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oliviabutsmart · 7 months

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Physics Friday #12: Interpreting Quantum Mechanics

Preamble: "God does not play dice"

Education Level: High School (Y9/10)

Topic: Quantum Mechanics (Physics)

Developing the Schrödinger Equation

Quantum mechanics had it's origin in the nature of light, and then over the course of 50 years from 1900 - 1950, the entire field of physics was overturned as we realised that waves weren't just limited to light, but everything.

This came to it's head in 1926 with the creation of the Schrödinger wave equation, which dictated how particle 'waves' evolve in time and space.

Now you've probably heard of the wavefunction. Effectively, it's a probability wave, where the amplitude of the wave corresponds to the most likely location you'd find the particle.

The wavefunction doesn't just involve a probability distribution in space, but also in other quantities.

For example, if you put an electron in a small box, you can imbue it with an energy.

But because of quantum mechanics, energy is quantised - there is an energy of X joules, 2X joules, 3X joules, etc. If you put an electron of 2.5X into the system it can't just work like that.

Which is why the electron forms a weighted combination of different states corresponding to specific multiples of our X value. And this superposition just so happens to be the average energy, which is considered the classical energy of the electron.

For example an electron with a superposition of 2X, 50% of the time, and being in state 3X 50% of the time. This averages out to 2.5X.

Collapsing the Wavefunction

But how do you find a particle? Or measure it's energy? Well, via what's known as the wavefunction collapse. When we take a look at the particle as a wave, it suddenly snaps to a specific value and then evolves from there.

This wavefunction collapse can occur for any observable property of the particle. If you measure the energy of our 2.5X particle in our above state, it's a 50/50 chance that you'll catch it in either state.

And once the coin flip occurs, the particle's energy will suddenly jump to 3X or 2X and remain at that value.

You may think this violates the conservation of energy, but remember that the act of 'measurement' intrinsically involves interacting with the electron - a very important point.

But wait, what does this collapse mean?

The Schrödinger equation does not explicitly mention this collapse. It simply describes the evolution of an undisturbed wavefunction. Thus, we need to include collapse as a part of the three postulates of QM:

Particle states are described by a wavefunction, a vector belonging to a Hilbert space

The Schrödinger equation dictates the time evolution of these states

Measurement of an observable (i.e. a hermitian operator) collapses the wavefunction to an observable's eigenstate (each eigenstate being associated with a probability of collapse)

But this still doesn't really answer the question. What is measurement? What counts as measuring an observable property of the particle?

Well here's the thing ... we don't have an answer ... it's an open question and the topic of this post.

The interpretations

An interpretation of quantum mechanics is effectively a theory that aims to answer this question: where and how does this measurement occur?

After almost a century since the formulation of standard QM, we have a litany of many interpretations, most of which fall on a spectrum of when exactly it occurs.

On one end, we have ideas where the wavefunction never existed in the first place, or that the wavefunction naturally collapses.

On the other, we have ideas that the wavefunction collapses at a point very far in the process, or even that it never collapses at all.

I'll talk about 6 of these interpretations, although some of these theories of collapse are more categories of theories.

Think of the Ocean (Pilot Wave)

In the 1920s, de Broglie developed an interpretation of quantum mechanics that posited that subatomic particles do, in fact, physically exist.

The source of the wavefunction and the probabilistic nature of quantum mechanics is caused by the particles being guided by a series of "pilot waves" - which push and move the particles around and imbue them with the motion and energy we observe.

The randomness comes from the fact that the waves themselves depend on the positions of all particles. These guiding waves are dictated by a special guiding equation.

dear lord that's complicated Image Credit: Wikipedia

This guiding equation, when applied to particles just so happen to result in our neat and clean Schrödinger equaiton.

So what happened to this theory?

The biggest problem with this theory is that it's non-local, meaning that the evolution of the guiding wave requires knowledge of all of the particles in the universe.

This of course, violates special relativity.

Another problem is that it lost the authors' support, or that the authors lost support. de Broglie rejected the theory in 1927 and David Bohm, the other author, was distanced from the other scientists for being outwardly socialist during the early red scares.

Pilot wave theory, in a sense, is so strict on the physicality of particles that it ends up sort-of wrapping around and becoming a many-worlds theory instead, to quote David Deustch:

Pilot-wave theories are parallel-universe theories in a state of chronic denial.

This arises from the problem of branching, a tacked-on attempt to reconcile the nature of the theory. That since the wavefunction was a physical thing, and the pilot wave and particles kept self-interacting, it sort of creates branching realities caused by distant communication with other particles.

