The String Theory

Think of a guitar string that has been tuned by stretching the string under tension across the guitar. Depending on how the string is plucked and how much tension is in the string, different musical notes will be created by the string. These musical notes could be said to be excitation modes of that guitar string under tension. 
 In a similar manner, in string theory, the elementary particles we observe in particle accelerators could be thought of as the "musical notes" or excitation modes of elementary strings. 
 In string theory, as in guitar playing, the string must be stretched under tension in order to become excited. However, the strings in string theory are floating in space-time, they aren't tied down to a guitar. Nonetheless, they have tension. The string tension in string theory is denoted by the quantity 1/(2 p a'), where a' is pronounced "alpha prime"and is equal to the square of the string length scale. 
 If string theory is to be a theory of quantum gravity, then the average size of a string should be somewhere near the length scale of quantum gravity, called the Planck length, which is about 10^-33 centimeters, or about a millionth of a billionth of a billionth of a billionth of a centimeter. Unfortunately, this means that strings are way too small to see by current or expected particle physics technology (or financing!!) and so string theorists must devise more clever methods to test the theory than just looking for little strings in particle experiments. 
 String theories are classified according to whether or not the strings are required to be closed loops, and whether or not the particle spectrum includes fermions. In order to include fermions in string theory, there must be a special kind of symmetry called super-symmetry, which means for every boson (particle that transmits a force) there is a corresponding fermion (particle that makes up matter). So super-symmetry relates the particles that transmit forces to the particles that make up matter. 
 Super-symmetric partners to to currently known particles have not been observed in particle experiments, but theorists believe this is because super-symmetric particles are too massive to be detected at current accelerators. Particle accelerators could be on the verge of finding evidence for high energy super-symmetry in the next decade. Evidence for super-symmetry at high energy would be compelling evidence that string theory was a good mathematical model for Nature at the smallest distance scales.

Watch Video:

The Doppler Effect

Suppose that there is a happy bug in the center of a circular water puddle. The bug is periodically shaking its legs in order to produce disturbances that travel through the water. If these disturbances originate at a point, then they would travel outward from that point in all directions. Since each disturbance is traveling in the same medium, they would all travel in every direction at the same speed. The pattern produced by the bug's shaking would be a series of concentric circles as shown in the diagram at the right. These circles would reach the edges of the water puddle at the same frequency. An observer at point A (the left edge of the puddle) would observe the disturbances to strike the puddle's edge at the same frequency that would be observed by an observer at point B (at the right edge of the puddle). In fact, the frequency at which disturbances reach the edge of the puddle would be the same as the frequency at which the bug produces the disturbances. If the bug produces disturbances at a frequency of 2 per second, then each observer would observe them approaching at a frequency of 2 per second.

Now suppose that our bug is moving to the right across the puddle of water and producing disturbances at the same frequency of 2 disturbances per second. Since the bug is moving towards the right, each consecutive disturbance originates from a position that is closer to observer B and farther from observer A. Subsequently, each consecutive disturbance has a shorter distance to travel before reaching observer B and thus takes less time to reach observer B. Thus, observer B observes that the frequency of arrival of the disturbances is higher than the frequency at which disturbances are produced. On the other hand, each consecutive disturbance has a further distance to travel before reaching observer A. For this reason, observer A observes a frequency of arrival that is less than the frequency at which the disturbances are produced. The net effect of the motion of the bug (the source of waves) is that the observer towards whom the bug is moving observes a frequency that is higher than 2 disturbances/second; and the observer away from whom the bug is moving observes a frequency that is less than 2 disturbances/second. This effect is known as the Doppler effect.

The Doppler effect is observed whenever the source of waves is moving with respect to an observer. The Doppler effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in frequency for observers towards whom the source is approaching and an apparent downward shift in frequency for observers from whom the source is receding. It is important to note that the effect does not result because of an actual change in the frequency of the source. Using the example above, the bug is still producing disturbances at a rate of 2 disturbances per second; it just appears to the observer whom the bug is approaching that the disturbances are being produced at a frequency greater than 2 disturbances/second. The effect is only observed because the distance between observer B and the bug is decreasing and the distance between observer A and the bug is increasing.

The Doppler effect can be observed for any type of wave - water wave, sound wave, light wave, etc. We are most familiar with the Doppler effect because of our experiences with sound waves. Perhaps you recall an instance in which a police car or emergency vehicle was traveling towards you on the highway. As the car approached with its siren blasting, the pitch of the siren sound (a measure of the siren's frequency) was high; and then suddenly after the car passed by, the pitch of the siren sound was low. That was the Doppler effect - an apparent shift in frequency for a sound wave produced by a moving source.

The Doppler effect is of intense interest to astronomers who use the information about the shift in frequency of electromagnetic waves produced by moving stars in our galaxy and beyond in order to derive information about those stars and galaxies. The belief that the universe is expanding is based in part upon observations of electromagnetic waves emitted by stars in distant galaxies. Furthermore, specific information about stars within galaxies can be determined by application of the Doppler effect. Galaxies are clusters of stars that typically rotate about some center of mass point. Electromagnetic radiation emitted by such stars in a distant galaxy would appear to be shifted downward in frequency (a red shift) if the star is rotating in its cluster in a direction that is away from the Earth. On the other hand, there is an upward shift in frequency (a blue shift) of such observed radiation if the star is rotating in a direction that is towards the Earth.

Watch video:

Time Travel

The concept of a time machine typically conjures up images of an implausible plot device used in a few too many science-fiction story-lines. But according to Albert Einstein's general theory of relativity, which explains how gravity operates in the universe, real-life time travel isn't just a vague fantasy.

Traveling forward in time is an uncontroversial possibility, according to Einstein's theory. In fact, physicists have been able to send tiny particles called muons, which are similar to electrons, forward in time by manipulating the gravity around them. That's not to say the technology for sending humans 100 years into the future will be available anytime soon, though.

