Posted on 12/20/2001 5:17:16 AM PST by Father Wu
Teleportation is a name given by science fiction writers to a procedure in which an object disappears in one place and reappears in another instantaneously (this is classic teleportation; some authors explore the possibility that the original object doesn't disappear, resulting in there being two sets of the same thing). A good analogy of how a teleporter works is that it works like a 3-D fax machine.
For a long time scientists thought that teleportation was impossible because it violated one of the basic laws of quantum mechanics (Quantum mechanics is a discipline that describes the structure of the atom and how the particles in and around an atom move and react with each other. It also explains how atoms absorb and give off electromagnetic energy. It explains that when an atom releases light energy it doesn't release it in a steady flow. Instead it releases it in bundles of energy called quanta.), called the Heisenburg Uncertainty Principle (I'll talk about this later), which says that you can never exactly copy something. Then, in 1998, an international group, made up of six scientists and centered at the University of Innsbruck, proved that classical teleportation was possible, but at the moment only possible for photons and electrons. We won't be able to teleport ourselves in the near future, but it is not impossible that one day we might be able to.
Werner Heisenburg was a great German physicist who is best remembered for his contributions to quantum theory. He was born on December 5, 1901 in Wuzburg, Germany. He studied under Arnold Sommerfeld and earned his doctorate in 1923. For three after this he worked with Niels Bohr in Copenhagen. During most of this time he was working on the problem of how to describe the path of an electron using a matrix, which is a set of numbers use to plot the path of something. He was awarded the Nobel Physics Prize for his work in 1932.
He discovered the Uncertainty Principle in 1927, one of his most important pieces of work. The U.P. (Uncertainty Principle), summarized, states that one cannot know the exact position of something and its velocity (all this would tell you exactly where the object would be any given time) at the same time. You can find out one or the other, but you can never know both. This rule holds true for the most accurate measurements that we can take. The principle works because with each measurement that you take you disrupt the particle's path and the path of the particle that you used to measure the object. So, you can never accurately get both the position and velocity of an object due to the disruption caused by the measurement.
Another part of the U.P. states that the more accurately an object is scanned the more it is disrupted (this relates to the first part of the theory). This eventually causes the object to become completely disrupted before the scan is complete.
This has always been a stumbling block for scientists who are trying to find a solution to teleportation, because to teleport an object you first have to completely scan the object before teleporting it; but the Innsbruck team found a way of getting around this by using another aspect of quantum theory called the Einstein-Poldosky-Rosen Effect, or entanglement. Albert Einstein, Boris Podolsky, and Nathan Rosen discussed this effect in a paper. When two particles are entangled (say a pair of photons), the share the same properties at all times. If you entangled a pair of die, the dice would always turn up on the same number, no matter how far away they were from each other. And the number would still be completely random. Einstein called entanglement a "spooky action at a distance".
For many years it was thought that entanglement had no use, other than to prove the quantum theory, because quantum mechanics was the only field that could explain the bizarre behavior.
The Innsbruck team used the EPR Effect to bypass HUP by entangling the object to be teleported. That way all the unscanned information in the object would be passed to the teleported object through EPR.
The form of quantum teleportation that the scientists at Innsbruck came up with works like this. Alice wants to teleport an object A to her friend Bob. To do this she firsts entangles objects B and C. The n she sends object C to Bob. Once she knows Bob has object C she scans objects A and B together. This disrupts both of them and causes B's state to become equal to A's state (this part is difficult to comprehend). Now since A=B and B=C, A=C. Once this is done the scanned information is sent to Bob by conventional means (radio, ex.) and Bob processes object A, formerly object C, accordingly. In the scanning process the original object A is destroyed, ending in only one copy of object A, a classical teleportation.
This differs from a classical fax in that the original copy is destroyed in the process. Another major difference between the two is that teleportation takes three objects instead of just two.