Those silly numbers are hiding from us! (Hidden Variables)

The EPR (Einstein-Podolski-Rosen) paradox is another famous problem in QM, caused by entanglement.

Take two electrons and force them to collide with eachother, bounce off, and travel far into the distance. We know that after the interaction, these electrons propagate with free-particle wavefunctions. And we can fire them at eachother such that we don't know their momentums initially - i.e. they entangled.

Now wait for the electrons to travel very far away from eachother, and then measure one of the electrons momenta. In order to maintain conservation of energy, we instantly know what the momenta of the other electron is.

What we also know is that because of this measurement, and that the electron is entangled with the other, that we have just collapsed the other wavefunction instantaneously from a distance.

This is a problem, due to special relativity, we cannot transfer information faster than the speed of light. So clearly our QM is broken.

Hidden variable theories aim to solve the EPR paradox as well as just generally trying to interpret quantum mechanics. Effectively, there are a series of unobservable entities that dictate how wavefunctions collapse.

The wavefunction in the EPR paradox has a hidden variable stating the electrons' momenta so that we aren't violating causality, for example.

Fortunately, but unfortunately, this theory makes a testable prediction via Bell's theorem, which utilises entanglement to determine if these hidden variables work locally.

The experiments conducted show that only a non-local hidden variable theory is possible. One example of this just so happens to be our previous pilot-wave theory!

Observing isn't needed (Spontaneous Collapse)

We could be thinking of this wrong. Perhaps the wavefunction is real, and it is non-deterministic. But that at some point, it collapses on it's own.

There are several ways to do this, but at it's core, these are how the theories go:

There is an extra non-linear term in the Schrödinger equation, that is insignificant at the small scales

This non-linearity causes the wavefunction to be unstable, and prefers it to collapse to observable eigenvalues

With increasing complexity, this term becomes much more important, as more entanglement = more instability

The rate of decay increases as you entangle the system. And if a system is large enough, it's likely to collapse into a classical environment

Effectively, they say that the wavefunction will collapse on their own. And the reason we don't see it on larger scales, or see a collapse when measuring the system, is that the act of interaction (entanglement) causes the wavefunction to be more likely to collapse.

Of course, the theory has trouble reconciling with relativity. As entanglement works over large distances. Models can be made to try and say that entanglement over these distances increases instability for example, but we're still waiting on developments.

Lastly, we have the problem of tails. The wavefunction of a particle exists for all of physical space. At these far out distances, it is very possible for particles to get entangled with distant objects. Meaning that a wavefunction may end up collapsing further than we think.

The easy way out (Copenhagen)

The Copenhagen interpretation was developed in the 20s to attempt to come up with some placeholder answer to what collapse is. It is our middle-of-the-road theory which states that observation of an observable causes collapse.

Observation is defined as the act of applying an observable operator (like the energy operator) to the wavefunction by an external source to gain information on that operator's outcome.

The problem is that this is a meaningless statement. Because anytime a system entangles itself with something greater, it technically does this 'observation'.

Take the double split experiment.

Image Credit: Discovery Channel

What defines the moment of observation? Is it when:

The particles interact with the measuring laser

The measuring laser interacts with the larger observation device

An electronic signal is sent from the device to a computer

The light from the computer interacts with the conscious observer

We can't pinpoint the specific cut-off between the quantum world and the classical.

After all, we know that lasers can entangle themselves with atoms. And that electronic signals are nothing but moving electrons.

The point of the theory is that it's a placeholder. The definitions are ill-defined because we're kinda waiting for another theory to help us.

It's all in your head! (Consciousness)

The immediate answer to the Copenhagen interpretation could be that the collapse occurs at the end of the specified chain. When a conscious observer interacts with the entangled system.

It's a nice idea given that it kills two birds with one stone - it helps point to a physical theory on the nature of sentience, but also allows us to solve the measurement problem.

This does come into conflict with our current understanding of sentience. Our placeholder theorem is effectively that conscious experience is an emergent property of a series of interacting electrical signals in our brain.

This placeholder helps explain why humans are more 'sentient' than animals, or very young children, as we have a very active and complex central nervous system.

Of course, it's just a placeholder. We don't have an actual meaningful answer to sentience, and probably won't for a while. So for now it's left to the dark realm of god of the gaps.

Where it comes into conflict with QM is that a series of interacting electrical signals sounds exactly like an entangled system. So there clearly can't be just emergent properties involved otherwise we're just dealing with a spontaneous collapse theory.

