Quantum entanglement is an absurdly simplistic concept but people try to make it way more complex than it actually is.

Let’s say me and my friend decide we want to get some ice cream, so I leave the house to go get some and she stays home. Before I leave, I ask her what flavor she wants, and she says, “I don’t know, get me whatever you’re getting.”

So I go to the store and find there is only two flavors: chocolate and vanilla. I decide to flip a coin: heads—chocolate, tails—vanilla. I then text my friend and explained the situation, that there was only two flavors, and I flipped a coin to pick.

But. I forgot to actually mention what flavor I got.

So the information she has is that: (1) there are two flavors, (2) I picked one of the flavors at random, and (3) whatever flavor I picked for myself, I also picked that flavor for her.

This information is now entangled because if she knows what flavor I got for myself, she will know what flavor she is getting. If she knows what flavor she is getting, she will know what flavor I got for myself.

There are four combinations, being vanilla-vanilla, vanilla-chocolate, chocolate-vanilla, and chocolate-chocolate. But two of these combinations are not possible: vanilla-chocolate and chocolate-vanilla, because we know that whatever I got, I also got for her. We know that they are entangled so if we know one, we know the other one. It’s 50% chocolate-chocolate or 50% vanilla-vanilla.

That’s literally all entanglement is. It’s a concept in statistics and not exclusive to quantum mechanics.

Let me rephrase everything I said above now in quantum computer terms.

The simplest quantum entangled state is called a “Bell’s state”.

A normal bit is either a 0 or a 1. A “qubit” is a 0 or a 1, or anything in between. It can be, for example, 50% a 0 and 50% a 1. This is called a superposition. This means that if you measure the qubit, then it has a 50% chance of being measured as a 0, or a 50% chance of being measured as a 1.

The |0⟩ symbol is just a fancy way of writing “this qubit has a 100% chance of being measured as a 0”. The [H] there is a logic gate called a Hadamard gate. It converts the |0⟩ into a superposition that is 50% a 0 and 50% a 1, so just like our fair coin, if we measure that qubit after it passes through the Hadamard gate, it will be a 0 or a 1 with equal probability of both.

The next logic gate which looks like •---⊕ is called C-NOT or a controlled NOT gate. The qubit that passes through the ⊕ will have its state flipped, so a 0 will become a 1 but only if the qubit that passes through the • is a 1.

But we don’t know if the top qubit will be a 1 because it has a 50% chance of being a 0 and a 50% of being a 1. Meaning, whether or not the qubit on the bottom is flipped also has a 50% of being a 0 or a 50% chance of being a 1. But the only possible outcomes are 00 and 11. The outcomes 01 and 10 are impossible.

The qubits are entangled. Because if you measure one, you know the value of the other one without measuring it.

The [math](|00⟩+|11⟩)/√2[/math] expression is just a fancy way of writing “the only possible outcomes are 00 and 11 with a 50% probability of each”.

It really is this simple. Quantum entanglement is an incredibly simple concept, but people try to make it seem a lot more difficult than it really is.

Why is this incredibly simplistic concept so interesting? Because my flip of the coin is deterministic, but quantum mechanics is not. The superposition truly is random until you measure it.

In the case of the ice cream, I only didn’t know what flavor I’m getting because I lacked some information, specifically being, I lacked the information on what the coin landed on. If I knew that information, I could know the that was picked, and then predict from that the outcomes for both people.

The only reason I didn’t know what ice cream I got was because I was missing this crucial piece of information, I was missing a “hidden variable”.

Bell’s theorem, however, suggests that quantum mechanics is truly random, that there is no “hidden variable”, that until I measure the superposition, the universe hasn’t decided yet whether the qubit should be a 0 or a 1. It suggests it is fundamentally impossible to predict the outcome no matter how much information about the universe you know. (Note: I say “suggests” because it is logically possible that quantum mechanics is reducible even with Bell’s theorem.)

This is interesting because if I run two qubits through the circuit above and entangle them, then separate them by a billion light years, the universe still hasn’t decided yet if the outcome is 00 or 11. If I then collapse the superposition on one of the qubits by measuring it, I will see the outcome, and at that very moment, the outcome of the qubit a billion light years away is also determined and known. The collapse of the superposition can happen simultaneously across any distance and is instantaneous.

First let us ask the question, why don’t we ever see the original scatter pattern and magnets involved in the experiment? It might be because the evidence isn't quite the “Slam Dunk” being presented in the mainstream pop-sci articles and most college level test books and lead to hard questions about the results that most academia can not answer. Let us assume we can grasp a fairly simple scatter pattern and go beyond the math and look at all of the evidence.

To fully explain what the experiment was trying to determine one has to determine what exact prediction made. In diagram 1. The quantum prediction of two very clear either up or down scatter patterns, that is because the spins were either up or down. In diagram 2. The classical prediction had a third line because some of the axis would be pointing directly in the path and the angular momentum of both spins would cancel each other out. Diagram 3. Neither predicted what seems at first two curved canted exactly 90 degrees of the original prediction of scatter patterns.

The original Stern-Gerlach scatter plate, below left. The scatter pattern, it looks exactly like two lines with some minor anomalies. That is exactly what I saw the first time I looked at it. However there are five critical components, below right. One and Two are the two predicted lines in the middle. No problem, its just the way the magnetic fields are aligned. Just one thing, how do you explain the two directions of the curves? Did the magnetic fields change that much? Then there is the magnetic anomaly, no problem, some atoms were pulled away. Just one problem, if you look at it, it is another curved line. Then there is a critical part, that everyone has missed. Its the two uniform parts above and below the curved lines. Is that the third line that Classical Models predicted?

So why should we worry about the edges, are they not just two curved lines intersecting caused by distortions in the magnetic fields? If that was the case then the two lines would over lap as in the first image below 1, however in the plates there seems to have two lines merging as in the second image below 2. There is a simple way to rule this out either way, just redo the experiment and move the edges of the north end of the magnet further apart, while widening the path of the silver atoms so that they still pass close to the edges of the north end of the magnet. A bit of a complex suggestion, can elaborate if asked.

So what is the problem with the incorrect predictions? First off both Predictions were based on the “Incomplete” Bohr’s Atomic Model, in which the experiment was designed for and all predictions made. We need to compare the results with a modern and more complete model of the electron shells. If a dumbbell shaped P-Orbitals has just one electron and the rest have two, what does that do to the magnetic field of the atom? I would guess it makes it inhomogeneous. So the two models are going to act completely different in magnetic fields and that is with out considering the proton arrangement inside of the atom.

