About the Meaning of Quantum Mechanics

Everyone who knows at least the basics of quantum mechanics knows how tricky and counter intuitive this highly successful theory is. Even one of the greatest minds among the developers of quantum mechanics, Richard Feynman, once said  that "if you understand quantum mechanics, you don't understand quantum mechanics."

One of the few similarities between classical mechanics and quantum mechanics is that there is a main equation which can be manipulated mathematically to derive the equations which describe how a physical system behaves.  For example Newton's  law's (+ the law of gravity) can be used to derive almost all the equations needed to describe classical physical systems (pendulums, rolling balls, sliding blocks and all such stuff).Similarly Schroedinger's equation can be manipulated to derive the wave function and the probability distribution, which tells us, for example, where it is most likely to find a particle. So why is it that quantum mechanics has the reputation of one of the most counter intuitive theories of physics?

It's mostly because of many paradoxes, which seem illogical and too strange to be real sometimes. For instance, it's all perfectly normal in terms of the laws ruling the quantum world, for a particle to be in two places at once. Also, a elementary particles and other objects have properties of both waves and particles. And I don't even wanna start talking about strangeness of quantum entanglement and the double slit experiment.

So what all do these paradoxes  tell us about reality? After all, it's hard for most of the people to believe that particles in reality can indeed be in two places at once and so on. This is where the opinion of scientists splits - some say there is no objective reality, some say there is some kind of objective reality but it can't be detected (due to the Heisenberg principle) and others believe that quantum mechanics is an unfinished theory. These opinions are reflected in a variety of different interpretations of quantum mechanics.

Actually, I've just found a great article, which talks about various interpretations of quantum mechanics and what they tell us about reality. You can find the link bellow. Also be sure to check out the website it is on. Nova has a bunch of great physics videos as well as amazing library of articles and other useful stuff.

Debating the Meaning of Quantum Mechanics

NOVA


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Evil Demons and Living in the Matrix

Perhaps the greatest thing about philosophy is that really crazy ideas are taken very seriously by philosophers. My favourite example is the so called Evil Demon theory (or sometimes it's called Evil Genius), which is basically a simple question - how can you be sure that you are not being deceived by an evil demon right now? That is, how can you really be sure that your senses are not deceiving you? After all, we have all had experiences when our sense fooled us at least once. This famous problem was formulated by one of the most important western philosophers Descartes. In his philosophical treatise Meditations on First Philosophy (1641) Descartes pondered the problems of truly knowing something and achieving knowledge.

So this problem seems to be extraordinary hard, but is it even possible to find an answer for such a problem? There other similar problems like the so called dream theory, which states that it is not possible to tell if you're dreaming when you're in a dream, so how can you be sure you're not dreaming right now? Or even better, how can you be sure that you're not in Matrix? All these problems share a main feature - they really on the fact that our senses can be fooled and that some times an illusion can be as realistic as reality is. So it's seems that the solution to these problems can be found only by discovering some kind of undeniable truths.  Descartes himself believed that we should base our believes only on undeniable truths. An example of such a truth would be the famous quote cogito ergo sum (I think therefore I am). But even if this tackles the problem (many believe that it's not the case, but let's leave that for the next time) it only shows that we exist and do not help us answering the question whether we are dreaming or not. Isn't it funny how the craziest questions end up being the hardest ones?

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Wonders of Physics: Search for ET's

Have you ever wondered what our lives would be if we lived in a universe similar to those depicted in Star Wars or Star Trek? What would it be like living in a universe full of various bizarre and amazing alien races? Well guess what, scientist are interested in the same questions. These days scientists not only believe in a possibility of extraterrestrial live out there, but they are even looking for it. And this is our strange and amazing fact of today.

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Arguments that Habitable Planets Might Exist

All life on  Earth requires special conditions. Life requires many minerals like: carbon, hydrogen, oxygen, nitrogen, sulfur and phosphorus as well as numerous other elements in smaller amounts. Another basic need for life is water. Many scientist believe that Earth was made of relatively abundant chemical elements formed from stars which have ended their lives as supernova and that it is very probable that there other planets which were formed in a similar way. The huge number of galaxies and planets has also inspired the believe of ET life forms.

So How Do We Search?


There are two main forms of search techniques for ET life forms - direct and indirect. Direct search mostly deals with meteorites from outer space and other planets. Whereas indirect deals with search of radio signals that might be sent by intelligent alien civilizations.


Direct Search


When these meteorites fall to Earth, they are analysed, as scientists hope to find some kind of proof of ET microbial organisms. This also gives great information about the environment on neighbour planets.


Another direct search technique is sending space probes to nearby planets. These probes analyse the surface of a planet and search for any proof of any life forms. This method has many advantages. Firstly it is possible to gain much more information than in indirect search methods, because it is possible to examine the surface of the planet, atmosphere (if it exists) and look for clues of water and other important chemical elements. The main disadvantage however is that, we can't reach planets that are out of the solar system.