1.by Worm-hole:

Since the 1930’s, physicists have speculated about the existence of "wormholes" in the fabric of space. Wormholes are hypothetical areas of warped spacetime with great energy that can create tunnels through spacetime. if traversable would allow a traveler to quickly move through great distances in space and also travel through time. The difficulty lies in keeping the wormhole open while the traveler makes his journey: If the opening snaps shut, he will never survive to emerge at the other end. 

For years, scientists believed that the transit was physically impossible. But recent research, especially by the U.S. physicist Kip Thorne, suggests that it could be done using exotic materials capable of withstanding the immense forces involved. Even then, the time machine would be of limited use – for example, you could not return to a time before the wormhole was created. Using wormhole technology would also require a society so technologically advanced that it could master and exploit the energy within black holes. 



Spacetime can be viewed as a 2D surface (to simplify understanding) that, when 'folded' over, allows the formation of a wormhole bridge. A wormhole has at least two mouths that are connected to a single throat or tube. If the wormhole is traversable, then matter can 'travel' from one mouth to the other by passing through the throat. While there is no observational evidence for wormholes, spacetime containing wormholes are known to be valid solutions in general relativity.

The term wormhole was coined by the American theoretical physicist John Archibald Wheeler in 1957. However, the idea of wormholes had already been theorized in 1921 by the German mathematician Hermann Weyl in connection with his analysis of mass in terms of electromagnetic field energy.

This analysis forces one to consider situations...where there is a net flux of lines of force through what topologists would call a handle of the multiply-connected space and what physicists might perhaps be excused for more vividly terming a ‘wormhole’.

The key characteristics of the application of wormholes for time control and time travel are presented in the picture below. This is followed by more detail describing the science below.

Definition

The basic notion of an intra-universe wormhole is that it is a compact region of spacetime whose boundary is topologically trivial but whose interior is not simply connected. Formalizing this idea leads to definitions such as the following, taken from Matt Visser's Lorentzian Wormholes.

If a Minkowski spacetime contains a compact region Ω, and if the topology of Ω is of the form Ω ~ R x Σ, where Σ is a three-manifold of nontrivial topology, whose boundary has topology of the form dΣ ~ S2, and if, furthermore, the hypersurfaces Σ are all spacelike, then the region Ω contains a quasi-permanent intra-universe wormhole.

Characterizing inter-universe wormholes is more difficult. For example, one can imagine a 'baby' universe connected to its 'parent' by a narrow 'umbilicus'. One might like to regard the umbilicus as the throat of a wormhole, but the spacetime is simply connected.

Schwarzschild wormholes

Diagram of a Schwarzschild Wormhole

Lorentzian wormholes known as Schwarzschild wormholes or Einstein-Rosen bridges are bridges between areas of space that can be modeled as vacuum solutions to the Einstein field equations by combining models of a black hole and a white hole. This solution was discovered by Albert Einstein and his colleague Nathan Rosen, who first published the result in 1935. However, in 1962 John A. Wheeler and Robert W. Fuller published a paper showing that this type of wormhole is unstable, and that it will pinch off instantly as soon as it forms, preventing even light from making it through.

Before the stability problems of Schwarzschild wormholes were apparent, it was proposed that quasars were white holes forming the ends of wormholes of this type.

While Schwarzschild wormholes are not traversable, their existence inspired Kip Thorne to imagine traversable wormholes created by holding the 'throat' of a Schwarzschild wormhole open with exotic matter (material that has negative mass/energy).

Traversability

Wormholes would act as shortcuts connecting distant regions of space-time. By going through a wormhole, it might be possible to travel between the two regions faster than a beam of light through normal space-time.

Lorentzian traversable wormholes would allow travel from one part of the universe to another part of that same universe very quickly or would allow travel from one universe to another. The possibility of traversable wormholes in general relativity was first demonstrated by Kip Thorne and his graduate student Mike Morris in a 1988 paper; for this reason, the type of traversable wormhole they proposed, held open by a spherical shell of exotic matter, is referred to as a Morris-Thorne wormhole. Later, other types of traversable wormholes were discovered as allowable solutions to the equations of general relativity, including a variety analyzed in a 1989 paper by Matt Visser, in which a path through the wormhole can be made in which the traversing path does not pass through a region of exotic matter. However in the pure Gauss-Bonnet theory exotic matter is not needed in order for wormholes to exist- they can exist even with no matter. A type held open by negative mass cosmic strings was put forth by Visser in collaboration with Cramer et al., in which it was proposed that such wormholes could have been naturally created in the early universe.

Wormholes connect two points in spacetime, which means that they would in principle allow travel in time, as well as in space. In 1988, Morris, Thorne and Yurtsever worked out explicitly how to convert a wormhole traversing space into one traversing time.[4] However, it has been said a time traversing wormhole cannot take you back to before it was made but this is disputed.

Faster-than-light travel

Special relativity only applies locally. Wormholes allow superluminal (faster-than-light) travel by ensuring that the speed of light is not exceeded locally at any time. While traveling through a wormhole, subluminal (slower-than-light) speeds are used. If two points are connected by a wormhole, the time taken to traverse it would be less than the time it would take a light beam to make the journey if it took a path through the space outside the wormhole. However, a light beam traveling through the wormhole would always beat the traveler. As an analogy, running around to the opposite side of a mountain at maximum speed may take longer than walking through a tunnel crossing it. You can walk slowly while reaching your destination more quickly because the distance is smaller.

Time travel

A wormhole could allow time travel. This could be accomplished by accelerating one end of the wormhole to a high velocity relative to the other, and then sometime later bringing it back; relativistic time dilation would result in the accelerated wormhole mouth aging less than the stationary one as seen by an external observer, similar to what is seen in the twin paradox. However, time connects differently through the wormhole than outside it, so that synchronized clocks at each mouth will remain synchronized to someone traveling through the wormhole itself, no matter how the mouths move around. This means that anything which entered the accelerated wormhole mouth would exit the stationary one at a point in time prior to its entry.

