything right. Ask them what's down there and nobody know :P

[Copycap]

@joseftran Tell your computer that physicists never get anything right.... *rolleyes*

[joseftran]

@Copycap Ok Fine ! What's the equation of the black hole? I want to do some space traveling? Whatever you folks are doing just isn't helping here. We're using technology that's millions of years old probably. The wheel is the best we've got huh? And the best is amplifying electrons using semi's huh? Tell you the truth. All this stuff is just mediocre. Sony tried to introduce 3D vision and i get a headache after wearing those glasses. WOW !

[ariuszarim]

Its too smart for me; however, it looks cool.

[Copycap]

@SuperMagnetizer

Well I think that's right. The core of the problem is the "relativity of simultaneity". Because every observer (a 4-velocity in Minkowski Space, i.e. a vector with norm -1) has his own planes of simultanity in spacetime, they describe simultaneous events differently. Because of that arises the problem that the results of length-measurments made by two distinct observers result in two different values. It's way too complex to describe it within a YouTube chatbox. ^^

[sixstanger00]

I still don't fully understand WHY the Lorentz Contraction happens.

[Copycap]

Basically Lorentz Contraction is the result of the two basic assumption of special relativity: The relativity principle and second the constancy of the speed of light.

In newtonian physics you don't want the basic equations to change under transformation between inertial frames. For example, if you transform from system X with coordinate x to X' with coordinate x' (for example via x = x+v*t), you want newtons second axiom F=dp/dt in X not to change, so F'=dp'/dt' in X'.

[Copycap]

The result of this examination is the Galileo Transformation. But in special relativity, you want the Maxwell Equations not to change under transformations between inertial frames. These transformations modify space and time, so you can observe such effects like lorentz contraction and time dilation.

[sixstanger00]

So has this been physically observed in an experiment, or is a purely a mathematical assumption?

[Copycap]

Time dilation effects are respected by GPS satellites - without corrections the theory of relativity provides, they would send wrong data. And it was checked too with too synchronized atomic clocks: one was packed into a plane and flew around the earth, the other remained on ground. They measured a time difference between the clocks.

Lorentz contraction was also approved regarding muon-detections from outer space.

[sixstanger00]

So why does the contraction occur? Is it the mass compensating for the excessive speed?

[Copycap]

The problem is related to actual measurment. If you take a staff of 1m in X at rest (you can always say for a specific time, that you're on rest) and you measure it, you will get as result 1m. But if you stay at rest in X and move the staff with high speed (mathematically you perform a Lorentz-Boost X->X') and measure the staff in X - you will recognize, that the staff is shorter than 1m.

But if you measure the staff in the moved system X' the staff will have the length of 1m. Quite tricky. ^^

[SuperMagnetizer]

Hi sixstanger00,

Here is my understanding of the Lorentz contraction. Long ago Michelson & Morley did an experiment to measure the speed of the Earth through the "ether" (which everyone believed in back then). Their optical apparatus should have found a difference in the speed of light as the spinnning, orbiting Earth traveled through this ether. But they found no difference. So Lorentz & Fitzgerald came up with an idea & a formula: Length Contraction. See part 2.

[SuperMagnetizer]

Hi again sixstanger00 (Part 2),

If the Michelson-Morley apparatus were to physically shrink in the direction of its motion through the ether, then that would exactly explain the null results. Over the years, people abandoned the Ether, but Einstein then used the same formula to explain Length Contraction in terms of relative motions rather than motion through an Ether. Like Lorentz, Einstein believed in "real" length contractions, which led to "real" time dilations.

[SuperMagnetizer]

PART 1

Here is my understanding of the Lorentz contraction, which should be called the "Lorentz shift." Relativity factor R or "gamma" = (1 - v^2/c^2)^-1/2. This factor, which works out to 2 at 0.866c, appears to contract objects to 1/2 their proper length in the direction of travel, just as Copycap expertly shows in this video. But here's what actually happens. See part 2.

[SuperMagnetizer]

PART 2

If a 2-mile long train is doing 0.866c, either toward or away from you, and its near end is 2 miles from you, its far end will be at 4 miles. But because of its speed, its far end will be relativistically shifted from 4 miles to 2 miles, and its near end will be shifted from 2 miles to 1 mile. Now the 2 ends of the train are 1 mile apart instead of 2. So it's an optical contraction as a result of an optical shift. Einstein wrote this was a real contraction, and ignored the shift.

[Copycap]

@SuperMagnetizer

Well I think that's right. The core of the problem is the "relativity of simultaneity". Because every observer (a 4-velocity in Minkowski Space, i.e. a vector with norm -1) has his own planes of simultanity in spacetime, they describe simultaneous events differently. Because of that arises the problem that the results of length-measurments made by two distinct observers result in two different values. It's way too complex to describe it within a YouTube chatbox. ^^

[SuperMagnetizer]

Thanks Copycap,

By the way, great job on the video. I have been working (using only very simple math and a lot of common sense) on the problem of time dilation / space contraction / relativity of simultaneity. And I have concluded that time dilation doesn't happen. It only seems to occur by ignoring the Lorentz shift -- a purely optical effect.