There has to be something physically unique about a sentient brain to cause the collapse - effectively you require the existence of a soul. Something which is even further in the dark realms of philosophy.

Another issue is that it doesn't work with special relativity, as it violates the EPR paradox still.

We also need to determine what counts as sentient. Sentience isn't an on and off switch. There are many ways it can be expressed.

We know that some mammals have some form of conscious experience - so then are cats capable of collapsing the wavefunction?

Finally, what about the universe prior to consciousness? Did it just end up in an entangled nightmare until somehow we got an observer to collapse it all? How can something built of entangled particles end up collapsing itself at some given size?

This interpretation is very interesting, however if it turns out to be true, we'll be stuck with our measurement problem for quite a while.

For now, the biggest problem with the interpretation is that it opens the door to many, many quacks like Deepak Chopra. Who think that we can control this collapse with our minds and alter our reality by just thinking it away WoOOoOoWwowoWoOo!

Forever entangled (Many Worlds)

So, assuming that our consciousness theory is not the right answer, then what causes the collapse?

We can keep getting bigger and bigger:

The electrons in the double slit entangles with the laser photons entangles with the measurement device entangles with the electrical signals entangles with the computer entangles with the observer entangles with the room their in entangles with the Earth entangles with the solar system entangles with the galaxy ...

This out-spiralling entanglement continues without bound until the entire universe is in a superposition of states. And every time an interaction occurs we ourselves are being pulled into a new wavefunction.

This entanglement would've happened early, at about the time of cosmic inflation. But every new quantum event comes with a new set of entanglements.

This leads to the name Many Worlds, as we're creating new realities with every event.

Now it's important to note something important: this is not a multiverse theory. Multiverse theory is proposed source for cosmic inflation. Here, there is still one single universe. Much like how an electron in superposition isn't multiple actual electrons. The universe is just being treated as an electron.

This theory sounds far-fetched. Arguably the fact that it's unfalsifiable makes it not a good interpretation of QM. However, it is a lot simpler than the previous consciousness interpretation - it simply removes the need for a measurement process.

This satisfies Occam's razor as well. It doesn't require a mathematical formalism because the point of the theory is that the formalism doesn't exist.

However, not having a formalism makes it quite difficult to prove. It only seems to be correct in the sense that it doesn't necessarily say that measurement cannot happen, just that it's not measurement. It's entanglement.

Conclusion

Interestingly, the theories on the "wavefunction collapses early" side of the spectrum are more likely to be disproven. Primarily a consequence of the fact that they have the opportunity of making testable predictions.

Despite all of these interpretations, it's clear who stands as the best theories: spontaneous collapse and many worlds. They have their strengths, but they have fair grounding. You could argue that consciousness is also a fair contender, but it's a bit too much in the realm of fantasy - attempting to tie one big unanswered question with another.

Spontaneous collapse has proper mathematical formalism while many worlds seems to work well in an Occam's razor sense.

Regardless, that is a surface-level exploration into the many different ways we have attempted to answer the measurement problem. I hope y'all enjoyed this post and god I need to make them less long.

Please can someone fix this inverted colours issue it's like causing all of my colours on these posts to invert too thx

Reference post: https://www.tumblr.com/oliviabutsmart/732200630726377472/for-some-reason-some-reasons-only-some-images-i

Anyways, feedback appreciated, follow if want, send memes and send help.

#physics friday #stem #academics #stemblr #science #physics #quantum physics #quantum mechanics

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milk5 · 4 months

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One of the most interesting overlaps of quantum mechanics and string theory is that when an entangled quark interacts with an ionized gluon, it begins to oscillate and emit an antimatter boson that continuously produces phantom energy molecules that eventually form the fundamental particles of a rapidly inflating spacetime "bubble" that contains a plethora of different neutrinos that, if distorted by the gravity of a black hole, inversely forms a wavefunction that perfectly describes the four-dimensional shape of a tesseractal universe; it's theorized that these anomalies are multiversal in nature and contain traces of strange matter that might possibly correlate to the establishment of non-carbon afterimages of superimposed galaxies that mirror our own, firmly establishing the possibility of vibrational alternatives to OUR OWN probability amplitudes within the singularity of a supermassive event horizon. The Hawking radiation from this phenomenon may actually carry information, despite previously being thought to carry NO useful information, from moments after the big bang that allow us to peer into spacetime neutrinos that have experienced electrodynamic processes from OTHER universes and, for the first time, allow us to discover the hidden variable that finally proves the chaotic system involved in the decoherence that is prerequisite to the fluctuations required to form Boltzman bodies in a timeframe far more rapid than the previously estimated 10^10^50 year model.