For example, consider two clocks at both mouths both showing the date as 2000. After being taken on a trip at relativistic velocities, the accelerated mouth is brought back to the same region as the stationary mouth with the accelerated mouth's clock reading 2005 while the stationary mouth's clock read 2010. A traveler who entered the accelerated mouth at this moment would exit the stationary mouth when its clock also read 2005, in the same region but now five years in the past. Such a configuration of wormholes would allow for a particle's world line to form a closed loop in spacetime, known as a closed timelike curve.

It is thought that it may not be possible to convert a wormhole into a time machine in this manner; some analyses using the semi-classical approach to incorporating quantum effects into general relativity indicate that a feedback loop of virtual particles would circulate through the wormhole with ever-increasing intensity, destroying it before any information could be passed through it, in keeping with the chronology protection conjecture. This has been called into question by the suggestion that radiation would disperse after traveling through the wormhole, therefore preventing infinite accumulation. The debate on this matter is described by Kip S. Thorne in the book Black Holes and Time Warps. There is also the Roman ring, which is a configuration of more than one wormhole. This ring seems to allow a closed time loop with stable wormholes when analyzed using semi-classical gravity, although without a full theory of quantum gravity it is uncertain whether the semi-classical approach is reliable in this case.

Metrics

Theories of wormhole metrics describe the spacetime geometry of a wormhole and serve as theoretical models for time travel. An example of a (traversable) wormhole metric is the following:



One type of non-traversable wormhole metric is the Schwarzschild solution:





2.by Black-hole:

Black holes can be used to travel into the future only. So far as we know, our universe prohibits traveling into the past.

According to Einstein's theory of general relativity, and to experimental evidence here on earth assembled by Harvard physicists Pound and Rebka, in the presence of a gravitational field, an external observer would see a clock in a strong gravitational field tick more slowly. This is analogous to the famous time dilation effect in special relativity, except that in the 'gravitational redshift' effect no motion between the observer outside the gravitational field and the clock located within the field, is required.

What this means is that if you were traveling into a strong gravitational field and sending out pulses of light every second, an observer watching these signals from a great distance would see the interval between the pulses increase from seconds to minutes and then hours as the field got stronger and stronger.

Black holes are fantastic sources of very strong gravitational fields. What a distant observer would see as your clock got closer to the so-called Event Horizon of the black hole is that the pulse interval would increase without limit from one second to one month and longer. The frequency of the light pulses would also get longer as the light lost more and more energy struggling to get out from the vicinity of the black hole. As your friend finally entered the black hole by passing across its event horizon, the last photon capable of making it to infinity is emitted at almost infinite redshift, meaning that if you originally emitted a gamma ray with an energy of 1000 billion electron volts, buy the time your friend received it far away, it would have lost enough energy to become a radio photon with an energy of 0.00001 electron volts! So, if it took your friend 1000 hours to travel from where you are to the black hole, the last photon he sent you just before entering the black hole, would arrive at your location 1000 hours from now, but when you looked at the interval between the last two pulses he sent, you would see that they are not the one second interval you started out with, but say 1 or 2 minutes or more. But here's the rub. According to your infalling friend, he/she is still sending the pulses out once each second!

In other words, one second to your friend falling into a black hole is several minutes to you and, in essence, your friend is aging more slowly than you and is traveling into the future faster than you are. If he/she could manage to put on the breaks just before crossing over the Event Horizon and escape to rejoin you, you would note that his/her clock reads a much earlier time than your clock. To your friend, only 2000 hours may have elapsed, however, YOUR clock would read perhaps 10000 hours or several weeks have elapsed depending how close to the Event Horizon your friend could get before escaping. The tidal gravitational forces are enormous near small black holes the mass of the sun, so your friend would be shredded into spaghetti within a few hundred miles of the Horizon. For supermassive black holes of several billion solar masses, however, the tidal forces near the Horizon are very small and survivable. This means you could accidently find yourself passing across this one-way barrier, and only realize your mistake when you tried to escape and found it impossible.

In principle, if you could get within a few millimeters of an Event Horizon before escaping, you could essentially time travel years or millenia into the future as measured by outside clocks. According to your clock, however, perhaps only a few hour or days actually elapsed.

Note, all of the above numbers are pretty darn approximate and are given to qualitatively show the magnitudes of the effects.

3.by travelling at the speed of light:

In the early 1900s, scientists held firm to the Newtonian view of the world. Then a German-born mathematician and physicist by the name of Albert Einstein came along and changed everything. In 1905, Einstein published his theory of special relativity, which put forth a startling idea: There is no preferred frame of reference. Everything, even time, is relative. Two important principles underpinned his theory. The first stated that the same laws of physics apply equally in all constantly moving frames of reference. The second said that the speed of light -- about 186,000 miles per second (300,000 kilometers per second) -- is constant and independent of the observer's motion or the source of light. According to Einstein, if Superman were to chase a light beam at half the speed of light, the beam would continue to move away from him at exactly the same speed.

These concepts seem deceptively simple, but they have some mind-bending implications. One of the biggest is represented by Einstein's famous equation, E = mc², where E is energy, m is mass and c is the speed of light. According to this equation, mass and energy are the same physical entity and can be changed into each other. Because of this equivalence, the energy an object has due to its motion will increase its mass. In other words, the faster an object moves, the greater its mass. This only becomes noticeable when an object moves really quickly. If it moves at 10 percent the speed of light, for example, its mass will only be 0.5 percent more than normal. But if it moves at 90 percent the speed of light, its mass will double.

As an object approaches the speed of light, its mass rises precipitously. If an object tries to travel 186,000 miles per second, its mass becomes infinite, and so does the energy required to move it. For this reason, no normal object can travel as fast or faster than the speed of light.

