Einstein's Thought Experiment

This morning I woke up in my Buggati, and I was wondering what if my car's speedometer reached the speed of light, 3x10^8 m/s. If my Buggati (I don't really have a Buggati) reached that electromagnetic speed, my car would transform from a Buggati to a DeLorean. However Albert Einstein thought up this scenario with trains or rockets before I did with my fictitious Bugatti.

Einstein's thought experiment derived a time-altering equation by using simple mathematics--algebra and the Pythagorean Theorem.

In Special Relativity, the speed of light is an universal constant; however, in General Relativity, a more complicated topic, light can be altered or bent in space time by gravity. The speed of light is a misnomer because there are other things--gamma rays, radio waves, X-Rays, microwaves, and Gravitons (if they exist)--that have the identical speed. Instead of the speed of light it should be appropriately called the electromagnetic speed.

For time travel to be plausible, the speed of light has to remain constant in any reference frame. For example, there is a car that is traveling at 40 m/s and there is a truck traveling behind it at 39 m/s. The truck will perceive--in its reference frame--that the car is traveling at 1 m/s. However, if the car is traveling at the speed of light, 3x10^8 m/s, and the truck is traveling at 2.8x10^8 m/s, the truck will still perceive the car traveling at 3x10^8 m/s instead of 0.2x10^8 m/s. With that being said, the equation that was derived from the video proves that time travel to the future is possible--not to the past. By traveling at the speed of light, time is infinitely slowed down--basically stopping time. To acquire this speed, however, is completely impractical; it will take an enormous amount of energy to accelerate to the speed of light, and humans--more than likely--will not withstand that force (F=ma).

But that's no fun. Let's say that time travel is possible. With time travel comes interesting paradoxes like the Grandfather Paradox...

or Stephen Hawking's experiment.

Although time travel does not appear possible by the last two videos, keep in mind these videos prove that time travel into the past is impossible. So there is still a chance that time travel into the future is possible.

Dead or Alive?

Quantum physics generates many profound metaphors that relate to the fundamental functions of the universe and our lives. Imagine a cat within a box that cannot escape. The lid of the box is closed, and there is no possible way of determining the cat's condition--dead or alive--without lifting the lid. This forces the observer to assume that the cat is both alive and dead simultaneously. Fortunately, when the box is open, the cat is alive.

This relates to one of the most bizarre experiments that have been done in quantum physics; it's called the double slit experiment. A physicist, Thomas Young, shot a laser through two narrow slits that landed on a wall behind them. Unexpectedly, the laser created vertical streams of light instead of two beams of light.

For this to happen, light has to be a wave; however, when the slits are a bit wider, the laser creates one stream of light as expected which means light is a particle. In the metaphor, the cat is both alive and dead in the box. The same goes for light; light is both a particle and a wave until observed. Bizarre, light seems to have complete control of it's state; it chooses to be a wave at the quantum level, but also it chooses to be a particle on a larger scale. Why does this happen?

This topic relates more than just to physics; it relates to our lives. We dream of the future; we want to alter the future; we want a pleasant future. However we get caught up in this fourth dimensional lifestyle that we forget about the present. You see, life is full of probabilities. This may happen or that may happen--no guarantee. Instead, you should accept what life throws at you because the most unexpected thing may happen, and that curve ball may hit you in the face. Accept life as it is. Assume that every possibility is equivalent to each other. Prepare yourself for the unexpected. Enjoy life not the dream that may happen.

The Universe is Based on Probability

The quantum world is filled with mystery and wonder. This equation, the Heisenberg Uncertainty Principle, shows probably the most intriguing aspect of quantum physics. In colloquial language, the equation states that there is no possible way to accurately measure a particle's position and momentum at the same time. Now for the mathematics, Δx represents the particles position; Δp, the particle's momentum. The fancy-looking h, ħ, is known as plank's constant which is approximately 6.626 x 10^(-34). To pronounce ħ, say "h-bar." This equation is truly non-intuitive because from the human perspective we can accurately measure an object's velocity, momentum, position, acceleration, and can even predict it's future velocity, momentum, position, etc. by using classical mechanics; however, in the quantum world classical physics breaks down and turns into probability.