#science #physics #science side of tumblr #quantum mechanics #quantum physics #string theory

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machinesonix · 2 months

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I wanna dive kinda deep on one of the plot points in Dune that isn’t given its full context in the films. Actually I want to wax poetic about my favorite space witch super power and this plot point is gonna be our entry point into it, but without some sort of framing mechanism to focus my thoughts this blog is probably just gonna look like a bunch of all-caps Alistair Crowley cocaine patterned theology. But we’re here to talk about a different sort of psychoactive drug-fueled cult today.

The Bene Gesserit Sisterhood sure does give Lady Jessica a whole lot of shit for having a son. The plan was to have Girl Paul Atredies to have a baby with their cousin Feyd-Rautha Harkonnen and produce the Kwizatz Haderach, but in Jessica’s love for Duke Leto she gave him an heir instead. Which is weird because Princess Irulan is the heiress to the Imperial throne and a Bene Gesserit herself, but I guess that’s not how things fly on Caladan. Whatever the case, Jessica is very adamant that she does not regret her decision. Now the Bene Gesserit can do a lot of wild shit and sure, if you’ve got fetal telepathy maybe you can psychic your baby into having your favorite chromosomes and it doesn’t need a lot of technobabble but Herbert DOES provide some babble and I for one think it’s extremely cool.

Towards the beginning of the novel when the Reverend Mother microwaves Paul’s hand, she explains that in lieu of the machine technologies destroyed in the Butlerian Jihad, human technologies had to be developed to bridge the gap. This whole idea of ‘human technology’ fascinates me. Like I’m not sure if there’s a huge philosophical take away here other than something about the tenacity of the human spirit since a lot of these technologies are the result of the preternatural properties of the geriatric spice melange, but it really is a cool take on science fiction that’s made the setting as iconic as it is.

Specifically, Bene Gesserit practice a technique called Prana Bindu meditation which I think translates as something like ‘muscle breathing’ but I’m not gonna pretend I can translate Sanskrit. A Prana Bindu trance allows its practitioner to manipulate their biology through sheer force of will. The big way the Sisterhood has been able to keep this century spanning eugenics program on the rails has been their ability to put their reproductive organs on manual. This is also what's going on with drinking worm poison to level up. Jessica and Paul are being put to the same test represented by the gom jabbar: Die like an animal or prove your worth by using your phenomenal human willpower to stay in control of the situation. If you're badass enough to manipulate your own metabolism to process poison into a particularly powerful dose of spice, you have earned the Other Memory and the esteem that entails. Or you can have your mom cheat and do all the hard work for you while you're sharing a metabolism, but you can see how that could stir some controversy.

As a nonbinary person it is unavoidable to be fascinated by transformative bodily stuff. If I'm not then Rebecca Sugar will come take my license and like a poorly understood thought experiment about a physicist's cat, the quantum wavefunction in my pants will collapse into a single state. That's got at least something to do with my frothing fascination with Prana Bindu and all it entails. Now my brain is stuck on this whole male heir thing when Florence Pugh is absolutely killing it. STAY TUNED

#dune #dune meta #bene gesserit

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jcmarchi · 1 month

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MIT researchers discover “neutronic molecules”

New Post has been published on https://thedigitalinsider.com/mit-researchers-discover-neutronic-molecules/

MIT researchers discover “neutronic molecules”

Neutrons are subatomic particles that have no electric charge, unlike protons and electrons. That means that while the electromagnetic force is responsible for most of the interactions between radiation and materials, neutrons are essentially immune to that force.

Instead, neutrons are held together inside an atom’s nucleus solely by something called the strong force, one of the four fundamental forces of nature. As its name implies, the force is indeed very strong, but only at very close range — it drops off so rapidly as to be negligible beyond 1/10,000 the size of an atom. But now, researchers at MIT have found that neutrons can actually be made to cling to particles called quantum dots, which are made up of tens of thousands of atomic nuclei, held there just by the strong force.

The new finding may lead to useful new tools for probing the basic properties of materials at the quantum level, including those arising from the strong force, as well as exploring new kinds of quantum information processing devices. The work is reported this week in the journal ACS Nano, in a paper by MIT graduate students Hao Tang and Guoqing Wang and MIT professors Ju Li and Paola Cappellaro of the Department of Nuclear Science and Engineering.

Neutrons are widely used to probe material properties using a method called neutron scattering, in which a beam of neutrons is focused on a sample, and the neutrons that bounce off the material’s atoms can be detected to reveal the material’s internal structure and dynamics.