We covered the original question, but what if we tweaked it to say, "What if you traveled almost as fast as the speed of light?" In that case, you would experience some interesting effects. One famous result is something physicists call time dilation, which describes how time runs more slowly for objects moving very rapidly. If you flew on a rocket traveling 90 percent of light-speed, the passage of time for you would be halved. Your watch would advance only 10 minutes, while more than 20 minutes would pass for an Earthbound observer.

You would also experience some strange visual consequences. One such consequence is called aberration, and it refers to how your whole field of view would shrink down to a tiny, tunnel-shaped "window" out in front of your spacecraft. This happens because photons (those exceedingly tiny packets of light) -- even photons behind you -- appear to come in from the forward direction. In addition, you would notice an extreme Doppler effect, which would cause light waves from stars in front of you to crowd together, making the objects appear blue. Light waves from stars behind you would spread apart and appear red. The faster you go, the more extreme this phenomenon becomes until all visible light from stars in front of the spacecraft and stars to the rear become completely shifted out of the known visible spectrum (the colors humans can see). When these stars move out of your perceptible wavelength, they simply appear to fade to black or vanish against the background.

Watch video:

1.


2.


3.



4.



Complete:
4.Into The Universe With Stephen Hawking: Time Travel

Quantum Mechanics

What is Quantum Physics?

Quantum physics is a branch of science that deals with discrete, indivisible units of energy called quanta as described by the Quantum Theory. There are five main ideas represented in Quantum Theory:

1. Energy is not continuous, but comes in small but discrete units.
2. The elementary particles behave both like particles and like waves. 
3. The movement of these particles is inherently random. 
4. It is physically impossible to know both the position and the momentum of a particle at the same time. The more precisely one is known, the less precise the measurement of the other is.
5. The atomic world is nothing like the world we live in. 

While at a glance this may seem like just another strange theory, it contains many clues as to the fundamental nature of the universe and is more important then even relativity in the grand scheme of things (if any one thing at that level could be said to be more important then anything else). Furthermore, it describes the nature of the universe as being much different then the world we see. As Niels Bohr said, "Anyone who is not shocked by quantum theory has not understood it." 

Particle/Wave Duality

Particle/wave duality is perhaps the easiest way to get aqua-tinted with quantum theory because it shows, in a few simple experiments, how different the atomic world is from our world.

First let's set up a generic situation to avoid repetition. In the center of the experiment is a wall with two slits in it. To the right we have a detector. What exactly the detector is varies from experiment to experiment, but it's purpose stays the same: detect how many of whatever we are sending through the experiment reaches each point. To the left of the wall we have the originating point of whatever it is we are going to send through the experiment. That's the experiment: send something through two slits and see what happens. For simplicity, assume that nothing bounces off of the walls in funny patterns to mess up the experiment.

First try the experiment with bullets. Place a gun at the originating point and use a sandbar as the detector. First try covering one slit and see what happens. You get more bullets near the center of the slit and less as you get further away. When you cover the other slit, you see the same thing with respect to the other slit. Now open both slits. You get the sum of the result of opening each slit. The most bullets are found in the middle of the two slits with less being found the further you get from the center.

Well, that was fun. Let's try it on something more interesting: water waves. Place a wave generator at the originating point and detect using a wave detector that measures the height of the waves that pass. Try it with one slit closed. You see a result just like that of the bullets. With the other slit closed the result is the same. Now try it with both slits open. Instead of getting the sum of the results of each slit being open, you see a wavy pattern; in the center there is a wave greater then the sum of what appeared there each time only one slit was open. Next to that large wave was a wave much smaller then what appeared there during either of the two single slit runs. Then the pattern repeats; large wave, though not nearly as large as the center one, then small wave. This makes sense; in some places the waves reinforced each other creating a larger wave, in other places they canceled out. In the center there was the most overlap, and therefore the largest wave. In mathematical terms, instead of the resulting intensity being the sum of the squares of the heights of the waves, it is the square of the sum.

While the result was different from the bullets, there is still nothing unusual about it; everyone has seen this effect when the waves from two stones that are dropped into a lake in different places overlap. The difference between this experiment and the previous one is easily explained by saying that while the bullets each went through only one slit, the waves each went through both slits and were thus able to interfere with themselves.

Now try the experiment with electrons. Recall that electrons are negatively charged particles that make up the outer layers of the atom. Certainly they could only go through one slit at a time, so their pattern should look like that of the bullets, right? Let's find out. (NOTE: to actually perform this exact experiment would take detectors more advanced then any on earth at this time. However, the experiments have been done with neutron beams and the results were the same as those presented here. A slightly different experiment was done to show that electrons would behave the same way . For reasons of familiarity, we speak of electrons here instead of neutrons.) Place an electron gun at the originating point and an electron detector in the detector place. First try opening only one slit, then just the other. The results are just like those of the bullets and the waves. Now open both slits. The result is just like the waves.

There must be some explanation. After all, an electron couldn't go through both slits. Instead of a continuous stream of electrons, let's turn the electron gun down so that at any one time only one electron is in the experiment. Now the electrons won't be able to cause trouble since there is no one else to interfere with. The result should now look like the bullets. But it doesn't! It would seem that the electrons do go through both slits. 

This is indeed a strange occurrence; we should watch them ourselves to make sure that this is indeed what is happening. So, we put a light behind the wall so that we can see a flash from the slit that the electron went through, or a flash from both slits if it went through both. Try the experiment again. As each electron passes through, there is a flash in only one of the two slits. So they do only go through one slit! But something else has happened too: the result now looks like the result of the bullets experiment!

Obviously the light is causing problems. Perhaps if we turned down the intensity of the light, we would be able to see them without disturbing them. When we try this, we notice first that the flashes we see are the same size. Also, some electrons now get by without being detected. This is because light is not continuous but made up of particles called photons. Turning down the intensity only lowers the number of photons given out by the light source.The particles that flash in one slit or the other behave like the bullets, while those that go undetected behave like waves.