For a classical reinterpretation would be, we have to first have to look at the magnetic field that the silver atoms in the Stern-Gerlach Experiment passed through, see below. The little grey box in the center represents the possible paths of all the atoms passing through that inhomogeneous magnetic field. The circle represents five sliver atoms passing by each other. It is very important to note that the atoms passing at the edges have stronger fields on one side, while the center atom would have even magnetic fields of north on both sides. This particular magnetic field would almost certainly have a profound effect on alignment of the silver atoms axis of momentum.

Here is a picture of the original Stern-Gerlach Magnets, to verify this is the shape of the inhomogeneous magnetic field.

So we do not “Get lost in the math”, it requires a few simple diagrams to describe why a classical spin becomes quantized in magnetic fields; with out resorting to the straw man “Hidden Variable” that is assumed to be fixed. Trying to keep as close to the classical explanations as possible, the following diagrams describe the mechanics of classical spin.

Diagram 7. This demonstrates how a classical axis of momentum in nature become quantized by the detector. As the Atom approaches the magnetic field the axis of rotation, which is probably caused by the negatively charged electron shells, that are pushed away from the strongest parts of the magnetic field produced by the north magnet. If you take the time out to visualize this effect, it really shows up on the scatter pattern plate image. Especially with the third curved line.

Diagram 8 - Why a particle moves up or down (in relation to a north south orientation of the magnets). As the vertically oriented axis leaves the magnetic field, the forward end is in a weaker part of the field and the angular momentum of the forward end pushes it in the direction that it is moving.

Diagram 9 - This is designed to demonstrate it depends entirely on the either clockwise or counterclockwise orientation of the angular momentum to path of the Atoms as to wether the spin is up or down. Or simply stated, the spin is relative to the observer.

The diagram below is a attempt to explain why there is a curved path between the full up and down spins and the zero spins at either the end of the possible path of the atoms. So we draw a line perpendicular to the path atoms through the center of the angular momentum. As the atom leaves the magnetic field, the magnetic field would be weaker in the front and stronger behind.

- If the axis of the angular momentum is also perpendicular, all of the momentum is either up or down in front of the atom.

- If the axis is at a angle to the path, say 45 degrees, then 25% of one angular momentum is in the front and 75% is in the back. That would mean that the up and down movement is smaller.

- If the axis is parallel to the path, as in the atoms at the edges, there is fifty percent up and fifty percent down angular momentum in front of the atom. This causes the angular momentums to cancel each other out and there is no up or down movement.

So if one looks at the axis as dials that can move either way, it makes perfect sense that two up and down scatter patterns curve in on each other to merge and create a third no spin line at either edge, thereby confirming the classical model in nature that becomes quantized when you measure it.

Now while this “Ad Hoc” hypotheses hardly constitutes proof, if one takes in account both predictions were wrong and modern models can create new predictions; doubt on the original conclusions is certain and the level of confidence needed to determine this either way has not been met. We can not simply say this is settled science.

In conclusion, this discussion may of been philosophical during the nuclear and electrons age when Scientists and Technologist dealt with trillions of particles at a time; however in the age of Nanotech and Quantum computers it is critical that we know if “Spin” is classical then quantized in a magnetic field or formless and then quantized. We can not allow philosophical ideologies to dominate quantum physics or simplify the math so we are only concerned with the results. We have to start looking at spin in a scientific manner and stop mystifying it to justify our preconceived notions. Furthermore the incomplete Bell’s Theorem, which does not take in account the effect of magnetic fields on the axis of the angular momentum of a electron shell needs to be cast aside; why that is still in the textbooks is beyond me. We need to go back to the Stern-Gerlach Experiment and redo the experiment, reverse engineer, rework predictions based on modern models of electron shells and exploit every possible angle to rule out all possibilities until we have a firm grasp of what spin is.

Because any and all observation (or indeed, any interaction of any kind) affects the state of whatever you observe. Any and all interaction transfers some energy; without energy being transferred, interaction doesn’t take place, and without interaction, things will just “pass through” without ever being detected.

You see because some photons are absorbed in your eyes and converted to signals in your brain. The photons absorbed by you have been stopped from passing further.
You hear because some of the energy in the soundwaves (usually in air) gets conveyed to your body, especially the little gizmos in your ear that do some additional converting, eventually resulting in you experiencing sound in your mind (though you can also feel some of the stronger, lower soundwaves with your entire body). If you were not there, the soundwaves would still have a notch more power.
You feel cold or hot depending on whether energy gets taken from or added to (or accumulates in) your body. The environment is either colder or warmer because you’re there.
You feel pressure because you’re pushing or being pushed against. Once again, the general energy levels of the system get perturbed.

Measuring equipment follows the same laws — cameras capture because they absorb photons, microphones have bits of them vibrated by soundwaves which lose energy in the process…

But what if we’re trying to measure something that’s really, really “tiny”? Like a single photon? In other words, something that either is, or gets very close to being a quantum of something (a quantum being effectively the least amount of something there can be — for instance, a single photon being a quantum of light or EM)? In other words, observing something on the quantum scale?

Since a quantum is the least amount of something there can be (according to what we know and by definition), and we need to either give or receive energy to interact, and thus observe … we are giving or taking energy from the thing we’re trying to observe. So it’s fundamentally impossible to not drastically affect the state of the quantum object we’re observing.

A table might not change that much as a whole because we turned on a lamp and “bounced off” some photons from it. It will be a tiny bit warmer and otherwise more energetic, but it will still fit within the state of being a table (unless you use a really, really powerful lamp and end up setting it on fire). But if you try to measure something which’s entire being is, or is very close to “the least that can actually do something” … trying to observe it can (and does) change its entire being.

It doesn't.

The phenomenon referred to here as "space quantization" is something of a misnomer if you simply read those words with the natural meaning they would seem to have today, rather than reading the words as they were understood when the Stern-Gerlach experiment was done.

It is actually a form of angular momentum quantization that is really being referred to.

At the beginning of the development of the old quantum theory, Niels Bohr had proposed a simple model of the atom in which electrons moved only along certain allowed circular orbits around the positively charged nucleus, and the angular momentum of the electron in the orbit was quantized, in integer units of the reduced Planck constant [math]L=n\hbar[/math].

Arnold Sommerfeld formalized and extended Bohr's treatment of the quantization conditions considerably, to the point where quite general integrable classical Hamiltonian systems could be quantized and even multi-electron atoms could be treated, using the action and angle variables. As part of this treatment he derived that the z-component of the angular momentum of the electron orbits in a hydrogen atom should be quantized too with respect to some axis in space: this arose from the rotational invariance of the system, and it was given the name "space quantization".

Actually, in German it was called "Richtungsquantelung", which is more like "direction quantization".