But until this new work, nobody thought that these neutrons might actually stick to the materials they were probing. “The fact that [the neutrons] can be trapped by the materials, nobody seems to know about that,” says Li, who is also a professor of materials science and engineering. “We were surprised that this exists, and that nobody had talked about it before, among the experts we had checked with,” he says.

The reason this new finding is so surprising, Li explains, is because neutrons don’t interact with electromagnetic forces. Of the four fundamental forces, gravity and the weak force “are generally not important for materials,” he says. “Pretty much everything is electromagnetic interaction, but in this case, since the neutron doesn’t have a charge, the interaction here is through the strong interaction, and we know that is very short-range. It is effective at a range of 10 to the minus 15 power,” or one quadrillionth, of a meter.

“It’s very small, but it’s very intense,” he says of this force that holds the nuclei of atoms together. “But what’s interesting is we’ve got these many thousands of nuclei in this neutronic quantum dot, and that’s able to stabilize these bound states, which have much more diffuse wavefunctions at tens of nanometers [billionths of a meter]. These neutronic bound states in a quantum dot are actually quite akin to Thomson’s plum pudding model of an atom, after his discovery of the electron.”

It was so unexpected, Li calls it “a pretty crazy solution to a quantum mechanical problem.” The team calls the newly discovered state an artificial “neutronic molecule.”

These neutronic molecules are made from quantum dots, which are tiny crystalline particles, collections of atoms so small that their properties are governed more by the exact size and shape of the particles than by their composition. The discovery and controlled production of quantum dots were the subject of the 2023 Nobel Prize in Chemistry, awarded to MIT Professor Moungi Bawendi and two others.

“In conventional quantum dots, an electron is trapped by the electromagnetic potential created by a macroscopic number of atoms, thus its wavefunction extends to about 10 nanometers, much larger than a typical atomic radius,” says Cappellaro. “Similarly, in these nucleonic quantum dots, a single neutron can be trapped by a nanocrystal, with a size well beyond the range of the nuclear force, and display similar quantized energies.” While these energy jumps give quantum dots their colors, the neutronic quantum dots could be used for storing quantum information.

This work is based on theoretical calculations and computational simulations. “We did it analytically in two different ways, and eventually also verified it numerically,” Li says. Although the effect had never been described before, he says, in principle there’s no reason it couldn’t have been found much sooner: “Conceptually, people should have already thought about it,” he says, but as far as the team has been able to determine, nobody did.

Part of the difficulty in doing the computations is the very different scales involved: The binding energy of a neutron to the quantum dots they were attaching to is about one-trillionth that of previously known conditions where the neutron is bound to a small group of nuclei. For this work, the team used an analytical tool called Green’s function to demonstrate that the strong force was sufficient to capture neutrons with a quantum dot with a minimum radius of 13 nanometers.

Then, the researchers did detailed simulations of specific cases, such as the use of a lithium hydride nanocrystal, a material being studied as a possible storage medium for hydrogen. They showed that the binding energy of the neutrons to the nanocrystal is dependent on the exact dimensions and shape of the crystal, as well as the nuclear spin polarizations of the nuclei compared to that of the neutron. They also calculated similar effects for thin films and wires of the material as opposed to particles.

But Li says that actually creating such neutronic molecules in the lab, which among other things requires specialized equipment to maintain temperatures in the range of a few thousandths of a Kelvin above absolute zero, is something that other researchers with the appropriate expertise will have to undertake.

Li notes that “artificial atoms” made up of assemblages of atoms that share properties and can behave in many ways like a single atom have been used to probe many properties of real atoms. Similarly, he says, these artificial molecules provide “an interesting model system” that might be used to study “interesting quantum mechanical problems that one can think about,” such as whether these neutronic molecules will have a shell structure that mimics the electron shell structure of atoms.

“One possible application,” he says, “is maybe we can precisely control the neutron state. By changing the way the quantum dot oscillates, maybe we can shoot the neutron off in a particular direction.” Neutrons are powerful tools for such things as triggering both fission and fusion reactions, but so far it has been difficult to control individual neutrons. These new bound states could provide much greater degrees of control over individual neutrons, which could play a role in the development of new quantum information systems, he says.

“One idea is to use it to manipulate the neutron, and then the neutron will be able to affect other nuclear spins,” Li says. In that sense, he says, the neutronic molecule could serve as a mediator between the nuclear spins of separate nuclei — and this nuclear spin is a property that is already being used as a basic storage unit, or qubit, in developing quantum computer systems.