Well, we are not about to be outsmarted by an electron, so instead of lowering the intensity of the light, why don't we lower the frequency. The lower the frequency the less the electron will be disturbed, so we can finally see what is actually going on. Lower the frequency slightly and try the experiment again. We see the bullet curve. After lowering it for a while, we finally see a curve that looks somewhat like that of the waves! There is one problem, though. Lowering the frequency of light is the same as increasing it's wavelength, and by the time the frequency of the light is low enough to detect the wave pattern the wavelength is longer then the distance between the slits so we can no longer see which slit the electron went through. 

So have the electrons outsmarted us? Perhaps, but they have also taught us one of the most fundamental lessons in quantum physics - an observation is only valid in the context of the experiment in which it was performed. If you want to say that something behaves a certain way or even exists, you must give the context of this behavior or existence since in another context it may behave differently or not exist at all. We can't just say that an electron is a particle, since we have already seen proof that this is not always the case. We can only say that when we observe the electron in the two slit experiment it behaves like a particle. To see how it would behave under different conditions, we must perform a different experiment.

The Copenhagen Interpretation

So sometimes a particle acts like a particle and other times it acts like a wave. So which is it? According to Niels Bohr, who worked in Copenhagen when he presented what is now known as the Copenhagen interpretation of quantum theory, the particle is what you measure it to be. When it looks like a particle, it is a particle. When it looks like a wave, it is a wave. Furthermore, it is meaningless to ascribe any properties or even existence to anything that has not been measured. Bohr is basically saying that nothing is real unless it is observed.

While there are many other interpretations of quantum physics, all based on the Copenhagen interpretation, the Copenhagen interpretation is by far the most widely used because it provides a "generic" interpretation that does not try to say any more then can be proven. Even so, the Copenhagen interpretation does have a flaw that we will discuss later. Still, since after 70 years no one has been able to come up with an interpretation that works better then the Copenhagen interpretation, that is the one we will use. We will discuss one of the alternatives later.

The Wave Function

In 1926, just weeks after several other physicists had published equations describing quantum physics in terms of matrices, Erwin Schrödinger created quantum equations based on wave mathematics, a mathematical system that corresponds to the world we know much more then the matrices. After the initial shock, first Schrödinger himself then others proved that the equations were mathematically equivalent. Bohr then invited Schrödinger to Copenhagen where they found that Schrödinger's waves were in fact nothing like real waves. For one thing, each particle that was being described as a wave required three dimensions. Even worse, from Schrödinger's point of view, particles still jumped from one quantum state to another; even expressed in terms of waves space was still not continuous. Upon discovering this, Schrödinger remarked to Bohr that "Had I known that we were not going to get rid of this damned quantum jumping, I never would have involved myself in this business."

Unfortunately, even today people try to imagine the atomic world as being a bunch of classical waves. As Schrödinger found out, this could not be further from the truth. The atomic world is nothing like our world, no matter how much we try to pretend it is. In many ways, the success of Schrödinger's equations has prevented people from thinking more deeply about the true nature of the atomic world.

The Collapse of the Wave Function

So why bring up the wave function at all if it hampers full appreciation of the atomic world? For one thing, the equations are much more familiar to physicists, so Schrödinger's equations are used much more often then the others. Also, it turns out that Bohr liked the idea and used it in his Copenhagen interpretation. Remember our experiment with electrons? Each possible route that the electron could take, called a ghost, could be described by a wave function. As we shall see later, the "damned quantum jumping" insures that there are only a finite, though large, number of possible routes. When no one is watching, the electron take every possible route and therefore interferes with itself. However, when the electron is observed, it is forced to choose one path. Bohr called this the "collapse of the wave function". The probability that a certain path will be chosen when the wave function collapses is, essentially, the square of the path's wave function.

Bohr reasoned that nature likes to keep it possibilities open, and therefore follows every possible path. Only when observed is nature forced to choose only one path, so only then is just one path taken.

The Uncertainty Principle

Wait a minute… probability??? If we are going to destroy the wave pattern by observing the experiment, then we should at least be able to determine exactly where the electron goes. Newton figured that much out back in the early eighteenth century; just observe the position and momentum of the electron as it leaves the electron gun and we can determine exactly where it goes.

Well, fine. But how exactly are we to determine the position and the momentum of the electron? If we disturb the electrons just in seeing if they are there or not, how are we possibly going to determine both their position and momentum? Still, a clever enough person, say Albert Einstein, should be able to come up with something, right?

Unfortunately not. Einstein did actually spend a good deal of his life trying to do just that and failed. Furthermore, it turns out that if it were possible to determine both the position and the momentum at the same time, Quantum Physics would collapse. Because of the latter, Werner Heisenberg proposed in 1925 that it is in fact physically impossible to do so. As he stated it in what now is called the Heisenberg Uncertainty Principle, if you determine an object's position with uncertainty x, there must be an uncertainty in momentum, p, such that xp > h/4pi, where h is Planck's constant (which we will discuss shortly). In other words, you can determine either the position or the momentum of an object as accurately as you like, but the act of doing so makes your measurement of the other property that much less. Human beings may someday build a device capable of transporting objects across the galaxy, but no one will ever be able to measure both the momentum and the position of an object at the same time. This applies not only to electrons but also to objects such as tennis balls and toasters, though for these objects the amount of uncertainty is so small compared to there size that it can safely be ignored under most circumstances.

The EPR Experiment

"God does not play dice" was Albert Einstein's reply to the Uncertainty Principle.Thus being his belief, he spent a good deal of his life after 1925 trying to determine both the position and the momentum of a particle. In 1935, Einstein and two other physicists, Podolski and Rosen, presented what is now known as the EPR paper in which they suggested a way to do just that. The idea is this: set up an interaction such that two particles are go off in opposite directions and do not interact with anything else. Wait until they are far apart, then measure the momentum of one and the position of the other. Because of conservation of momentum, you can determine the momentum of the particle not measured, so when you measure it's position you know both it's momentum and position. The only way quantum physics could be true is if the particles could communicate faster then the speed of light, which Einstein reasoned would be impossible because of his Theory of Relativity.