But it was translated into English as "space quantization". The orbits at that time were still thought of as being basically classical orbits, even though they were quantized and in some sense stationary, that is: electrons in such orbits were supposedly not radiating unless a jump to another quantized and allowed orbit was made. So the electron could in fact be thought of as orbiting around the nucleus at a particular set of positions in space in the old quantum theory. So it is not so strange that this subtle change in meaning crept in to the translation.

Today it's known that in a rotationally symmetric system the quantum mechanical operators [math]L^2=L_x^2+L_y^2+L_z^2[/math] and [math]L_z[/math] commute with the Hamiltonian and have well defined characteristic values in all of the quantum states, and we call what Sommerfeld and Bohr called "Richtungsquantelung" just the quantization of [math]L_z[/math].

Now of course, there is nothing special about the [math]z[/math]-axis - the Sommerfeld conditions implied that the angular momentum component along an arbitrarily chosen axis should be quantized, so [math]L_x[/math] or [math]L_y[/math] would have served just as well.

Since the component of the orbital angular momentum pointing along an axis was expected to be quantized, it followed that you expected the atom to have a magnetic moment associated with the current caused by the electron whirling around its orbit, and the size of this moment pointing along some axis was expected also to be quantized.

In the Stern-Gerlach experiment itself, what was done was that neutral silver atoms were formed into a beam and then passed through an inhomogeneous magnetic field, and silver atoms with two different angular momentum states were then observed to be separated out of the beam.

This result verified the "space quantization" that was part of the Bohr-Sommerfeld quantization conditions, or programme, if you like.

It was discovered later on, the electron spin was actually invented by Goudsmit and Uhlenbeck, that electrons also have half-odd integer intrinsic spins as well as orbital angular momenta, and the electron configuration of a silver atom is [Kr] [math]4 d^{10}\,5 s^1[/math]. So there is just one unpaired electron and all the rest of the spins and angular momenta of all of the other 46 electrons couple to total angular momentum zero. The unpaired electron is in an s-state, so it has no orbital angular momentum at all.

So what was detected in the original Stern-Gerlach experiment was actually the projection along the magnetic field of the magnetic moment associated with the spin [math]s=\frac{1}{2}\hbar[/math] of that single unpaired electron in a silver atom.

It was the first real detection of the electron spin if you want to be really precise about it, though no one realized that at the time.

Nevertheless, this result was considered a success and a confirmation of the old quantum theory, and the technique of using neutral atomic and molecular beams in inhomogeneous magnetic fields became very basic in the development of atomic and molecular theory and of the new quantum theory, when that arrived, after the work of Schrödinger and Heisenberg, Born and Jordan, Kramers, and others too numerous to mention, and finally Dirac.

Repeated applications of the Stern-Gerlach experiment, with the inhomogeneous magnetic field pointing in different directions demonstrated the incompatibility of subsequent measurements of different components of the angular momentum - so this became a very fundamental experiment revealing the way into the full quantum theory.

I.I. Rabi developed basically the same technique to a very high art, whereby precise atomic and molecular states could be selected very accurately from the beam and their energies measured using resonance.

The problem lay people have when they try to understand quantum mechanics--well, one of them, anyway--is they get hung up on the word "observer."

To a physicist, an observer is not a person looking at something. An observer is anything whose state depends in a thermodynamically irreversible way on the state of the thing being observed. In the thought experiment with the cat in the box, the observer is not the person who opens the box and looks inside. You can't put a cat into a superposition of states--at least not like that. The radiation detector that responds to radioactive decay and releases the poison is an observer. Its state depends on the state of the thing being observed.

An observer is not a person. An observer need not be conscious. An observer need not be alive. If it interacts with something, it's an observer.

Understanding what an "observer" is clarifies many strange things about quantum mechanics (and helps dispel a lot of superstitious spiritual quantum woo).

So glad someone asked this! I’ve been blogging about it recently.

Quantum contextuality is a bit of a misnomer, in that it’s technically not a feature of quantum mechanics itself. But it is a required feature of any classical hidden variable theory which aims to reproduce the successful predictions of quantum mechanics.

Quantum contextuality is one of the strongest arguments you can make against hidden variable theories. It demonstrates that in order to construct an accurate “classical” model of the world, you would need to have a theory that is in some ways even weirder than standard quantum mechanics.

In this context (no pun intended!), what I mean by a classical theory is… one in which every measurable property of the world has a single well-defined value at all times.

For example, consider the theory that we’re living in a computer simulation, where the value of each microscopic property is generated using a pseudorandom number generator, in such a way that’s designed so it will reproduce all observable behavior of a quantum system. When I say “property” I mean things like the position, velocity, momentum, energy, mass, or charge of a subatomic particle: any quantifiable thing you can measure about it. The Kochen-Specker theorem proves that even if there were a supercomputer powerful enough to simulate such a system (which would require exponentially more storage space and compute power than what you’d need to simulate a classical universe), that still wouldn’t be enough to match the results of experiments unless you allowed for the possibility that these properties change spontaneously depending on which particular set of them you decide to measure at once. It’s this feature of things suddenly changing depending on what you choose to measure about the system that’s referred to as “quantum contextuality”

Unlike with a classical computer, a quantum computer can simulate any quantum system smaller than itself without requiring any contextuality. In mainstream quantum mechanics, if something has a definite value *before* a measurement, it will have the same value when you measure it… and as long as any other properties you decide to measure along with it also have definite values, the value you get back for any one of them does not depend on which others you decide to measure along with it.

It’s very easy to confuse quantum contextuality with the standard features of quantum mechanics such as the uncertainty principle and non-commutativity. So I’ll try to clarify what the difference is, and why contextuality is *not* a feature of standard quantum mechanics while the other two are.

With the uncertainty principle, there are some properties referred to as “non-commuting observables” such as position and momentum, which cannot simultaneously have well-defined values. The uncertainty principle was already known and understood to apply to any kind of wave (even classical waves) long before quantum mechanics was discovered. When waves come in pulses, you can either precisely define the position of the pulse or the wavelength of the wave, but they can never both be precisely defined at once. A single instantaneous pulse has a well-defined position, but no defined wavelength since it’s not a periodic signal… that’s just not a property it has when it’s that localized in space. And if it’s a long enough train of pulses, then it has a well-defined frequency, because it’s periodic… but the more pulses you have the further it gets spread out in space, so it no longer makes sense to ask what the “position” of the wave is: it’s not at one position but many.

So in standard quantum mechanics, it’s true that the results of measurements often depend on the order in which you make them… but importantly, this is *only* true if you try to measure two properties which can’t both have well-defined values at the same time. If you measure the horizontal position of a particle, and the vertical position of a particle it doesn’t matter which order you measure them in… either way, you’ll get the same results every time you repeat the measurement. Same if you measure them both at once. No matter how many times this is repeated, you’ll always get the same results back. It’s only if you try to measure the momentum in one of those directions, where the results will be unpredictable, and disturb the repeatability of any future measurements of the position in that direction.