The first action in the teleportation experiments done by the Innsbruck group is to create two entangled particles. This is done by sending a pulse of ultraviolet light through a type of crystal called a calcite crystal. This type of crystal is called a "non-linear crystal", probably because it splits photons (I wasn't able to find the definition). Inside of the crystal the UV photon is split into two photons whose polarization is entangled (polarization is the electrical charge of the photon. The polarization constantly changes). These first two photons are photons (objects) B and C. After the photons exit the crystal the UV pulse is reflected back through the crystal, while B and C are reflected to different stations. Photon C goes on to the receiving station where the teleported object will end up. Photon B is directed to the sending station. The pair of entangled photons are detected and the experiment starts. When the UV pulse is reflected back through the crystal photon A is created. A is sent to the sending station where a Bell-State measurement is performed on it and on photon B at the same time. A Bell-State measurement is the type of measurement the changes the state of C into the state of A. During the measurement A is scanned and the information is sent to the receiving station. There is a 25% chance that photon C will turn out exactly like A. So if the polarization is determined to be not the same polarization as A was it is sent through a crystal that will rotate its polarization until it matches A's (A's polarization could have been up, down, right, or left). The process has not been perfected yet and has a success rate of 75%.
The future of quantum computing is a promising one. Unfortunately, we won't be able to teleport humans in the foreseeable future. This is for a variety of reasons, all of them engineering. One of the problems is that the object to be teleported has to be completely isolated. That would be hard to do with a living organism. Another problem would be entangling the objects, although it could be done with large objects. Entanglement has already been demonstrated with Buckyballs, molecules made up of 60 atoms of carbon.
One of the most promising aspects of quantum teleportation would be in the field of quantum computing. Quantum computing is an experimental field of computing that uses atoms and molecules as bits. It is ultra-fast, about 1x10^9 times faster than today's super computers (the most powerful computer in the world could download the entire Internet in 2 seconds). This means that it would take a quantum computer 1 year for something that would take a conventional computer 1,000,000,000 years. Quantum computers have another advantage over conventional machines. Conventional computers will eventually hit physical limits or the facilities used to manufacture them will become too expensive to build.
Nobody thought much about the theory of quantum computing until 1994. A scientist named Peter Shor at AT&T discovered that how you could factor the prime factors of a number using a quantum computer much faster than with a conventional computer. The discovery fascinated scientists and horrified the security industry. It started off a wave of research in the field.
The great speed of quantum computers comes from the way they use atoms for qubits, or quantum bits. Unlike conventional computers a single qubit can represent more than one conventional bit. This is called superposition, or one thing representing more objects or ideas than just it. Qubits can do this because the atom or molecule that it is made up of can be made up of usually have more than one characteristic (ex. Electrical charge, spin axis, etc.) that fluctuate. Scientists control and measure the effects of these characteristics. They then are able to transform them into an extremely powerful computer.
In 1996 Neil Gershenfeld set out to build a quantum computer with a group at the University of California. Their first problem was to find a material that could be completely isolated and could have information entered, calculated, and measured with out decoherence occurring (decoherence occurs when an object or substance that is totally isolated interacts with outside forces or objects. This would cause calculation to become impossible in a quantum computer. It's like you were reading a book and then somebody started changing the script, ripping out some pages, added in new ones, and scribbled over other pages). The group then realized that liquids would be perfect, instead of isolating a single atom or molecule (this is for a very low powered quantum computer). Since all the molecules or atoms in the liquid would be the exact same, it wouldn't matter if the molecules interacted during the computations.
An atom's nucleus is constantly spinning like a gyroscope. The direction of the spin of the nucleus of an atom depends on the outside magnetic forces that are influencing it (like a magnet). The spin can either be parallel with the magnetic field (this would be like a gyroscope spinning on top of your finger, right side up) or anti-parallel (this is like a gyroscope spinning on your finger upside down). Now, when you apply an outside magnetic field, the spin axis of the nucleus will spin (like a gyroscope starting to wobble on your finger). If you turn a magnetic field on and off very fast it will cause the spin axis to completely rotate (you could rotate the spin axis 90 degrees or 180 degrees; it just depends on how long and how fast you turn the magnet off and on). Then, when you turn the magnet off the spins go out of alignment, until the magnet is turned on again. When the spins go out of alignment the atoms lose energy, which they emit in the form of radio waves. So if you rotated a spin 90 degrees it would give off a different amount of energy than if it had been rotated 180 degrees. The radio signals are picked up and translated by the same device that sent out the magnetic field. This process of manipulating and reading the energy emitted from the atoms is called NMR or Nuclear Magnetic Resonance. It works exactly like a MRI does. Different frequencies of NMR affect atoms of different elements in different ways. Like a hydrogen atom might remain the same while a carbon atom is rotated.