In 1982, Alain Aspect, a French physicist, carried out the EPR experiment. He found that even if information needed to be communicated faster then light to prevent it, it was not possible to determine both the position and the momentum of a particle at the same time.This does not mean that it is possible to send a message faster then light, since viewing either one of the two particles gives no information about the other. It is only when both are seen that we find that quantum physics has agreed with the experiment. So does this mean relativity is wrong? No, it just means that the particles do not communicate by any means we know about. All we know is that every particle knows what every other particle it has ever interacted with is doing.

The Quantum and Planck's Constant

So what is that h that was so important in the Uncertainty Principle? Well, technically speaking, it's 6.63 X 10^-34 joule-seconds. It's call Planck's constant after Max Planck who, in 1900, introduced it in the equation E=hv where E is the energy of each quantum of radiation and v is it's frequency. What this says is that energy is not continuous as everyone had assumed but only comes in certain finite sizes based on Planck's constant.

At first physicists thought that this was just a neat mathematical trick Planck used to explain experimental results that did not agree with classical physics. Then, in 1904, Einstein used this idea to explain certain properties of light--he said that light was in fact a particle with energy E=hv. After that the idea that energy isn't continuous was taken as a fact of nature - and with amazing results. There was now a reason why electrons were only found in certain energy levels around the nucleus of an atom . Ironically, Einstein gave quantum theory the push it needed to become the valid theory it is today, though he would spend the rest of his lift trying to prove that it was not a true description of nature.

Also, by combining Planck's constant, the constant of gravity, and the speed of light, it is possible to create a quantum of length (about 10^-35meter) and a quantum of time (about 10^-43 sec), called, respectively, Planck's length and Planck's time. While saying that energy is not continuous might not be too startling to the average person, since what we commonly think of as energy is not all that well defined anyway, it is startling to say that there are quantities of space and time that cannot be broken up into smaller pieces. Yet it is exactly this that gives nature a finite number of routes to take when an electron interferes with itself. 

Although it may seem like the idea that energy is quantized is a minor part of quantum physics when compared with ghost electrons and the uncertainty principle, it really is a fundamental statement about nature that caused everything else we've talked about to be discovered. And it is always true. In the strange world of the atom, anything that can be taken for granted is a major step towards an "atomic world view". 

Schrödinger's Cat

Remember a while ago I said there was a problem with the Copenhagen interpretation? Well, you now know enough of what quantum physics isto be able to discuss what it isn't, and by far the biggest thing it isn't is complete. Sure, the math seems to be complete, but the theory includes absolutely nothing that would tie the math to any physical reality we could imagine. Furthermore, quantum physics leaves us with a rather large open question: what is reality? The Copenhagen interpretation attempts to solve this problem by saying that reality is what is measured. However, the measuring device itself is then not real until it is measured. The problem, which is known as the measurement problem, is when does the cycle stop? 

Remember that when we last left Schrödinger he was muttering about the "damned quantum jumping." He never did get used to quantum physics, but, unlike Einstein, he was able to come up with a very real demonstration of just how incomplete the physical view of our world given by quantum physics really is. Imagine a box in which there is a radioactive source, a Geiger counter (or anything that records the presence of radioactive particles), a bottle of cyanide, and a cat. The detector is turned on for just long enough that there is a fifty-fifty chance that the radioactive material will decay. If the material does decay, the Geiger counter detects the particle and crushes the bottle of cyanide, killing the cat. If the material does not decay, the cat lives. To us outside the box, the time of detection is when the box is open. At that point, the wave function collapses and the cat either dies or lives. However, until the box is opened, the cat is both dead and alive.

On one hand, the cat itself could be considered the detector; it's presence is enough to collapse the wave function. But in that case, would the presence of a rat be enough? Or an ameba? Where is the line drawn? On the other hand, what if you replace the cat with a human (named "Wigner's friend" after Eugene Wigner, the physicist who developed many derivations of the Schrödinger's cat experiment). The human is certainly able to collapse the wave function, yet to us outside the box the measurement is not taken until the box is opened. If we try to develop some sort of "quantum relativity" where each individual has his own view of the world, then what is to prevent the world from getting "out of sync" between observers? 

While there are many different interpretations that solve the problem of Schrödinger’s Cat, one of which we will discuss shortly, none of them are satisfactory enough to have convinced a majority of physicists that the consequences of these interpretation s are better then the half dead cat. Furthermore, while these interpretations do prevent a half dead cat, they do not solve the underlying measurement problem. Until a better intrepretation surfaces, we are left with the Copenhagen interpretation and it's half dead cat. We can certainly understand how Schrödinger feels when he says, "I don't like it, and I'm sorry I ever had anything to do with it." Yet the problem doesn't go away; it is just left for the great thinkers of tomorrow.

The Infinity Problem

There is one last problem that we will discuss before moving on to the alternative interpretation. Unlike the others, this problem lies primarily in the mathematics of a certain part of quantum physics called quantum electrodynamics, or QED. This branch of quantum physics explains the electromagnetic interaction in quantum terms. The problem is, when you add the interaction particles and try to solve Schrödinger's wave equation, you get an electron with infinite mass, infinite energy, and infinite charge. There is no way to get rid of the infinities using valid mathematics, so, the theorists simply divide infinity by infinity and get whatever result the guys in the lab say the mass, energy, and charge should be. Even fudging the math, the other results of QED are so powerful that most physicists ignore the infinities and use the theory anyway . As Paul Dirac, who was one of the physicists who published quantum equations before Schrödinger, said, "Sensible mathematics involves neglecting a quantity when it turns out to be small - not neglecting it just because it is infinitely great and you do not want it!". 

Many Worlds

One other interpretation, presented first by Hugh Everett III in 1957, is the many worlds or branching universe interpretation. In this theory, whenever a measurement takes place, the entire universe divides as many times as there are possible outcomes of the measurement. All universes are identical except for the outcome of that measurement . Unlike the science fiction view of "parallel universes", it is not possible for any of these worlds to interact with each other.