Contrast the above two paragraphs with quantum contextuality, which is not true in any mainstream interpretation of quantum mechanics, but *is* an essential feature of hidden variable theories such as the classical computer simulation theory I mentioned. If you assume that all microscopic properties are well-defined at all times, then the computer must store a specific value for each of them in some memory location… even when no macroscopic device is requesting to access them. When nothing is trying to copy and record their values permanently in a large redundant storage system we say that the microscopic system is “isolated” or “closed”, because it’s separated from the rest of the environment, ie not under active observation or measurement.

Quantum contextuality means that in this classical computer simulation, even mutually well-defined values in ordinary quantum mechanics such as the vertical and horizontal positions of a particle are context-dependent. When you try to copy a set of values into permanent storage, the result you get for each value can depend on which other values you’re trying to copy. Again, in mainstream quantum mechanics, something similar to this does happen with non-commuting observables—if you try to copy the position and the momentum at the same time, the results you get will depend on the order in which they are accessed. But at least in that case, there are consistent well-defined rules that tell you which sets of values you can read at once without worrying about getting unpredictable results due to one or both not having definite values. For theories involving contextuality, there’s a seemingly bigger problem of being unable to read even a set of mutually well-defined properties without changing the values while measuring them because of which other values you were measuring… which *should* be independent, based on everything else we know.

Put a 2 Tesla neodymium magnet on the left side at one end of an air hockey table. Put a 1 Tesla neodymium magnet on the right side at the same end of an air hockey table.

That creates a non-uniform magnetic field at that end of the air hockey table. Allow the air hockey area (width x length) to adjust as necessary to make this thought experiment clear.

Put a bunch of 5 Gauss (that’s 0.0005 Tesla) weak magnets on tiny air hockey pucks and push them along an identical straight line trajectory from one end of the air hockey table to the other end that has the non-uniform magnetic field - the straight line trajectory passes right through the exact center of the gap between the 2 neodymium magnets. The physical orientation - the alignment - of the N/S dipole of each 5 Gauss weak magnet is RANDOM as they track along their straight line trajectory between the two neodymium magnets.

I claim that I can adjust the spacing gap between those two neodymium magnets to produce a VARIETY of ‘scatter patterns’.

With the right spacing between the 2 neodymium magnets, the random orientation of the dipoles on the 5 Gauss weak magnets will track straight down the center (the 2 neodymium magnets are far apart) so the ‘scatter pattern’ will be a single dot centered in the gap between the 2 neodymium magnets; or there will be a ‘line-like’ continuous scatter pattern (the 2 neodymium magnets are closer together but not close enough to be a complete attraction of the N pole and a complete repulsion of the S pole of the weak magnets)…

….or the 2 neodymium magnets are close together enough that the attraction/repulsion forces between them forces the 5 Gauss magnets to be either strongly attracted or strongly repelled by the 2 neodymium magnets resulting in a “North pole dot” and “South pole dot” scatter pattern.

I claim I can adjust the physical shape of the neodymium magnets to produce that same range of outcomes (‘no effect on trajectory of the 5 Gauss magnets’, ‘varying effect on the 5 Gauss magnets depending on the orientation of their dipoles’, and ‘hardcore attract or repel reaction of the 5 Gauss magnets resulting in a “2 dot scatter pattern”).

I claim that I can adjust the magnetic strength differential between those 2 neodymium magnets to produce those same 3 outcomes. If I utilize these ‘degrees of freedom’:

1. size of the gap between the differential field magnets
2. physical shape of the two differential field magnets
3. magnetic strength of the two differential field magnets

as Stern and Gerlach must have done in all their preliminary setups they tried for the SG experiment — different scatter patterns could be obtained.

The experimental setup was probably chosen after mucking around a bit to get the historically reported outcome. Chances are good that Stern and Gerlach DID NOT start out with a non-uniform field. They got the expected results then introduced a MAGNETIC FIELD STRENGTH DISPARITY.

There is a similar quantum problem in the idea that ‘an electron gives off a photon of specific frequency X of visible light when it loses energy by falling into a lower orbital.’

A single motion of an electron from a higher to a lower orbital will not produce any frequency of light. Just as turning on an oscillator for 90 degrees then turning it off will not produce a full sine wave.

In order to produce an electromagnetic wave of frequency X, the electron must bounce in between energy levels briefly. It must FULLY OSCILLATE a few cycles to produce the electromagnetic wave of visible light.

The argument sometimes heard is “a photon is a quantum of light”. You cannot escape the physical reality that visible light electromagnetic waves, or radio transmitter electromagnetic waves, are generated by accelerated/oscillated electric charges.

NOT a simple ‘fall from a higher energy orbital to a lower energy orbital’ - a one-way move that somehow creates a photon that magically, identically mimics the normal oscillatory motion of an electromagnetic wave.

PS. If you tell a professional musician (ie. who can read music) that “those sharps and flats in the key signature — they are not absolute. There is a continuum of ‘sharp’ and a continuum of ‘flat’ frequencies”

Many will respond just as most “I need conventional physics to get grant money to eat” physicists will: “That’s not how I was trained.”

Learn everything you can then put it to the test. In physics, the #1 priority should be “physical reality first, math is shorthand for describing the physical reality”

NEED AN EXAMPLE of where this can go wrong? THE TOKAMAK ‘HOT’ FUSION REACTOR. It has been around for 60 years and in all that time has NEVER PRODUCED *ONE WATT* of output power exceeding the input power.

WHY? Because after 60 years, the containment field relies on electromagnetic methods to contain the plasma. The Tokamak is a hot fusion device as is our Sun.

The Tokamak is a 60 year failure because it does not have gravity field containment. The Sun’s fusion works because of its immense gravity field.

The exact physical nature of gravity is KNOWN. But if the technical steps to produce artificial gravity became common knowledge, the Tokamak would not be a 60 year failure. This could be one reason why gravity research was shut down in the 1950s.

EDIT: I’m not shooting down the Stern Gerlach experiment if its intent was to demonstrate that sub-microscopic particles have a magnetic dipole (magnetic moment). Anything more than that, we need to hear the full story of the complete history of the experimental setup. How was the specific differential (non-uniform) magnetic field chosen? Surely several options were considered. How was the size of the gap between the 2 magnets chosen? Surely several options were considered. How was the physical (geometry) shape of the 2 magnets arrived at? Surely several options were considered.

Most importantly, “what were the scatter patterns for all the above options?”

“Surely you did not instantly choose, at the very beginning, the experimental setup that provided the historical experimental outcome.”