Indirect Search 


Many scientists believe that a civilization, at least as advanced as our civilization is right now, would transmit some kind of radio signals to outer space. That is what indirect search deals with. Scientists try to catch these radio signals with huge antennas and radio telescopes. Perhaps the most famous indirect search program is the so called SETI.  SETI or Search for Extra-Terrestrial Intelligence is a project with an aim of finding ET intelligence in space by examining radio signals from space. Of course, there are many critics of such an approach, as ET's might be using other forms of communication, or very different frequencies from our ones. 


The interesting thing about SETI is that everyone around the world, who has a computer, can help the search for ET intelligence. SETI@home is a unique project that examines radio signals from space by using home computers of people from all around the world. The best part is that you can download SETI@home and use a small part of your computer power to help the search for ET.

What if We Find ET's?

So what happens if we find intelligent alien civilizations? Some people believe that it will be the first step towards a galactic civilization like in Star Wars or Star Trek. Others, on the other hand, think that it might not be such a great idea. Stephen Hawking once said that sending a message to aliens wouldn't be a great idea, as we can't be sure, whether they are peaceful or not. So what do you think about this? How would our lives change if aliens were found?





Links: SETI@home project

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Wonders of Mathematics: Complex Numbers

Everyone, who came across complex numbers in mathematics knows how strange they are. But do these numbers really exist? Are they important?

First let's look at what complex numbers are. More than 2 thousand years ago, ancient Greeks believed that every number can be expressed as a fraction, for example 1/2, 2/5 and so on. However, they were shocked, when they realised that a hypotenuse of a right triangle with sides of length 1 cannot be expressed using natural numbers or fractions. As we all know, the length of the hypotenuse of such a triangle is a square root of 2 (which is 1.414...). This showed ancient Greeks that there is more than a single number system, in this case it's the real number system (which includes counting numbers as 1, 2...., negative numbers, fractions, square roots and so on).

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Until complex numbers were found and were used in mathematics, it was thought that all the number systems were already found. So what is a complex number? It's easy. It's a number that is a square root of a negative number.

But do such numbers have any physical meaning? After all, even when calculating simple quadratic equations, younger students are told to ignore negative answers, as negative areas do not exist. Surely such negative areas might not exist, but complex numbers constantly show up in various applications, which shows that even though we can't visualise a square root of -1, it still exists in mysterious ways.

The strange thing about complex numbers in fact is that they almost seem to be existing and not existing at the same time. For example, when solving differential equations, in electrical engineering (also in many other fields), the behaviour of electrical circuits depends on whether the solutions are real or complex numbers.

Another example is quantum mechanics. The wave function, that describes behaviour of microscopic particles is found using complex numbers. That is something real and physical is described by laws which use complex numbers.

The so called Mandelbrot Set shows a set of complex numbers generated by a simple equation:

Source

Some physics theories even use complex number plane to represent time, whereas real numbers represent spatial dimensions.

But the real question is whether complex numbers represent something physical. When it comes to square roots of positive numbers, we can clearly visualise what they mean. For example, if we know an area of a rectangle is 16 meters, we can take the square root of this number and find out that the side of the rectangle is 4 meters. But when it comes to complex numbers, a similar situation cannot be found.

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More Strange Facts of Physics

We already discussed time travel, which is a huge topic, so let's relax for a while and look at some random strange facts.

Everything is Moving

More than 2000 years ago ancient Greek philosophers used to argue, whether anything ever changes. Some thinkers were convinced that everything is constantly moving and changing, whereas other wise men believed that nothing moves. Now you might think that believing that nothing ever moves is strange, as you can clearly move as well as many other things around you. But a guy named Zeno actually had some interesting arguments to back up his beliefs. The so called Zeno paradoxes supposedly show that movement is only an illusion. The simplest form of Zeno's paradox goes as follows: suppose you have to walk from point A to point B. In order to do that you firstly have to walk half of the distance, however to do that you should firstly travel one forth of the distance and so on. Since there is infinity of such parts of the distance, you can never even start moving.

Today we know that Zeno's conclusions were wrong, as simple maths can help solving the paradox. By adding an infinite number of fractions you can get a finite answer.

So is everything moving then? The answer is probably yes. Even though many objects around us appear to be stationery, in reality, everything is constantly moving. If you had a powerful microscope, you could actually see that molecules of every object are constantly moving due to temperature (temperature is in fact kinetic energy of molecules) and since temperature cannot reach absolute 0 Kelvins, molecules always move. Furthermore, as you are sitting comfortably in your chair, Earth is flying in outer space at thousands of miles per hour. But that's not all, as even space itself is expanding every moment.