In QC (quantum computing) the spin of an atom (parallel, 90 degrees, anti-parallel, and anti-parallel 90 degrees) stands for a qubit. Parallel equals 0,0, ninety degrees equals 0,1, anti-parallel equals 1,1, and anti-parallel 90 degrees equals 1,0. Scientists measure the energy levels emitted by the atoms and are able to tell what qubit an atom represents.
Another thing the spins of an atom are affected by is the spin of its neighboring atom. In molecules atoms of different atoms are often side by side. In the molecule of chlorophyll (CHCl3) the spin of the carbon atom is dictated by the spin of the hydrogen atom next to it. This could have been a liability to deal with while designing a qc (quantum computer) but instead it forms the basic unit of computing, called the logic gate. In a computer a logic gate data is processed. Microchips are made up of logic gates. The interactions of the carbon and hydrogen atom forms a type of logic gate, the exclusive-OR logic gate. This is sometimes called the controlled-NOT gate. A NOT logic gate is the simplest type of logic gate. All it does is inverts the input. On a controlled-NOT gate the output depends on the state of the inverter (the output will be different depending on the spin of the hydrogen atom). Once the spin of the carbon atom has been inverted it sends out a radio signal which the operator of translates into the output.
Using an array of these devices that are all coordinated together it would be possible to create a super supercomputer, billion times faster than today's super computers.
Quantum teleportation might eventually be used for transferring information between logic gates. It will be a while before we will be able to build a quantum computer that is fast enough to compete with today's fastest computers, but it will definitely be worth the wait. One huge advantage to qc is that they are much easier and cheaper to manufacture than conventional computers.
Ah yes, and its a good thing to or Causality woulda been whacked!
I will admit that in theory, at least, you can have unlimited dimensions (otherwise, why calculus?). The calculus to which you refer is useful even in one dimension. It’s full name is the Calculus of Infinitesimals, reminding us that it really does not address the dimensionality. There are, of course, other calculi, such as vector and tensor ones, for which the dimensionality is of the essence.
Lunch break, errand running... But I see we have much to discuss. I will try to post a more complete explanation later
Lafroste
Here's an interesting thought. Considering 1/n: if n=0 1/n= infinity. As n approaches infinity 1/n become infinitely close to zero. Almost an inverse relationship. I've often wondered how the concept of limits and infinite series (Taylor's and Mclaurens Theorems) could be applied to physics.
How would one build a 2-d object and interact with it? (will I need a soldering iron?) How does going from 3-d space to 2-d space make teleportation possible? Hmmmmm.
/john
And I was trying to tell you that this is not the case.
Regarding your post referring to potential and kinetic energy, I was and am talking only of potential energy related to gravitational fields, ie. E=mgh. Whether or not this holds true in other potential systems remains to be seen (for that matter it remains to be seen whether it holds in this one lone case as well). Anyway, I view potential energy as nonsense because it is a manifestation of a deeper phenomenon (keep in mind, this is ALL MHO). Specifically, an object's potential energy does not increase (or decrease) as it moves through a gravity field, indeed the object's energy state does not change at all. What is changing is the space around it. The object's rest mass (E=mc^2) is constant in all situations and exists independently of the generally recognized 4 dimensions, but its apparent energy state changes as the space around it changes.
More specifically, time is the variable. The apparent 4-D energy state is modified in such a way as to satisfy the 5-D equality. Time slows down as you approach a massive body (the extreme being the event horizon of a black hole, where time stops completely) and presumably speeds up to some (scalar) constant at a point in space very far from any mass. However, time is nearly never treated as a variable; for example V= dx/dt implicitly implies that t is constant. If t is a variable then the above expression needs to be reworked to take that into account. Possibly dx/dt = dx/dQ//dt/dQ, but I am still working on the function Q. But I digress...