You are perhaps being confused by the term “observer”. In the very early days there was a view that an observer was a human or some equivalent. Nowadays, anything with sufficiently large mass to be treated classically, such as a test instrument, is counted as an observer.

The more modern view is that quantum weirdness remains only so long as the objects involved are tiny - though the limit of tiny is constantly being stretched. When a particle interacts with a large enough mass, the quantum uncertainty gets ironed out. This is, indeed, the universe doing what it pleases - which is to say that large masses have to make their minds up.

If you put a compass in a uniform magnetic field it will turn to align the needle with the field lines. A compass is just a small bar magnet. So we can take any magnet and it will also tend to align. However at some point, as we shrink the magnet, we won't be able to see the magnet and watch this alignment. This alignment force is called a torque and it is sensitive to the orientation of the magnet. In space that orientation can point in any of 4pi steradians.

In a uniform magnetic field, there is only a torque. However if the magnetic field were nonuniform, then there would also be an orientation dependent linear force. This is just the magnetic force that most people experience with fridge magnets. The interesting thing is that it is a linear force and it is orientation sensitive.

For any random ensemble of magnets we would expect that there would be a range of possible linear forces.

The Stern-Gerlach apparatus generates a nonuniform magnetic field. A beam of atoms is passed through the field. The linear force would be expected to spread out the beam according to the randomly oriented magnetic moments of the atoms. Instead the beam separated into two distinct beams! It's as if the atoms only had two possible orientations.

This is the first result to identify that angular momentum was quantized.

Allrighty, here goes.

I have a ball in front of a wall. That ball can roll back and forth, but no matter how had I try, I can’t roll it to the other side of the wall.

But what if I make the ball really, really small? Like, electron small?

Electrtons, and any other fundamental particle for that matter, have some very weird properties. The first of these is known as superposition. If you’ve dabbled at all in quantum mechanics, you’ve probably heard of Schrodener’s cat. The basic idea is you take a cat and seal it in a box. When you open the box, the cat will be either alive or dead. However, we’re interested in what happens between when we put the cat in the box and when we open it. You don’t know for sure if the cat is alive or dead until you observe it. Still with me so far?

Until you open the box and observe the cat, the cat is both alive and dead at the same time. In other words, the cat is in superposition.*

A cool little image that gets the point across.

Now in the quantum world, we can do a similar thing. You have a particle. This particle has a “quantum spin,” and that spin can be either up or down. You put the particle in a box, and open it a day later and measure it’s quantum spin.

Until you observe the particle, it has both up and down quantum spin, and once you observe it, it “collapses” into one spin state. This effect is known as the Heisenberg Uncertainty Principle, and what it says is “until a particle is observed, it remains in all possible states simultaneously, in other words; superposition. Upon being observed, a particle collapses into one possible state.”

It is worth noting that ”observation” in this context is anything which could tell you something about the particle. It’s basically any interaction. If a quark bumps into an air molecule, it collapses out of superposition because it can now be measured indirectly.

Quantum tunneling uses Wave-Particle Superposition to magically zoop through walls.

Another really weird property that quantum particles have is wave-particle duality. basically, sometimes quantum particles act like waves, and sometimes they act like particles. Because of the uncertainty principle, when unobserved, they are both a wave and particle at the same time.

Now, our ball cant go through the wall. But, what if our ball was made of light? If the wall were translucent, we could roll our ball straight through.

That’s essentially the idea behind quantum tunneling. It’s a way to cheat the universe’s rules by being a wave.

When a particle quantum tunnels, it is observed in the process, and collapses. Most quarks (the things that make up protons and neutrons) and leptons (electrons and their friends) collapse into particles most of the time, and most bosons (light and friends) collapse into waves most of the time. Once a particle collapses into a particle, it’s stuck there until it is once again unobserved.

Particles can theoretically tunnel to anywhere in the universe, as long as there is an energy well there, but they prefer close locations.

You might be wondering, though, “wait a minute, if electrons can do it, why can’t I?” Well, technically, you can. However, every elementary particle in your body needs to decide to quantum tunnel at the same time, and to the same location. Considering that quantum tunneling is a random event, and position is also random, the chances of you sucessfully quantum tunneling are so miniscule they may as well be zero. In fact, they are so small that you could have a trillion people walking into a wall for the entire time the universe has existed, and the chance of one of them going through it is STILL practically zero.

Hope that answered your question!

-Horatio

*Of course, if you tried this experiment in real life, the cat would never enter superposition because the cat is observing itself.

The universe does do what it pleases, but remember, you are a part of it. You are an inextricable part of the universe.

Since we are talking about quantum physics and the observer affect we should remind ourselves that the universe is one giant quantum system. Any observation or measurement will be done using the same quantized bits of matter/energy that constitute the thing being measured or observed. It is impossible for these two connected by temporarily distinct systems to not affect each other (every object or thing is fundamentally a locally coherent quantum system inside a larger oceanic like quantum system we call the universe).

If we want to be certain about a thing, we must check to see if it agrees with our assumptions. That checking/observation is the act that creates certainty. We literally use one quantum system to check another. Before this checking, we can’t be certain.

Once again, it is impossible for them to not impact each other. We don’t notice this converging, or decoherence, or lack of distinction at our level of experience because things are big and the quantum world is beyond small.

When observing one quantum bit/fundamental particle, the impact of observation is monumental, simply because we are using one particle to look at another. The act is like throwing one basketball against another. You will see an effect, a happening. Using your eyes to look at a door is like throwing a handful of sand at beach. Yes, you did impact it, it’s just very hard to tell.

First of all that statement belongs only to some interpretations of quantum mechanics, some other interpretations avoid any considerations regarding ‘measurements’ or ‘observations’. But for the ones which do:

Nature does not seem to require any ‘measurements’ or ‘observations’ to procede with its evolution. Interactions happen naturally and their outcomes are governed by probabilistic rules. We can tell a lot about the history of the universe before any Life existed because the universe is full of information which we can use to infer what its past must have been like.

The same happens in our normal macroscopic world, events happen naturally all the time regardless if any living being is around or not. But when studying quantum physics in carefully isolated lab experiments, scientists found that the same is not necessarily true in that domain. We can prepare systems in such a way that we keep them in an undefined state, what is called a superposition of possible realities. This is genuinely different from saying that we do not know in which state the system is, it really means that the system is in more than one state at once, states which normally are mutually exclusive.

It is in these exceptional carefully prepared lab conditions that we can say that the system does not take any definite state until we ‘observe it’, that is until we make it interact with a larger environment in such a way that the superposition is no more physically viable. It is in this context that we can say that the act of observation created reality, created a definite state out of several different possibilities which were in superposition until then.

And in very precise experiments we can even say that our observation ‘created the past’. We can indeed have a system with a certain time history, and by adopting certain decisions in the future we can alter the system’s history.

