Tracing light, tracing history, tracing truth ?

So i just completed my first raytracer in C++.

In computer graphics, ray tracing is a technique for generating an image by tracing the path of light through pixels in an image plane and simulating the effects of its encounters with virtual objects. The technique is capable of producing a very high degree of visual realism, usually higher than that of typical scanline rendering methods, but at a greater computational cost. This makes ray tracing best suited for applications where the image can be rendered slowly ahead of time, such as in still images and film and television visual effects, and more poorly suited for real-time applications like video games where speed is critical. Ray tracing is capable of simulating a wide variety of optical effects, such as reflection and refraction, scattering, and dispersion phenomena (such as chromatic aberration).

source

By mathematics to represent a digital image of projected objects.

Here is my first render, 3 reflective spheres, shadows and reflections calculated at each pixel.


Full HD resolution

It looks stunning imho, but somehow too perfect. And so up the current season of the year, in some parts of the world.

The "light" is calculated in perfect conditions, which makes it look plastic-perfect. You could distort the image with various particle, smoke or temperature effects, but it will be very costly in processor work. As we have seen on the latest graphics cards. Some with 8 cores, and severely many registers. All sharing a cache of memory to speed up rendering, are getting very close to real life looking photos.

Back in the Commodore 64, Amiga, Amstrad days, this was almost impossible to achieve in real-time, as of today. Tricks and extreme insight in vision and how the human brain is absorbing these data, have helped to make several mathematical shortcuts, so it was possible to render a fairly life-like picture, in the smallest amount of time. There by rendering more images per second than the eye can distinguish.

This means we do know how the basics of stuff works, and we can by mathematics calculate our way back in time to give us an image of how stuff looked like back then. Like the theory of the Big Bang and so. Actually, if you took a spaceship and moved it farther away from earth, than the speed of light, you would be able to see time go backwards, coz of the speed, or would it be black, since the light cannot reach your spaceship with that speed? What if you traveled with the twice amount of lightspeed in 2 years, then stopped, and began recording light. Sending this data back would give you an image of our earth from 2 years ago... but damn, the signal will take 2 years to reach us.
So... can this "simple math" be used to expose some of the worlds most controversial hoaxes, conspiracies? Could you apply the mathematics to for example, prove the moon landings, or disproving them?

Like some tried to mathematically explain how Building 7 fell on 9/11, but had to use special algorithms and formulas to make the entire "quibble" work out as assumed, then later on refused to release their real calculations on how they derived at their conclusion. Fueling the 9/11 conspiracy even more.

So we are left with the question - is science the answer that can tell us the real truth, or should we rely on the experts undefined explanation ?

Extraordinary people have managed to put the worst atrocities in history to some mystic physic behavior, time and time again. Spinning the facts, manipulating the numbers, and make up 'new' facts on the fly - and somehow we still buy it? Given the abundance of information we got in form of the internet itself...

Maybe "we" should help the experts...

If mathematics cannot provide us with a definite answer, what else can ? And when mathematics proves something absolute, who will believe it ?

Btw, the renderer mentioned can be found online
www.youtube.com...
- do your own experiments

I hear that the mathematics used in optics is brutal. This thread just proved that. So, what program did you use to make the image?

**Found render!

a reply to: gorsestar

Brutal, yeah... it is in the eye of the beholder

a reply to: kloejen

Mathematics could work in a strictly deterministic reality...

but we do not live in such a place. In this reality, math (calculating values) only works byway of approximation. That is, values, in this place, are only estimations, and no value is finite. True story.

Another true story... did you know there is an equation that proves that not everything can be mathematically solved? Read up on Gödel's incompleteness theorems.

Look at it like this: everything changes because of changing forces. To calculate everything, you need something to be static, but nothing seems to be static. And even if we are capable of understanding all of the forces present today, the very forces that made today's forces could be forces that are no longer existant and without remnants. Think about that: what if the force that made gravity no longer exists? What if it went the way of the dinosaur, and evolved into a bird? Crazy to think about, huh? That we cannot ever know.

Of course we cannot teach our kids this because they wouldn't listen to our rules then. They would become hedonist, and society would self-destruct.

Mind you, I made the above comments absent of any spirituality. If I posted with spirituality, then the post would be much different, but I thought I'd humor you.

a reply to: Bleeeeep

Thanks for the reply & info

Yea i know that everything cannot be computed by mathematics, simply because we don't know everything. Thank "some higher entity" for that.