Sugar Cubes and Humans

I bet you already knew that atoms are basically 99.9999..% empty space. But here's another amazing fact - if you would take all the matter that makes up all humans on Earth, remove the empty space from atoms and squeeze the matter, you could compress it to a size of a sugar cube.

 Source

The Faster You Move The More Massive You Become

Another fun fact is from special relativity. As an object moves in high speeds it becomes more massive. Hey but don't worry all of you who are trying to lose weight, as long as you're not moving at almost the speed of light, you will be OK.

Earth and the Moon

Everybody knows that the Moon orbits Earth, but did you know that the opposite is also true? In fact, both Earth and the Moon orbit their common centre of mass, which happens to be inside of Earth (as our planet is far more massive than its satellite).

 Source


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Strangest Facts of Physics: Time Travel to the Past

Is it Possible? 

Last time we looked at time travel to the future, which is indeed real, but how about time travel to the past? Is it possible?

This is where opinions of scientists split up. Some believe that time travel to the past is possible, though we don't have the technology yet, whereas others believe that it isn't possible due to various paradoxes.

Nevertheless, time travel to the past, at least theoretically seems to be possible. And that is the strange fact of today.

Seeing the Past 


So let's look at some ways to travel back to the past. First of all, we see past all around us, as the light from any object takes time to travel to our eyes. Even though light is extraordinary fast, it takes very long periods of time to travel from distant stars. This means, that if we were to look through a telescope, we would see distant stars as they were billions of years ago. In a sense, this is a form of time travel, as we can see the past. But is there any real way to not only see the past but also travel to it?

Black Holes

The possibility might hide deep in the far reaches of the space. Mysterious massive objects known as black holes might hold the key to time travel. But what is a black hole? When a very massive star runs out of fuel to burn, it collapses. If the star is massive enough, there is simply nothing that can hold the gravitational collapse. Thus such a star collapses rapidly down to a singularity (infinitely dense and small region of space). As the gravitational pull of such a singularity is extraordinary strong, even light can't escape the gravitational pull near the star.

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From special relativity we know that the faster an object moves the slower time runs for it. If an object reaches light speed, time completely stops running for it. Now following this logic, some scientists believe, that if something moved faster than light, time would run backwards. So this gives an idea how we could travel through time. If we were to fall down to a black hole, at some point we would end up travelling faster than light.

However, there's one "little" problem. The gravitation of the black hole would simply tear our bodies apart. So travelling back to time using this kind of black holes is out of the question.

But don't worry, there might be another type of black holes. In 1962 New Zealand mathematician Roy Kerr, proposed a working theory of a rotating black hole. According to Kerr such a black hole would be spinning, thus wouldn't collapse to a singularity. In theory, it would be possible to travel near such a black hole without getting torn apart. So at least in theory, it might be possible to travel back to past, although we have no proof of such black holes existing.

Roy Kerr:

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Wormholes


Every sci-fi fan probably knows what wormholes are and how they work. But could they exist in reality? Could we be travelling back in time like those guys in Star Trek?

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First let's look at how wormholes actually work. The idea is that a wormhole is a tunnel connecting two points in space-time. A wormhole that connects two points in space-time in a specific way, so that one point is in the past, might be used for time travel.

The problem is that, even though such wormholes seem theoretically possible, in reality they would be very unstable and probably wouldn't exist for a long time.

Closed Timelike Curves

It's amazing, but ideas of time travel to the past span back more than half a century ago. Back in the 1940s Austrian mathematician Kurt Gödel  was working with the solutions of Einstein's general theory of relativity. In 1949 Gödel discovered interesting solutions of the equations of the general theory of relativity. These solutions showed that there might exists objects called closed timelike curves, which would allow time travel. A CTC is a world line that a particle or a person can follow which ends at the same space-time point (the same position and time) as it started.

Kurt Gödel:

Source

Unfortunately, CTC's seem to exist only if space-time has a special form (it should have holes sort of like a doughnut shape).

Cosmic Strings 


Some scientists believe that strange objects called cosmic strings (not to be confused with strings in string theory) might exist. These massive and extraordinary thin objects might help in time travel. If two such strings could be brought close together close timelike curves might be created.

As always, this has some problems. First of all, these strings might not even exist. Furthermore, energy required to manipulate such strings to create CTC's would be enormous.

Paradoxes


So as you can see there are many great problems with time travel to the past. Naturally, there are scientists who do not believe in time travel to the past. To defend their position they often use famous paradoxes, which show that time travel might not be logical. The most important and popular paradox is the so called grandfather paradox. It goes like this: let us say you go to the past and for some reason decide to kill your grandfather before you were born. Would it be possible? I mean if you'd kill your grandfather in the past, you would never been born and thus wouldn't travel back in time and kill your grandfather, which is not logical. Of course some say, that there would always be something stopping you from killing your grandfather (which doesn't sound realistic to me). Others believe, that you would kill your grandfather in a parallel universe, which wouldn't cause a paradox.