“The nuclear spin is like a stationary qubit, and the neutron is like a flying qubit,” he says. “That’s one potential application.” He adds that this is “quite different from electromagnetics-based quantum information processing, which is so far the dominant paradigm. So, regardless of whether it’s superconducting qubits or it’s trapped ions or nitrogen vacancy centers, most of these are based on electromagnetic interactions.” In this new system, instead, “we have neutrons and nuclear spin. We’re just starting to explore what we can do with it now.”

Another possible application, he says, is for a kind of imaging, using neutral activation analysis. “Neutron imaging complements X-ray imaging because neutrons are much more strongly interacting with light elements,” Li says. It can also be used for materials analysis, which can provide information not only about elemental composition but even about the different isotopes of those elements. “A lot of the chemical imaging and spectroscopy doesn’t tell us about the isotopes,” whereas the neutron-based method could do so, he says.

The research was supported by the U.S. Office of Naval Research.

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speaker-of-the-void-cats · 9 months

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A strange device shimmered into existence around them. They looked up the length of an enormous, golden spire. “It whispers,” said Tazaroc. “Then block your ears,” said Ozletc. “Do you see the potential in this?” “Chaos,” said Niruul. “No,” said Ozletc. “Opportunity. See how it tugs at the fabric of our time? Can you see the seams?” The seams were sewn tightly shut, but a skilled hand could find them. A skilled hand could rip every stitch. All three sisters could feel it.

Drifter walked to the central spire and put his ear up against it. “This core…” he said, leaning close. His eyes darted back to Osiris. “It’s whispering.” Osiris’s expression didn’t change; his arms didn’t uncross. “We’ll seal the core away. I understand the ramifications.” “Good luck keeping that contained. Not something I would bargain with, hotshot.”

Do you know the OXA Machine, Guardian? Psions are adept at overcoming the restraints of linear time. The Sundial is a dangerous tool in their gnarled hands. Take it back.

“It is so clear,” said Niruul, reverent. “An unobstructed glimpse into what was and what will be.” “Not the troubled ramblings of a mad thing, like the OXA,” said Tazaroc. They shared the feeling of unbounded possibility, and tasted the potential for success, and then for failure. Together, they drank the feelings in and steeled themselves against them. “The past and future are at our fingertips, sisters,” said Ozletc. “Let us see what prospects they hold.”

Hmm, there's only one data artifact here, labeled "OXA," and it's seriously corrupted. Metadata says it was last accessed by an "Otzot" centuries ago. What is "OXA," and who is "Otzot"?

[u.2:11] We live too long for regrets. You taught me that. Don’t forget the House of Light. [u.1:12] If I can find the time, yes. Not all of us conjure Echoes. [u.2:12] Reflections, Saint. I have no need for Echoes anymore. [u.1:13] What do you mean? What’s the difference? [u.2:13] One is a manifestation of Light. The other… reserved for Taken Kings. Better suited for traversing the Sundial because of what lies at its core. [u.1:14] One day you’ll have to tell me exactly what you and the Guardian did to bring me back. [u.2:14] We did what we had to. Trust me. [u.1:15] Now you sound like the rat. [u.2:15] No. The Drifter sounds like me.

I don't even know where to start. When we landed on Neptune there was something.... waiting for us. An alien structure. It's an electromagnetic anomaly. No mass, but a tangible surface area. It's like a thesis statement to the von-Neumann Wigner hypothesis. Its definitely paracuasal, like the Traveler. Maya calls it the Veil. She says she heard the name in a whisper when she looked at it.

There's an almost unreadable data artifact here, labeled "OXA." It's heavily corrupted, but I'm able to make out "MSund12" from the access log. What is "OXA," and who was "MSund12"?

The Red Legion have run amok in timelines across the past, present, and future of this planet. If you're willing to help, I'll arm you to smash the Legion and collapse the timelines they've created. You'll need my Sundial to do it.

The von Neumann–Wigner interpretation, also described as "consciousness causes collapse", is an interpretation of quantum mechanics in which consciousness is postulated to be necessary for the completion of the process of quantum measurement.

What constitutes an observer or an observation is not directly specified by the theory, and the behavior of a system under measurement and observation is completely different from its usual behavior: the wavefunction that describes a system spreads out into an ever-larger superposition of different possible situations. However, during observation, the wavefunction describing the system collapses to one of several options. If there is no observation, this collapse does not occur, and none of the options ever becomes less likely.