There is also the Heisenberg Uncertainty principle.
wiki

The lack of mathematical understanding of black holes, are one of the thorns in the eye of current knowledge.

Actually my example of raytracing, is only an approximation, since you cannot ever know how real light reflects on a curved surface, since you need PI to calculate it, and PI is an irrational number. - Well played "higher entity"

Btw, hope you have seen the movie "Hitchhikers guide to the galaxy"? The answer to everything is 42!
Actually if you used PI with 42 digits, the error at the end of the universe, which apparently is about 13.7 billion lightyears away, would only be 1 meter

Ohh and then there are the understanding of women... a never ending encyclopedia

But getting back to the issue. With all the accumulated knowledge, videos and pictures of today. Tons of data-gathering from all over the planet. I'm sure in the future higher levels of mathematics will prove and disprove these times mysteries fully. 9/11, JFK, Moonlandings... Question is, will we be around that long? Or will it matter when we realize the absolute truth of these events in a hundred years?

a reply to: kloejen

Actually my example of raytracing, is only an approximation, since you cannot ever know how real light reflects on a curved surface, since you need PI to calculate it, and PI is an irrational number.

Well in reality there is no such thing as a "curved surface", everything is quantized at the fundamental particle level. Everything is made out of elementary particles, and when a photon hits a surface it will generally be absorbed by one of the electrons in one of the atoms, then after a short period of time the electron will eject the photon back out at some random angle. The photon can even bounce around under the surface of the material before coming back out, a phenomena called subsurface scattering.

Most objects do not have perfect reflective surfaces, they tend to be some what translucent and some materials like glass are completely translucent. However some materials like dense metals do actually have their atoms aligned in such a way that it prevents the photon from penetrating the surface of the metal because the photons get reflected by the EM field set up by the atoms. I guess that is why the backing on glass mirrors is often coated with silver or aluminum.

EDIT: it's also worth noting that the reason we see different colors reflected by different materials is because when the photon get absorbed by the electron, the electron wont always emit the same type of photon or even the same number of photons, it will eject photons which correspond to the atomic orbitals of the atoms which the material is made out of. The reason we know what the sun is made of is because we can look at the spectrum of photons emitted by it and then determine what type of atoms emit those types of photons.

a reply to: ChaoticOrder

Nice insight!

You are maybe right that there are no such thing as "curved surfaces", since we dont know the nature of particles at that level, as you point out. And for that we have no clue what a photon is really. First of all if it travels at the speed of light it would have no mass? So why is it that photons have an impact on nature - heating things up, make them illuminate? Photons/phantoms, are the ones who shed light in our universe, thou we cannot define them.

The interaction between the collision of the photon and the particular particle, makes it shake, thereby heating it up.

It takes a photon about 100.000 years to penetrate the sun, and when it leaves the surface eventually, it will travel forever in the direction it escaped, dying upon impact. Unless it was lucky and hit a reflective surface. Or maybe even got twisted by several black holes on the trip, curving the photon. So maybe the universe is a mirrored perspective of itself in trillions of different angles?

Of course that cannot be true either.

a reply to: kloejen

And for that we have no clue what a photon is really. First of all if it travels at the speed of light it would have no mass? So why is it that photons have an impact on nature - heating things up, make them illuminate? Photons/phantoms, are the ones who shed light in our universe, thou we cannot define them.

I wouldn't say we have no idea what photons are, we have a pretty good idea actually, photons are quantized wave packets of electromagnetic energy which propagate through the medium of space-time. The reason they have energy but no mass is because they are moving at the speed of light and therefore have an energy associated with their momentum. If you increase the velocity of any normal object it will actually gain mass and get heavier because you are adding energy to it and as we know E=mc^2. The math says that in order to reach the speed of light the mass of the object would have to become infinite, which is why anything with mass cannot reach the speed of light.

The photon is kind of tricky because it gets around this problem by having no mass in the first place. As you slow down a photon it will lose energy, and if you made the photon come to a complete stop it would have absolutely no energy, so the only energy a photon has is the energy due to it's velocity. So the photon can only exist while it's moving, but we also know that energy cannot be destroyed or created and that all forms of energy can be converted into any other type of energy, and this is precisely why photons have an impact on nature. If you focus a high enough energy laser on a small enough point in space you can actually create particles which have a mass out of the photons.

It takes a photon about 100.000 years to penetrate the sun, and when it leaves the surface eventually, it will travel forever in the direction it escaped, dying upon impact.