While this creates an unthinkable number of different worlds, it does solve the problem of Schrödinger's cat. Instead of one cat, we now have two; one is dead, the other alive. However, it has still not solved the measurement problem! If the universe split every time there was more then one possibility, then we would not see the interference pattern in the electron experiment. So when does it split? No alternative interpretation has yet answered this question in a satisfactory way. And so the search continues…

Watch Video:

Higgs Boson

Particle physics usually has a hard time competing with politics and celebrity gossip for headlines, but the Higgs boson has garnered some serious attention. That's exactly what happened on July 4, 2012, though, when scientists at CERN announced that they'd found a particle that behaved the way they expect the Higgs boson to behave. Maybe the famed boson's grand and controversial nickname, the "God Particle," has kept media outlets buzzing. Then again, the intriguing possibility that the Higgs boson is responsible for all the mass in the universe rather captures the imagination, too. Or perhaps we're simply excited to learn more about our world, and we know that if the Higgs boson does exist, we'll unravel the mystery a little more.

In order to truly understand what the Higgs boson is, however, we need to examine one of the most prominent theories describing the way the cosmos works: the standard model. The model comes to us by way ofparticle physics, a field filled with physicists dedicated to reducing our complicated universe to its most basic building blocks. It's a challenge we've been tackling for centuries, and we've made a lot of progress. First we discovered atoms, then protons, neutrons and electrons, and finally quarks and leptons (more on those later). But the universe doesn't only contain matter; it also contains forces that act upon that matter. The standard model has given us more insight into the types of matter and forces than perhaps any other theory we have.

Here's the gist of the standard model, which was developed in the early 1970s: Our entire universe is made of 12 different matter particles and four forces [source: European Organization for Nuclear Research]. Among those 12 particles, you'll encounter six quarks and six leptons. Quarks make up protons and neutrons, while members of the lepton family include the electron and the electron neutrino, its neutrally charged counterpart. Scientists think that leptons and quarks are indivisible; that you can't break them apart into smaller particles. Along with all those particles, the standard model also acknowledges four forces:gravity, electromagnetic, strong and weak.

As theories go, the standard model has been very effective, aside from its failure to fit in gravity. Armed with it, physicists have predicted the existence of certain particles years before they were verified empirically. Unfortunately, the model still has another missing piece -- the Higgs boson. What is it, and why is it necessary for the universe the standard model describes to work? Let's find out.

Higgs Boson: The Final Piece of the Puzzle

As it turns out, scientists think each one of those four fundamental forces has a corresponding carrier particle, or boson, that acts upon matter. That's a hard concept to grasp. We tend to think of forces as mysterious, ethereal things that straddle the line between existence and nothingness, but in reality, they're as real as matter itself.

Some physicists have described bosons as weights anchored by mysteriousrubber bands to the matter particles that generate them. Using this analogy, we can think of the particles constantly snapping back out of existence in an instant and yet equally capable of getting entangled with other rubber bands attached to other bosons (and imparting force in the process).

Scientists think each of the four fundamental ones has its own specific bosons. Electromagnetic fields, for instance, depend on the photon to transit electromagnetic force to matter. Physicists think the Higgs boson might have a similar function -- but transferring mass itself.

Can't matter just inherently have mass without the Higgs boson confusing things? Not according to the standard model. But physicists have found a solution. What if all particles have no inherent mass, but instead gain mass by passing through a field? This field, known as a Higgs field, could affect different particles in different ways. Photons could slide through unaffected, while W and Z bosons would get bogged down with mass. In fact, assuming the Higgs boson exists, everything that has mass gets it by interacting with the all-powerful Higgs field, which occupies the entire universe. Like the other fields covered by the standard model, the Higgs one would need a carrier particle to affect other particles, and that particle is known as the Higgs boson.

On July 4, 2012, scientists working with the Large Hadron Collider (LHC) announced their discovery of a particle that behaves the way the Higgs boson should behave. The results, while published with a high degree of certainty, are still somewhat preliminary. Some researchers are calling the particle "Higgslike" until the findings -- and the data -- stand up to more scrutiny. Regardless, this finding could usher in a period of rapid discovery about our universe.

Watch Video:

General Relativity

General relativity was Einstein’s theory of gravity, published in 1915, which extended special relativity to take into account non-inertial frames of reference — areas that are accelerating with respect to each other. General relativity takes the form of field equations, describing the curvature of space-time and the distribution of matter throughout space-time. The effects of matter and space-time on each other are what we perceive as gravity.

The theory of the space-time continuum already existed, but under general relativity Einstein was able to describe gravity as the bending of space-time geometry. Einstein defined a set of field equations,which represented the way that gravity behaved in response to matter in space-time. These field equations could be used to represent the geometry of space-time that was at the heart of the theory of general relativity.

As Einstein developed his general theory of relativity, he had to refine the accepted notion of the space-time continuum into a more precise mathematical framework. He also introduced another principle, the principle of covariance. This principle states that the laws of physics must take the same form in all coordinate systems.

In other words, all space-time coordinates are treated the same by the laws of physics — in the form of Einstein’s field equations. This is similar to the relativity principle, which states that the laws of physics are the same for all observers moving at constant speeds. In fact, after general relativity was developed, it was clear that the principles of special relativity were a special case.

Einstein’s basic principle was that no matter where you are — Toledo, Mount Everest, Jupiter, or the Andromeda galaxy — the same laws apply. This time, though, the laws were the field equations, and your motion could very definitely impact what solutions came out of the field equations.

Applying the principle of covariance meant that the space-time coordinates in a gravitational field had to work exactly the same way as the space-time coordinates on a spaceship that was accelerating. If you’re accelerating through empty space (where the space-time field is flat, as in the left picture of this figure), the geometry of space-time would appear to curve. This meant that if there’s an object with mass generating a gravitational field, it had to curve the space-time field as well (as shown in the right picture of the figure).