Conclusion 


Even though many scientists don't believe in time travel to the past, it is still theoretically possible. We don't have a sufficient technology to test it, however such a technology might be available in the future. And even though time travel to the past seems unlikely, only time will tell...


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Strangest Facts of Physics: Time Travel to the Future

When I was a child and was only starting to learn physics, one thing for me was stranger than anything else. You might guess it was the strangeness of quantum mechanic. But actually (even though quantum mechanics is very very strange and fascinating) the thing that really caught my attention was time travel.

Time travel is one of the most popular subjects of science fiction. Starting with Star Trek ending with newer shows like Lost most of the sci-fi shows have a fare share of time travel. But have you ever wondered if time travel is possible? Well the answer is yes! And that is our strange fact of today.

First let's look at time travel to the future. Even though Einstein's special theory of relativity is a part of high school course, not many people know that time travel to the future is actually a scientifically proven fact. It's not only proven, it's a big part of communication technology, as even GPS services wouldn't work without the precise calculations from the special and general theories of relativity. But what does this have to do with time travel?

Einstein back in 1905, when his special theory of relativity was created, showed, that time runs slower for fast moving bodies. To get a grasp of how this works, let's check out this mechanism called photon clock. It consists of two mirrors with a photon (particle of light) trapped between them. Every time the photon hits the mirror a unit of time passes.

Source

When the clock is not moving, the photon just bounces up and down vertically. However, if the clock is moving, as you can see in the image, the photon needs to go diagonally from the upper mirror to the lower one and vice versa. It's clear that when the clock is moving, the photon has to travel a greater distance from one mirror to another. In other words, time passes slower for a moving photon clock. But the interesting thing is that this is true not only from photon clocks, but for any moving objects, as Einstein showed in his theories. Even the photons in the atoms of our bodies must travel a longer distance between the nuclei and electrons when our bodies are moving.

This simply means that the faster some object moves, the slower time runs for it. This gives rise to the famous twin paradox. It goes like this. Let's say there are two twins. One of them decides that life on Earth is boring, so he jumps on a fast rocket and flies away for let us say 50 years at a speed of 75% of light speed. Then after 50 years, he get's back to Earth, and is amazed, as his twin brother appears to be 25 years older than him.What happened was that time ran slower for the brother, who was in the rocket, which basically made him travel to the future, as time on Earth was running faster.

A video about Twin Paradox:

You might be wondering does this have any proof? The answer is yes. Two super precise atomic clocks measured time, while one of them was in a plane flying around the world, whereas the other clock was stationary on the ground. The difference in the clocks, when the plane completed its journey, was a very very small (nanoseconds), but it agreed with Einstein's theories.

So time travel to the future is really possible, though our current technology is not advanced enough to make use of it. Rockets, travelling at almost the speed of light would be required to travel to actually travel to the future. Also going back from the fancy future would be much more difficult (some believe even impossible), but more about that next time.

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Strangest Facts of Physics: We Are Empty

Let me ask you a question. Have you ever really thought about our universe? Have you ever asked yourself how did our universe start? Or how about what is time? Or even is there something more in our universe besides the matter and energy that we can measure?

If you did, and even tried to look for the answers, I bet the conclusion that you made about the universe is that it's very strange...

There's a saying that reality is stranger than fiction. I agree with it 100%, as I've never heard, read or seen something, that was more amazing and jaw dropping, as the mysterious facts about our universe. So let's check out some of the strangest facts of physics.

Let's start by a simple, yet fascinating fact: a human body is made of 99.9999999999999 % empty space. The atoms that make our bodies, as well as everything around you, are made mostly of empty space.

So how come, do we see all the matter around us and not only empty space? And let's make a step further: how come we can't walk through walls? The answer to these questions is that atoms are not all there is. Every atom is made up of smaller particles - protons, neutrons and electrons. Protons and neutrons make up the nucleus of an atom, where's electrons are attracted to the nucleus with an electromagnetic force. This electromagnetic force (transmitted by particles of light called photons), can be both attractive and repulsive. This electromagnetic force is what causes the repulsion of the atoms, when many of them are put close together. That's exactly why we can't go through walls, as the atoms of the walls push away the atoms in our body.

Composition of an atom:

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Also, atoms can reflect and absorb light. We actually see objects, when a light ray reaches an object and reflects from it to our eyes. Naturally light can only reflect from atoms and not from empty space, thus we can't see empty space. Also there are billions of billions of atoms literally everywhere, as well as billions of billions photons bouncing of them. All of this light makes up the illusion that all objects around us are made of continuous matter.

Photon radiated  from an atom:

Source

When you really think about it, it's really bizarre. I mean, what we see around us is only an illusion. I guess the universe is really more than meets the eye.

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