Well like I said energy is never destroyed so it never really dies, it may be absorbed by an electron and then emitted by the material as heat energy (which btw is just photons in the Infrared spectrum). The photon doesn't really exist after it has been absorbed by the electron but the energy the photon held is now contained in the electron until the electron decides it wants to let go of that extra energy by emitting one or more photons and move back down to a lower energy state.

a reply to: ChaoticOrder

Thanks for your contribution. Your Answers make me question even more.
So, photons exist as a wave of electromagnetism, or is it a wave of particles ? That imho, is the fundamental question.

If you follow the raytracer build in the videos, you will probably notice that PI is NEVER used..

Here is an animation just for the fun of it

a reply to: kloejen

So, photons exist as a wave of electromagnetism, or is it a wave of particles ? That imho, is the fundamental question.

The best way to describe photons is as a "wave packet". You might think of it like a ripple traveling through a rope. It's clearly a wave but it travels through the rope like a packet of energy. You can isolate the ripple from the rest of the rope and call it the "wave packet". In the case of the photon, space-time is the rope and the photon is the ripple, well maybe not exactly but it's a good enough analogy. The photon wave packets are so tiny that you can essentially just think of them like little particles and it will work most of the time. The weirder thing is that all particles are really wave packets, meaning you can also think of any elementary particle as a wave or as a particle. That is why the double slit experiment will also work when you do it using electrons. That is what they call particle-wave duality.

If you follow the raytracer build in the videos, you will probably notice that PI is NEVER used..

I didn't actually notice that link at the end of your opening post until you mentioned it just then. It does seem like a very interesting project, it's actually something I've been wanting to do for a while so I probably will watch all the videos. Thanks for the share.

EDIT: btw here is a lecture you may find interesting:

Have you noticed the double-slit experiment, which magnifies the enigma of light? This puzzle is still on

Here it is explained


Therefore you cannot say that light is a "packet" of particles. Yes you can, in some circumstances, but it won't work with other instances. Therefore the knowledge of light is still incomplete...

a reply to: kloejen

Therefore you cannot say that light is a "packet" of particles.

I didn't say that light is a packet of particles, I said that each photon is a wave packet, a packet containing a quantized wave with a frequency which determines the energy of the photon. A wave is spread out over space and therefore can travel through both slits at the same time. It is experiments like the double slit experiment where you cannot think of each photon as a single particle. In fact you cannot think of any elementary particle as a single particle with a specific location in space. All matter will exhibit particle-wave duality under the right conditions.

EDIT: here's a typical wave packet diagram:

Figure 02a shows pictorially the wave packet as a function of x (centering around xo) and the weighting function (centering around ko). A measurement on the wave packet will detect the particle at certain value of k. This is the Copenhagen Interpretation, which asserts that the wave function collapses to a single state in response to the measurement.

Interesting. So light is not a particle, but in your thinking a wave of ... what ?
Electromagnetism? Then it has to be particles? hmm... Like the way you present things.
I'm really no expert on the matter, no pun intended, but i love these thought experiments.

Ill get back to this... i need to think - thanks for the inspiration

If we had a powerful enough telescope and knew exactly where to look we would be able so see the Earth's past. Globular clusters and black holes bend light around them, light from the past. We should be able to see events unfold on Earth in the past using such techniques, if only we had the tech.

Also, kloejen, you mention PI isn't used in those raytracing examples. Really? No trigonometry is used at all?

originally posted by: kloejen
Interesting. So light is not a particle, but in your thinking a wave of ... what ?
Electromagnetism? Then it has to be particles?

Yes photons are thought to be an electromagnetic wave packet. The electric and magnetic fields are said to work together in a complicated way which allows the EM wave to propagate through the empty vacuum of space. The electric and magnetic aspects are both fields so I'm not sure why you said it has to be particles. The reason it seems confusing is because the photon can behave like a particle or a wave depending on the circumstances. The answer is that a photon, and any other elementary particle, can act like a wave or a particle depending on how you interact with it, that's what particle-wave duality means.

a reply to: circlemaker

Heh. i thought about that too. So lets say we make a mega Hubble telescope and send it thousands of years away from us, in an instant. Yep - there it is a billion light years away, recording all the light from Earth. If that was possible, yeah, it would record planet earth as it stood from a billion years ago, but the light has to travel to the super-hubble. And then transferred back to earth - that would take 2 billion years - we got no further...

PI Question:
Yeah, i was amazed too. PI isn't used anywhere. The closest is the square-root of the angular light, as i understand it. He is using basic trigonometri, thats all:
Download the code here:
sourceforge.net...