Because the results were completely unexpected and there wasn’t even a quantum mechanical explanation of this bizarre result. Before this SG experiment it was known that when you measure something there is uncertainty but when you repeat the experiment you obtain a distribution of results. In this experiment there wasn’t any distribution: the electrons outcomes were either up or down - showing two spots instead of a continuous line, although we know that electrons can be prepared in any orientation -vertical, horizontal or at any angle, yet when observed in a magnetic field they are only up or down. This was a new form of quantization - it is discrete. New mathematical descriptions had to be introduced in the form of Pauli spin matrices. This mystery was resolved only when Paul Dirac obtained the spin matrices as a solution of the relativistic equation for the electron.

Thanks for the A2A.

Take a sample of silver atoms and enclose them in a lead box, with a fine slit. The sample emits silver atoms through the slit. Introduce a region of inhomogeneous magnetic field, followed by a screen.

The screen displays two bright spots on it: due to the two spins([math]\pm\dfrac{1}{2}[/math]) which are of equal intensity and hence, are equally probable. Now, lets suppose that the magnetic field is inhomogeneous about the z axis. This is the SZ-z arrangement. Now, block out the negative spot on the screen after the SZ-z arrangement. Take the positive spot and let it be incident upon an SZ-x arrangement. The result is, again 2 spots which are of equal intensities. Now, block out the negative spot from the SZ-x arrangement. Let the positive spot be incident upon the SZ-z arrangement again. There are, again, 2 spots on the screen which are equally intense.

But why did this happend? The negative part of the second SZ-z arrangement shouldn’t have appeared. We blocked it out from the first SZ-z arrangement, didn’t we? Except that we really didn’t. When the positive spot from the SZ-x arrangement was made incident on an SZ-z arrangement, the state contained equal contributions from the positive and negative states. This is superposition. The x polarised states can be expressed as a superposition of the z polarised states and vice versa.

In a single sentence: We accept, in addition to "classical" solutions (that we can intuit or visualize), their superpositions (linear combinations) as valid descriptions of physical systems.

This is what the math is all about: Promoting classical variables to, e.g., operators (or whatever other entities we can use that can represent those linear combinations) acting on a wavefunction or some other representation of the state of the system.

The fact that it is called “quantum” physics is, in fact, a bit misleading, kind of a historical accident. It is true that this branch of physics was developed, in part, to explain why, for instance, atoms only emit or absorb light in specific units (quanta). And this does come out as a consequence of the theory. But fundamentally, “quantizing” a physical system is not about chopping it up into little bits; it is about doing what I said above, turning a classical mathematical description of a physical system into something richer, something that allows solutions that make no sense classically or intuitively, and then asserting (and validating through experiment) that these richer solutions are also valid descriptions of observed reality.

In Quantum Mechanics, what, in layman's terms, is the simplest set of things that must happen for an "observation" to take place? E.g. Does it require an "observer"? If so, what is the simplest collection of atoms that can "collapse a wave function"?

The thing that throws most people is “observer” - people assume that means a sentient entity is involved.

Actually, it’s any event that is thermodynamically irreversible (in the “you can’t un-scramble an egg” sense). And that means that it could potentially be down to a single photon or electron if you’re doing stuff like x-ray crystallography. Once that x-ray has scattered off the target, it’s really hard to un-scatter it.

And in fact, the single biggest problem in building a quantum computer is trying to keep stray photons and electrons from collapsing the wave function too early. That’s what they mean by “decoherence” means - something collapsed it before it was fully cooked.

A2A

Amber is right. Anologies are indeed misleading and will tempt the lay person to draw incorrect conclusions. I have plenty of examples.

One of them is picking up from Tom. Dipping the thermometer does alter the measurement. The error in measurement increases as the size of cup of water decreases n relation to the thermometer and also dependents on the nature of the thermometer; a higher specific absorbs more heat increasing the error. Quantum mechanics states that there exists a limit where if the cup of water is small enough, the water develops a probability that it could be ice, liquid or steam depending upon the nature of the thermometer.

Another example is a stick and three people with glasses. Assume the stick is 0 degrees. A person with a good vision observes to be at 0 degs. Person 2 with an eye condition observes the same stick to be at 10 degs. When person 2 puts on corrective glasses the stick is at 0 degs. OK the question is when they both observe at the same time what do they see? Person 1 and person 2 without glasses observe the same stick. Intuitively or according the special relativity, person 1 should see it at 0 degs while person 2 without glasses should see it at 10 degrees. But that's not what happens. They both observe at 5 degs. What happens when person 2 puts on corrective glasses? They both observe the stick to be at 0 degs. Again seems counter intuitive but that's how it is. From the perspective of person 1, the action of person 2 putting on corrective glasses seems bizarre, since the stick seems to turn 5 degs back to 0 deg with no input from person 1. When a third person enters with faulty eye sight what happens? The orientation of the stick would be (nobody is wearing glasses) (0 + 10 + 10)/3 = 6.6 degs. They would all see the stick at 6.6 degs. If person 2 puts on glasses then they would all see (0 + 0 +20)/3 = 3.3 degs. From the perspective of 1 & 3 the act of 2 putting seems like the stick magically turned to 3.3 degs without their input.

In short the orientation of the stick, depends on the nature of the observer. But the mysterious question remains…. what is the original orientation of the stick? How is the stick ororientation without observers? Does the stick even exist without observers? If no one's in the forest to hear the sound, was there a sound?

I am too lazy/no time to write all my examples. I periodically write about physics. You check my feed periodically for more.

You already have answers that point to the fact that a NET charged particle would have other forces (electric and magnetic) imposed on it that would complicate or ruin the experiment. Therefore neutrons were the favorite choices.

However, no one answered your WHY? MC Physics suggests that a neutron is just a proton with a few extra weak charges to make it overall charge neutral. A proton is made of 6 mono-charges (3 positive and 3 negative, of different electric charge strengths) in an 1 X 2 X 3 alternating arrangement so that opposite type mono-charges ‘touch’ for maximum attraction charge forces and like type charges are further apart. The overall positive charge on the proton particle comes from a difference in the charge strengths of Q1+, Q2- and Q3+)

Add to that proton an electron charge on the outside and you have an overall neutral particle to test, but with a negative charge to the side to cause a unbalanced charge moment.

As is often the case with quantum mechanics, the answer is “Sort of, but not really”. To explain, let’s think of a simple test case:

Consider an electron; it has an intrinsic angular momentum (spin) of 1/2, which means that if you make a measurement of the electron spin along some axis, you will either measure [math]\frac{\hbar}{2}[/math] (spin up) or [math]-\frac{\hbar}{2}[/math] (spin down). Assuming nothing else is interacting with the electron, you can measure the spin along some axis (let’s say the z-axis) and get an answer (let’s say spin up). If you wait a while and measure again along the z-axis, you will get spin up again. You KNOW the spin of the electron along the z-axis, and you can observe it in its “natural state”.