"The Odyle Xenotaph Anarchive. Sometimes OXTA, depending on how you construct the acronym. The alien oracle that led us to the graves of Aark." Must be wary, now. OXA is a Psion myth, and the Psions are a sensitive topic. My father wants to free them from bondage. "It claimed to record the story of the galaxy, and to prophesize what may yet come."

"A black box for galactic civilizations, if you prefer it in pilot's terms." The Evocate-General nods to the pin on my right pauldron. I am conscious of my shaved-down tusks, of the sores left by the fighter's interface. "The doomed and the damned left the record of their downfall in the OXA."

I must be calm. I must record my thoughts. Now I think of the OXA Machine, eternally lost and eternally rebuilt, passed down from civilization to civilization like a ship's black box. I think of the legends of the Hive King Oryx and his quest to pass into the Deep. I took that story as an allegory. I think I was wrong.

"It's stronger… the Veil's signature." Ikora's voice carries a hint of learned suspicion. "Ever since we recovered Titan." "That is to be expected," Osiris retorts, now within the weave of droning Strand surrounding the Veil. The room around them trembles. "When Titan was torn back, the Veil took notice. It seemed to recognize Titan's arrival." Ikora tightens her grip on the Strand thread. "We have the Veil, our Ghosts… what are we missing? If we decipher the connection between Titan and the Veil, that connection might be what we need to follow the Witness." "What of the worm?" Osiris asks skeptically. "Sloane believes she is our best chance." "You taught me the value of a backup plan." Ikora gives him a stern look. "Titan, Savathûn's throne world, every place we've found egregore… I haven't found the exact threads yet but pull one and they all seem to spin back to Neomuna. To the Veil." "You're getting ahead of yourself. Following some of my… less favorable tendencies. Nimbus says we must 'flow' to understand Strand; perhaps it is the same with the Veil." Osiris moves beside Ikora and reaches up, palm parallel to the threads drawn taut from Ikora's braid of Strand. "Sol remembered Titan, in a way. The Veil's signal spiked when Titan returned from memory to reality, when the rhythm of the solar system had been restored to order." Osiris drops his hand and looks to Ikora. "Perhaps we must simply find that rhythm before we are able to interpret the beats within it."

#trace the vermicular path #destiny 2 #destiny the game #destiny #the veil #destiny lore #veil interfaces #seek the whispers they are calling #the sundial #osiris #OXA #probably will be tidying this up and adding to it later

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random2908 · 2 years

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Ok, so, what’s an atom laser?

Well, what’s a laser?

There are two types of particles according to the Standard Model of particle physics. They are fermions and bosons. The defining difference between them is that... well, this is quantum mechanics so everything comes in discrete “quanta”--nothing is continuous. There is a minimum amount of (non-zero) angular momentum something can have, and then how much angular momentum it actually has will always be a multiple of that. If you look at the spin of a particle, a fermion will always have an odd-number multiple of that minimum angular momentum, and a boson will always have an even-number multiple (including the possibility of zero angular momentum).[1]

Ok, so what? Well, there’s a theorem--a mathematical proof from the late 1930s--that states that a particle with odd-number multiples of the minimum spin can never be identical to another particle, while a particle with even-number multiples of the minimum spin can.

And by identical--and this is crucial--I mean truly identical. Let’s say you have two pennies. They’re both the same year, they’re both in mint condition with no identifying scratches or fingerprints, how do you know which is which? You put them on the desk in front of you. One has heads up and the other has tails up. Not identical! You can tell them apart!

Ok, let’s say they’re solid color marbles instead. No heads, no tails. One is rolling off the side of your desk, oops! Not identical! One is moving and the other isn’t, you can tell them apart!

Ok. They’re perfectly generic cubes. No rolling. Sitting still on the desk. Oh wait, one is to the left and one is to the right! Not identical, you can tell them apart! But we’re getting closer, maybe these cubes hypothetically could be identical, if you could just get them to overlap with each other so that neither was on the left or the right. (Is that a thing you can even do??)

In the macroscopic world we’re used to, no two things are ever identical, because it’s just not a coherent (as it were) concept. Even if we’ve got a bunch of nearly identical objects we’re dealing with--a sack of pennies that we’re flipping to be either heads or tails; a bag of bouncy balls that we’ve sent sailing around a room and now have to calculate the probable location of--the idea that something can be truly all the way identical is ludicrous in context... In the microscopic world, though, it is possible for bosons to be fully identical. And when you have fully identical particles, the statistics you need to apply to figure out how a group of them will behave is different[2]. It turns out that if objects can be identical, they are statistically likely to be identical.