As far as Einsteinian mechanics goes then, this explains (for example) why light always appears to proceed from a source at c regardless of the source's velocity. What is happening is that when the source speeds up, its time slows down precisely enough to maintain the illusion of c, which also demonstrates that mass, and light are independent of time, but more importantly are different aspects of the same phenomenon (hence, E=mc^2, which demonstrates that).
If you play with it some more you can come up with alot of other interesting implications, such as:
1. The universal gravitational constant is neither universal nor constant, but varies;
2. Definition of an absolute reference system is possible (bye-bye relativity, hello absolutivity); and
3. gravity can be artificially produced by manipulating time fields.
Hope this helps, now that you are convinced I am a whack-job.
Specifically, an object's potential energy does not increase (or decrease) as it moves through a gravity field, indeed the object's energy state does not change at all. Firstly, “object's potential energy” is a rare but true example of imprecision of speech that penetrated physics. We must keep in mind that the object does not have any potential energy: it is the system comprised of the Earth and the object that has U=mgh.
Secondly, if the aforementioned system is closed, then the total energy does not change, but the potential energy does. This is why a ball moves faster as it falls to the ground.
What is changing is the space around it. Now you appear to step into the General Relativity, where no one would use U=mgh (it is an approximation even in classical mechanics applicable to small distances only.
The object's rest mass… is constant in all situations and exists independently of the generally recognized 4 dimensions. The object’s mass is merely a proportionality constant in the expression for kinetic energy T = m (v^2 /2). The factor m in the expression U = m g h is not even the same mass. None of them hover, has anything to do with the dimensionality of the space-time.
More specifically, time is the variable... However, time is nearly never treated as a variable; for example V= dx/dt implicitly implies that t is constant I am sorry to disagree but the expression dt is a time increment If anything, limits (of which the derivative dx/dt is one) involve variables, not constants. As far as Einsteinian mechanics goes then… What is happening is that when the source speeds up, its time slows down precisely enough to maintain the illusion of c, which also demonstrates that mass, and light are independent of time… The constancy of the speed of light is an assumption of the Theory of Relativity. It is made to describe even a universe with one particle. It happens to agree with the empirical evidence, which is why this assumption is accepted.
If you play with it some more you can come up with alot of other interesting implications, such as: 1. The universal gravitational constant is neither universal nor constant, but varies; 2. Definition of an absolute reference system is possible (bye-bye relativity, hello absolutivity); and 3. gravity can be artificially produced by manipulating time fields. It is very commendable that you tackles fundamental issues such as these – few people have courage to do that. But I am afraid the devil here in the details, some of which I have outlined above.
Regards, TQ.
Well, maybe the date and maybe the location, but not both!
While the (x,y,z) dimensions are global in effect, time is local in effect. Whatever space you are using, local means "in the vicinity of a given point." The word "vicinity" is refined somewhat differently within differential geometry and topology (even here it can have different meanins), but the essense is the same. When understood thusly, time is not local but relative --- to the reference frame. Within that frame is is not local.
I do not mean to put words in your mouth and cannot deduce myself the precise meaning of your words, but you appear to confuse time with intervals therof: it is the intervals between the same world events that differ in different frames. If a frame is falling into a black hole, the intervals of time, as measures with respect to it, indeed become greater.
In any case, I do not mean to broaden our discussion too much. I was trying to point out the role of the red shift in your statement.
Regards, TQ.
The question then is: "Is time a dimension?" Yes, of course.
If it is, it is a variable one, unlike spatial dimensions. Dimensions do not vary. Geometry may, but dimensions do not vary.
I guess it really boils down to what exactly constitutes a dimension. By definition:
The dimension of a module over a ring is the maximal number of its elements that are linearly independent.It is then proven that this number does not depend on the choice of the elements, hence indeed the property (invariant) of the module.
In geometry, and in Relativity Theory in particular, this is applied to linear spaces over fields of real or complex numbers, in which case the elements of the module (space) are called vectors.
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