Now let’s say you want to know the spin along the x-axis. This is a problem—when the electron is in a state of definite spin along the z-axis, it’s spin along the x-axis is an equal superposition of spin up and spin down! That means the electron doesn’t HAVE a spin along the x-axis. If you measure along the x-axis, you force the electron to one of the x-spin states, with a 50/50 chance of getting either. But it didn’t have that spin before you started.

Does that mean that you can’t know anything about the electron spin? NO! It just means that the correct way to describe the spin along the x-axis wasn’t “up” or “down” —it was “equal parts up AND down”. The math of quantum mechanics predicts this exactly, so the “fact” of the electron state is well known to us.

Of course, there’s another situation which is harder. If you give me an electron and ask me to tell you what its CURRENT state is using only one measurement, I cannot do that—I can do a measurement and tell you its spin state AFTER the measurement, but not before. If you give me many identical copies of that electron (each in the same state) I can, through repeated measurements along different axes, reconstruct the whole spin state. What I’m missing here is prior information about the electron spin; once I know the spin, I can track it for all time, but if I don’t know it at all, my first measurement destroys the information of the initial state unrecoverably.

Spin is proportional to the magnetic moment, and thus determines the direction the particles (silver atoms if I recall) will move when a magnetic field is applied. The magnetic force works via cross products, so that direction matters too, and we can use the location at which the atoms are hitting the detector to backpedal and find the spin in one particular direction.

If spin were not quantized, we would expect to see a random distribution of magnitudes and directions, i.e., one would expect to see something like a normal distribution on the detector, with the most particles hitting in the middle and then less and less as you go outward.

But what was observed was two clusters around single values, one above middle and the other below. Exactly two. Thus, it would lead one to believe that the electron (the last valence electron of the silver atom that determines its spin) can only have two possible spin states in any particular direction: spin up and spin down. A quantized state.

When you say “observer effect”, are you talking about the “collapse of the wavefunction” and all that? If so, the very first thing you should mention is that the terminology is very unfortunate, since most people have the illusion that an “observer” is totally passive and does not interact with the phenomenon being observed. If this were really the case, the wave function would not collapse!

It would be better to call it the “measurement effect”, although people might also think that measurements can be entirely passive.

Better still the “interaction effect” or “interference effect” (except that “interference” is a term usually understood in Physics to refer to the interference of waves…) — the idea being that if you don’t mess with it, the wavefunction doesn’t “collapse”.

When we “observe” something small enough to be obviously governed by quantum mechanics, it usually means we bounce a photon off it and then detect where the photon goes. Sort of like determining the location of a billiard ball by bouncing marbles off it, except that the billiard ball’s qualitative behavior is not governed by quantum mechanics. (If it were, billiards would be a game of chance, not a skill.)

Volume III of the Feynman Lectures on Physics has a great description of what happens if we try to “hit” the electron more and more “softly” (with lower and lower energy photons): the wavefuntion of the electron “collapses” less and less, until at some point the photon offers no information and the wavefunction is undisturbed.

I hope that helps a little.

Quantum physics is complicated. So, it maybe not possible to explain it very well in simple words To really understand it to the point you can use it, you need mathematics. So you have asked a very difficult question.

If what you want is a glimpse of why it is so complex, it may be useful to start here, with this:

Nature does not care how we think about things, it does what it does. At the smallest scale, matter and energy behave rather differently than our experience at more human scales. To think about quantum physics, people like to use comparisons to familiar human scale observations. For some parts of quantum physics, it is often useful to compare it to how macroscopic waves behave. For other parts, it is useful to compare it to how macroscopic particles behave. But quantum scale behavior is neither of those things.

Quantum physics uses a lot of probability rules. You can calculate where a billiard ball will go and if you are careful, your prediction will be accurate. Often it is not possible to predict the future for a subatomic particle, no matter how accurate your measurements and calculations are.

Quantum physics creates different classes of things and there are completely different behavior rules for these different classes.

An ordinary object can often be measured with three numbers for position (X, Y, Z coordinates), three numbers for velocity, a number for mass, and perhaps you may want more numbers for things like hardness, or magnetic and electrical properties. But quantum objects have a whole different set of values for things that have no direct ideas in the human scale. The physicists have come up with a whole new set of descriptors for these properties. Learning these things feels odd, and the physicists have chosen to use ordinary words with ordinary meanings, to describe these completely different properties. In quantum physics, words like ‘spin’, ‘color’, and ‘charm’ do not mean what they would mean outside physics.

If this explanation is not sitting well with you, then take some time to get more comfortable with it. Or get into the subject a bit deeper.

Indeed it does. I suspect you have a misconception or two about the “observer effect”. That’s really a bad name for it, IMNERHO, because “observer” connotes consciousness, and so everyone jumps to the conclusion that what really matters is that the “observer” is a conscious being. Again IMNERHO, that’s nonsense.

The disruption of the interference pattern for two slits (for example) has to do with interactions, not “observations”; the only reason the latter gets mixed in is that there is no way to observe without interacting.

There is an excellent discussion of this in Vol. III of the Feynman Lectures on Physics; I can’t do any better.

The quantum nature state of an “unobserved” system is undefined, quantum physics tells us that it is really undefined, not merely unknown, and experiments have confirmed this, the quantum system is in a superposition of the several (possibly many) states it may be in, while being consistent with its past.

An 'observation' or 'measurement' is anything that produces an irreversible change in the information which can lead to a different future. In quantum terms, this means anything which demands a quantum entity to take one definite state out of the several (possibly many) states it might be in. Any future event will be "computed" by nature from whatever events lie in its past light cone. These events, such as the outcome of an experiment performed by humans today, constitute the information which nature will use to compute what the future must be like.

In terms of the famous double slit experiment, when an electron is not 'observed' it appears as if it behaved as a wave, as if it passed through both slits simultaneously. This actually means that both possibilities coexist in our universe as a superposition, they both contribute 50/50 to our current 'now' reality, because a universe in which there is no path information that could possibly influence the future is just one universe, it can never become two different futures because of our experiment.

You might imagine that there could still be 2 different universe histories, one in which it passed through slit A but this will not affect the future in any way, and another where it passed through slit B but also that will not affect the future in any way. But in practice those 2 imaginary universes would be identical, their futures are identical until the end of times, so nature is economical and merges those 2 options as one single universe reality which is in fact a 50/50 superposition of both in the present, and with a same common future, i.e. the future will never depend on whether it passed through A or B because the information A or B simply does not exist, our experiment did not generate that information.