Without matter, space-time is flat (left), but it curves when matter is present (right).

In other words, Einstein had succeeded in explaining the Newtonian mystery of where gravity came from! Gravity resulted from massive objects bending space-time geometry itself.

Because space-time curved, the objects moving through space would follow the “straightest” path along the curve, which explains the motion of the planets. They follow a curved path around the sun because the sun bends space-time around it.

Again, you can think of this by analogy. If you’re flying by plane on Earth, you follow a path that curves around the Earth. In fact, if you take a flat map and draw a straight line between the start and end points of a trip, that would not be the shortest path to follow. The shortest path is actually the one formed by a “great circle” that you’d get if you cut the Earth directly in half, with both points along the outside of the cut. Traveling from New York City to northern Australia involves flying up along southern Canada and Alaska — nowhere close to a straight line on the flat maps we’re used to.

Similarly, the planets in the solar system follow the shortest paths — those that require the least amount of energy — and that results in the motion we observe.

In 1911, Einstein had done enough work on general relativity to predict how much the light should curve in this situation, which should be visible to astronomers during an eclipse.

When he published his complete theory of general relativity in 1915, Einstein had corrected a couple of errors and in 1919, an expedition set out to observe the deflection of light by the sun during an eclipse, in to the west African island of Principe. The expedition leader was British astronomer Arthur Eddington, a strong supporter of Einstein.

Eddington returned to England with the pictures he needed, and his calculations showed that the deflection of light precisely matched Einstein’s predictions. General relativity had made a prediction that matched observation.

Albert Einstein had successfully created a theory that explained the gravitational forces of the universe and had done so by applying a handful of basic principles. To the degree possible, the work had been confirmed, and most of the physics world agreed with it. Almost overnight, Einstein’s name became world famous. In 1921, Einstein traveled through the United States to a media circus that probably wasn’t matched until the Beatlemania of the 1960s.

Watch Video:

Black Holes

What Is a Black Hole?

A black hole is a place in space where gravity pulls so much that even light can not get out. The gravity is so strong because matter has been squeezed into a tiny space. This can happen when a star is dying.

Because no light can get out, people can't see black holes. They are invisible. Space telescopes with special tools can help find black holes. The special tools can see how stars that are very close to black holes act differently than other stars.

A black hole is a region of space-time from which nothing can escape, even light.

To see why this happens, imagine throwing a tennis ball into the air. The harder you throw the tennis ball, the faster it is travelling when it leaves your hand and the higher the ball will go before turning back. If you throw it hard enough it will never return, the gravitational attraction will not be able to pull it back down. The velocity the ball must have to escape is known as the escape velocity and for the earth is about 7 miles a second.

As a body is crushed into a smaller and smaller volume, the gravitational attraction increases, and hence the escape velocity gets bigger. Things have to be thrown harder and harder to escape. Eventually a point is reached when even light, which travels at 186 thousand miles a second, is not travelling fast enough to escape. At this point, nothing can get out as nothing can travel faster than light. This is a black hole.

Do they really exist?

It is impossible to see a black hole directly because no light can escape from them; they are black. But there are good reasons to think they exist.
When a large star has burnt all its fuel it explodes into a supernova. The stuff that is left collapses down to an extremely dense object known as a neutron star. We know that these objects exist because several have been found using radio telescopes.
If the neutron star is too large, the gravitational forces overwhelm the pressure gradients and collapse cannot be halted. The neutron star continues to shrink until it finally becomes a black hole. This mass limit is only a couple of solar masses, that is about twice the mass of our sun, and so we should expect at least a few neutron stars to have this mass. (Our sun is not particularly large; in fact it is quite small.)
A supernova occurs in our galaxy once every 300 years, and in neighbouring galaxies about 500 neutron stars have been identified. Therefore we are quite confident that there should also be some black holes.

How Big Are Black Holes?
Black holes can be big or small. Scientists think the smallest black holes are as small as just one atom. These black holes are very tiny but have the mass of a large mountain. Mass is the amount of matter, or "stuff," in an object.

Another kind of black hole is called "stellar." Its mass can be up to 20 times more than the mass of the sun. There may be many, many stellar mass black holes in Earth's galaxy. Earth's galaxy is called the Milky Way.

The largest black holes are called "supermassive." These black holes have masses that are more than 1 million suns together. Scientists have found proof that every large galaxy contains a supermassive black hole at its center. The supermassive black hole at the center of the Milky Way galaxy is called Sagittarius A. It has a mass equal to about 4 million suns and would fit inside a very large ball that could hold a few million Earths.

How Do Black Holes Form?
Scientists think the smallest black holes formed when the universe began.

Stellar black holes are made when the center of a very big star falls in upon itself, or collapses. When this happens, it causes a supernova. A supernova is an exploding star that blasts part of the star into space.

Scientists think supermassive black holes were made at the same time as the galaxy they are in.

If Black Holes Are "Black," How Do Scientists Know They Are There?
A black hole can not be seen because strong gravity pulls all of the light into the middle of the black hole. But scientists can see how the strong gravity affects the stars and gas around the black hole. Scientists can study stars to find out if they are flying around, or orbiting, a black hole.

When a black hole and a star are close together, high-energy light is made. This kind of light can not be seen with human eyes. Scientists use satellites and telescopes in space to see the high-energy light.

Could a Black Hole Destroy Earth?
Black holes do not go around in space eating stars, moons and planets. Earth will not fall into a black hole because no black hole is close enough to the solar system for Earth to do that.

Even if a black hole the same mass as the sun were to take the place of the sun, Earth still would not fall in. The black hole would have the same gravity as the sun. Earth and the other planets would orbit the black hole as they orbit the sun now.

The sun will never turn into a black hole. The sun is not a big enough star to make a black hole.


Watch Videos:

1.

2.

3.