Now you may be asking, "why is it so hard to measure these quantities? Don't we have advance microscopes to measure these values?" Firstly, to view an individual particle we need to shed light on it, so it becomes visible. Photons, light particles, can cause a disturbance to the particle's position like when a pool player hits a ball; the ball will accelerate to a different location. Shedding light is equivalent to millions of photons hitting the particle we want to observe. This causes a problem when we look through a microscope. Instead let's just use one individual photon instead of millions to view the particle.When the individual photon bumps the particle, the photon acquires a new direction as well as the particle. So when the photon arrives to the microscope at a new angle, it hits the lens causing it to refract even more (refraction is when light bends). Since we perceive the particle from where the photon is coming from, the measurement is completely inaccurate because of the photon's collision and refraction.

This issue forces us to use probability to locate the individual particle.

This is a probability wave. The probability is measured on the y-axis which is labeled p; the x-axis measures the particle's location which is labeled x. The peaks, or crests, show the highest chances of the particle being at that location. While the bottom peaks, or troughs, show the lowest chances of the particle being there. By using the concept of the derivative, these likely and unlikely possibilities are easy to find (we'll talk about derivatives in a future blog).

That leads us to a question, "is our world governed by probability?" Each human is made up of these infinitesimally small particles, and these same particles have the characteristic of probability. It's like seeing a friend sitting next to you in class, but he can also be sitting across the world in China. Since that probability is extremely low in our perspective, it's almost guaranteed that he or she is sitting next to you. However, having a high probability does not eliminate the other chances. So that very small chance of your friend sitting in china is still plausible. Are we misunderstanding particles' actions? Is there something that controls the universe that deceives us, the observers, to conclude that the universe is based on probability? There has to be something we're missing... I'll leave you with one of my favorite quotes from Einstein.

"God doesn't play dice with the universe." - Albert Einstein

Infinite Sums are Weird

What if I told you that 1-1+1-1+1-1+... = 1/2, and I proved it?

So lets take an infinite series, S.

S = 1-1+1-1+1-1+1-1+...

Now lets factor out a negative one from the second term to infinity...

S = 1-(1-1+1-1+1-1+...)

The grouped values are identical to the original series, S. 

S = 1-S

Now with some help from algebra, we can solve for S.

S = 1-S

2S = 1

S = 1/2

Therefore,

1-1+1-1+1-1+... = 1/2

Who knew? Well actually this is categorized as mathematical hocus pocus because this breaks math. In order to use the basic properties of arithmetic (i.e. associative property, commutative property, etc.) the series has to converge. For a series to converge the sum of the infinite series has to add up to a finite number. In this case, we are unsure what the series converges to because it can add up to 0, 1, or 1/2--which is it? If you want to see a visual proof on YouTube check out this video.

Euler, a mathematical gangster, disobeyed the rules of mathematics and found even more surprising values for infinite sums. He concluded that 1+2+3+4+5+... = -1/12. Although this sounds nonsensical, this does apply to quantum physics. Physicists go by the rule that says nothing in the universe has an infinite measure, and these insane values surprisingly appear in their experiments. Although I don't know the details or the direct application to the field, I find it amazing that there is physical proof of nonsense existing. 

Physics generally follows this order: develop an equation and experiment with it (or vice verse). Excitingly, physicists found that math is wrong--in the quantum world--and experiments are correct. Usually, math is correct and the experiments are wrong. This is mind boggling because which one should we believe? 

In our lives, we know what's nonsense and what's correct. However, our field of view is limited from our frame of reference. A human experiences the universe on a human level. If we break out of this perspective and look from a planet's perspective our view changes dramatically. We'll see--as a planet--empty space and feel like we're floating amid nothingness. We'll see our counterparts: stars, asteroids, galaxies, planets, etc. Or instead of a planet's perspective, we look through a quantum perspective. We'll see particles whizzing by, we'll feel the electrical force, and we'll possibly see other dimensions (as theorized from String Theory). What if we take this a step further? What if there is a world smaller than the quantum world or a realm larger than the universe? Is this where all the mathematical hocus pocus is spawned? 

I'm an advocate for being open-minded. I like to accumulate many theories, ideas, and suggestions and determine which is correct and wrong (based on my opinion). This is not only limited to math and science, but also to real life situations. Teachers may provide life lessons in their classrooms and so do parents in their homes. People completely ignore the teacher and follow their parents advice because it's ethically correct--some may think. I believe that one should not completely ignore suggestions due to bias or alleged nonsense; instead one should take in both and generate a more appropriate conclusion. The same goes for math and science. Who knows? Maybe there are parallel universes, time travelers, different dimensions, green aliens, flying pigs, etc.