On the other hand if we create a record which will keep the information of whether the electron passed through slit A or through B, even if we do not observe that record, the information exists. We may bury it deep in a concrete block 100 meters underground, or send it to space without looking at it, but the information is somewhere in the universe. It could be eventually found by someone, millions of years from now and millions of light years away.
And the future where that someone would look at it and find that it passed through slit A is definitely not the same future where he looks and finds that it passed through slit B.

Two different possible futures means that we can not have the two different presents in superposition now, that would be an inconsistency, so nature has to choose and define a single present, which has 50% chance of being slit A and 50% chance of being slit B, and then the information A or B is generated and stored. But the superposition of both is discarded, and of course if we or anybody in the far and remote future ever decide to look at the record, he will find either A or B, but not the interference pattern.

When you think about it, it is actually completely logical, it could not be otherwise. What is actually amazing is that as long as the futures are identical, all the possible options consistent with that future do actually coexist in superposition in the form of waves creating an interference among them, a kind of blurred reality consisting in a haze of all the possible realities, all the possible 'nows' which while being different are still completely consistent with that future.

The classic test of observer subjectivity, or the “reality” of the measurement is the Wigner's friend paradox. The Wigner's friend paradox asks if Wigner's friend makes a measurement inside a lab completely isolated from outside influences, then will Wigner, who is outside the lab agree that his friend has or has not made a measurement. This thought experiment has been performed a couple of times in a very restricted sense, and both times the result is that the measurement appears to be subjective. The most recent paper suggests that reality cannot be consistent with all three of; locality, free will, measurement objectivity. This is a more elaborate version of the Bell's inequality test.

Yes. Even though the scientific terminology is confusing to a layman, what quantum mechanics is talking about is perfectly ‘natural’. An observer in QM is not the same as an observer in the common meaning of the word. It doesn’t have to be a conscious, it doesn’t have to be a human, it can be any macroscopic object. A human, a cat, a brick, a speck of dust, a drop of water, a cup of coffee, planet Earth.

The only important thing is that it is very large and very hot — compared to the quantum system. Such hot and big things (everything you see around in you) are accurately described using classical mechanics. If such a classical object interacts with a quantum system, it collapses its wavefunction, producing the ‘measurement’ or ‘observation’.

In theory, there is no such thing as a classical object. After all, everything around you is comprised of billions of billions of quantum particles, with the same rules applied to them as to the carefully set up experiment involving a single particle. It’s simply a practically unimportant (even though philosophically interesting) shortcoming of the Copenhagen interpretation of quantum mechanics. In this framework, you simply have to accept it as a postulate of the theory. More advanced theories, like quantum field theories, don’t have to rely on observers though, so this inconsistency between quantum and classical is, more or less, solved.

It doesn't really matter. Because any observation involves you. You can't be eliminated from the equation. So there is no way to pare it down to some minimal set without it becoming a matter of question-begging existentialism.

Beyond that it's just a matter of convenience. A superposition is an equilibrium, and gets harder and harder to maintain at anything beyond a single atom at very cold temperatures. There's no sharp cutoff, beyond the fact that you can't do the math any more. So either you do it bottom up and maintain the equilibrium as long as your arithmetical skills allow, or you do it top down and just say “everything here is a macro scale object that will decohere any superposition it touches”. And if you want to talk about an actual result rather than a thought experiment, you must always end up switching to the second approach.

Certainly! The Quantum Cheshire Cat effect is a fascinating phenomenon in quantum physics where a particle's physical properties (like its position) can be separated from its associated properties (like its momentum). This separation occurs in a way that seems paradoxical in the context of classical physics.

The name "Cheshire Cat" is a reference to Lewis Carroll's "Alice's Adventures in Wonderland," where the Cheshire Cat disappears while leaving its grin behind. Similarly, in the Quantum Cheshire Cat effect, the particle's properties appear to exist in separate locations, like a cat and its grin.

This effect has been demonstrated experimentally using a beam splitter and neutrons. The significance of this phenomenon lies in challenging our classical intuitions and pushing the boundaries of our understanding of the nature of particles and their properties in the quantum realm. It highlights the unique and often counterintuitive nature of quantum mechanics, where particles can exhibit behaviors that defy classical logic. The Quantum Cheshire Cat effect contributes to ongoing discussions about the fundamental nature of reality and the mysteries of quantum mechanics.

THATS IT 🌟🌟🌟🌟👍

Quantum mechanics is supported by a wide range of experimental evidence that has been accumulated over decades of scientific research. The Stern-Gerlach experiment is just one example. Here are some additional experiments and phenomena that support the principles of quantum mechanics:

1. **Double-Slit Experiment:**

- The double-slit experiment demonstrates the wave-particle duality of particles, such as electrons. It shows that particles can exhibit both wave-like and particle-like behavior, depending on how they are observed.

2. **Photoelectric Effect:**

- The photoelectric effect involves the emission of electrons from a material when exposed to light. This phenomenon was crucial in establishing the particle nature of light and confirming the quantization of energy.

3. **Quantum Entanglement:**

- Experiments demonstrating quantum entanglement, such as the Bell test experiments, provide evidence for non-local correlations between particles. Changes in the state of one particle instantaneously affect the state of its entangled partner, even if they are far apart.

4. **Quantum Tunneling:**

- Quantum tunneling refers to the phenomenon where particles can pass through potential energy barriers that classical physics would predict to be insurmountable. This effect is observed in various systems, including alpha decay in nuclear physics.

5. **Quantum Interference:**

- Quantum interference occurs when the probability amplitudes of different quantum paths interfere constructively or destructively. It is a fundamental aspect of quantum mechanics and is observed in various experiments, including those involving photons.

6. **Atomic and Molecular Spectroscopy:**

- Spectroscopic techniques, such as the observation of discrete energy levels in atoms and molecules, provide strong evidence for quantized energy states. These experiments support the quantization of angular momentum and energy levels.

7. **Quantum Computing Demonstrations:**

- Experimental progress in quantum computing, including the implementation of quantum algorithms and the development of quantum devices, serves as contemporary evidence for the principles of quantum mechanics.

8. **Quantum Hall Effect:**

- The quantum Hall effect is a phenomenon observed in condensed matter physics, particularly in two-dimensional electron systems subjected to strong magnetic fields. It demonstrates the quantization of electrical conductance.

9. **Electron Spin Resonance (ESR):**

- Electron spin resonance experiments provide direct evidence for the quantized nature of electron spin, a fundamental property in quantum mechanics.

These experiments, among many others, collectively contribute to the robust experimental foundation supporting the principles of quantum mechanics. The consistency of quantum predictions with experimental results has made quantum mechanics one of the most successful and predictive theories in physics.