Sensei

Right, you are free to measure any distence you want in any units of length you want. Nothing will fundamentally depend on the units you use. However, some units are more suitied to some measurements than others. Sensiable units for measuring the distence between two cities include miles or kilometres. The numerical answer would look horrible in cm or inches, but you are free to do so. The same for measuring it in light-years, astronomical units, parsecs and so on. You could quote the distence between cities in those units, but it would seem rather unnatural.

 

The same is true of electric charge. You have coulombs, ampere-hours, often just units of the fundamental charge are used, so that is e, or you could use units of the Planck charge. None of these change the fundamental physics, they just give sensiable units of charge for different situations.

That's true only if unit is not quantized at some level, and might be dividable infinitely.

If you have quantized electric charge unit, you can have charges: 0, 1*e, 2*e, 3*e, 103834773*e, etc.etc, but never fraction of e. If you have fraction, you violated quantization..

Which obviously does Planck charge, which is 11.706 * e...

Computer analogy: you cannot have half of bit (which is 0 or 1, mutually exclusive, values)..

Then years later, well after leaving college and going on to other things, I was reading about economics. The math was again way over my head BUT it was using the same or similar mathematical things, like tensors, matrixes, etc. I remember it being quite an emotional shock. How could it be that the "creator's language" (and I use that word figuratively) can also be used for such mundane and pedestrian things as cash flow, net cash value, GDP etc.

Good that you didn't see any modern computer game source code..

They do more vector/matrix/multiplications/transformations in one second than the all physists did in the whole history of science..

If you have 1 million triangles @ 60 fps, object to world transformation will be 180 million multiplications of 3d vector by matrix 4x4. There is needed to multiply it by 2, because each vertex must be projected from 3d world coordinate space to 2d screen coordinate space. And you end up with 360 million vector * matrix calcs per second. These calcs are proportional to quantity of triangles (complexity of geometry).

And that's before any texturing and lighting. For 1920x1080 Full HD resolution it's 2 Mega pixels @ 60 fps = 124 million pixels to process, with 4x anti-aliasing it's 0.5 billions/s.

OpenGL supports up to 8 lights (it can be extended by using pixel-shaders manually), so it's 8 dot products between vector and vector. That gives ~4 billion dot products per second.

Math is just a way to simulate thing that we want to simulate, whatever it is.

Gravitational waves were not confirmed.

Device LIGO used for years to try to detect them was deconstructed.

 

[cut crap]

 

now be off with you im off for a beer

I think you have drunk too much already..

Radioactive decay, ionization of molecules, causing inpredicatable chemical reactions are indeed one way to speed up evolution. Especially for bacteries and viruses. But for multi-cells organisms, in the most of times it ends up in creating dead cells and cancers. That's why it takes so long time to evolve one species to another.

If random change in genes allow better surviving, gene is spreaded to the next generation. If change in genes disallow hiding (f.e. color change of skin which make easier to be seen by predators), or disallow normal living (additional unwanted leg etc.), living organism is consumed or dies other way, without spreading its useless change in genes for future generation.

f.e. if you would release 100 hundreds white mouses/pigeons in the forest, they wont last long. The only survivers will be their childs that changed color to gray or other hard to be seen by predators. White branch of evolution will disappear.

"Gravity is an exceptionally weak force on the scale of atoms".

Any equation which uses inverse-square law is the strongest with the smallest r.

f.e.

Strengths of Earth's, Sun's gravity comes from quantity of atoms, not from distance, in the first place.

When OP said sub-atomic he probably meant inside of nucleus, "between quarks".

Sun mass is 1.9891*10^30 kg and average density 1.4 g/cm^3

The smallest star must have mass ~8.3% of it,

1.9891*10^30 kg * 0.083 = 1.650953*10^29 kg

Gold has density 19.3 g/cm^3. That's 13.8 more than average Sun density.

If there could exist object with radius r=126,619 km all made of gold, it would have the same mass as the smallest possible star.

That's 82% higher radius than Jupiter (~69,911 km).

If time travel would be possible within single Universe, we could travel to our past, then our atoms would be in two places at the same time. Then we and our own copy could enter time machine again, and travel again to our past, and there would be 4 "clones" of our atom, etc. etc. Repeat it infinite number of time, and Universe mass and energy would go to infinity.. It would violate the all known conservations of energy, mass, momentum, baryon and leptons..

Please note that atoms used for our body now, exist in nature all the time, they are in air, ground, other animals, or even Sun, or other stars, at any time (f.e. some proton 1 milion years ago was emitted by star, traveled through whole galaxy, and ended up on Earth, then joined with some O-H ion forming H2O, and ended up in our body that started traveling in time), so we don't need literally meet our own clone. Our atoms during time travel to past might be anywhere in the planet or anywhere in galaxy/Universe at that time.

If time travel would be possible in multi-universe, one Universe would be loosing energy-mass, and other Universe would be increasing its energy-mass.

It would violate conservations as well. Matter would disappear and appear from nowhere in space from point of view of single Universe.

Been reading too much recently! How does Classical Physics possibly differ from Quantum Theory?

Quantum physics is quantized.

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

In classic physics f.e. i=q/t

1 A = 1 C/1 s

Where i,q and t can be any value. And t>0.

In quantum physics 1 C is dividable by elementary charge 1.6*10^-19 C.

So you can only have 0 C, 1*1.6*10^-19 C, 2*1.6*10^-19 C, 3*1.6*10^-19 C etc.

Basically you cannot have half of electron, half of photon, half of proton etc. etc, or other fraction of particle.

You need a closed system. You would not get momentum conservation if matter was entering or leaving your system or it was being acted on by some external force.

"Closed system" is purely theoretical physics term.

In true Universe none system is perfectly close, neutrinos are flying through, photons are absorbed and emitted all the time, constantly changing state of system. Not to mention charged particles, and molecules.