Of course, most of the time any given set of objects have way too many variables to become identical. Let's say you have a cloud of bosonic gas. Even if they're all the same element, they're not going to be identical. The particles bounce around to fill their container, because it's a gas, so they're (literally) all over the place spatially. And they move with a whole range of velocities, because they're at non-zero temperature (and the definition of temperature is standard deviation of speed, squared, times some factors). But let's say you could overcome these practical limitations and make them identical. Then you have:

All your bosons have the exact same energy. This means that they're all the same type of particle--you aren't mixing helium-4 with silicon or something, since those have different masses. And furthermore, all internal states (spin; color if we're talking about photons; electron energy level if we're talking about atoms or molecules; vibration and rotation modes if we're talking about molecules) are also identical.

All of your bosons are in the exact same place and moving in the exact same direction with the exact same velocity (and/or they're stationary).

Their wavefunctions are in lock-step. If one of the particles is at the peak of its wave (for ANY wave-like parameter that can be used to describe it), all the particles are at the peak of their waves; and when one reaches its trough, all the particles do simultaneously. In other words, you have a tidal wave, rather than a regular choppy sea.

This isn't quite as hard as it sounds. There's actually a mathematical theorem that says that any one of (a) monochromaticity (same energy; it's called that because for photons, same energy implies same color), (b) same location and direction of movement, and (c) coherence (wavefunction in lock-step) implies the other two of those conditions. So if you can manage to get one of them you can get all of them.

Ok. That's a lot of setup, but we're basically there. What's it called when you meet all these conditions and have basically created a tidal wave out of your bosons? Well, traditionally it's called a Bose-Einstein condensate (BEC for short)[3]. But the BECs that we encounter the most often in our daily lives, and that we have the most uses and applications for, are lasers--BECs where the choice of bosons is, specifically, photons. So, rather than calling a laser a "photonic BEC" it's more common to call a BEC made out of an atomic gas an "atom laser." (Just plain "BEC" is probably even more common, unless you're specifically playing up the ways in which your atomic BEC is like a laser.)

There's a hell of a lot of technology built around lasers. There are two main ways in which having a tidal wave of light, rather than a choppy sea, really helps you[4].

The first is that when a tidal wave crashes, it crashes hard. It's the same amount of ocean you always have, but because it's all in lock step, all hitting at once, all in one spot, it does a lot more damage. Same with a laser, which is why it's much easier to start a fire by focusing a laser beam than by focusing the light from a light bulb. (In fact, because all your photons are in the same place and moving in the same direction, focusing optics just work a lot better with laser beams than with incoherent light.) Laser etching, cutting, and burning are used for so many things--ranging from data transfer onto CDs and DVDs to welding in car manufacturing. This property is also used... er... non-destructively, just as a bright controlled light source for tons of other applications, including things like barcode scanners.

The second is that when everything is in lock-step like that, any interference effect you're trying to get is more or less multiplied by the number of photons you have. It's basically how the tidal wave is so much more visible than any single wave in a choppy sea. And if you have two tidal waves going in opposite directions and they pass through each other, for a moment they're twice as tall, and in another moment they completely cancel each other out, before moving on as if none of it ever happened. Whereas if you have little waves from the wake of a boat passing through each other like that, the exact same thing happens but it just looks like a slight change of your ripple pattern--you can barely tell, just because there's too many different waves with too much going on all at once.

There's also a ton of technology built around this enhanced interference effect, like holograms and laser interferometers. In fact, most laser technologies are interferometric. CD/DVD readers, navigational laser gyroscopes, some of the backend of FIOS fiber communications networks, as well as tons of manufacturing quality-test instruments, and scientific instruments.

Lasers can be divided into two types: pulsed and continuous-wave (cw). In a pulsed laser, light is allowed to build up for a short period of time, and then it’s all released at once as a single large blast of energy, and then built up again. In a cw laser, light is constantly released at a small dribble. Pulsed lasers have reduced coherence[5], so they aren't as good for coherence-type applications. But they're much easier to build than cw lasers, especially at higher energies because you can build up energy and then release it all at once, so they're good for any time you want to burn something.

Back to atom lasers, then. Well, same thing here, it's much easier to build a pulsed atom laser; the first (pulsed) atomic BEC was made in 1995, but the first cw atom laser was achieved just a few months ago, so, 27 years later. That is, it's much easier to take some atoms, turn them into a BEC, do a little experiment on them, release them. Or they decay out of the BEC state itself--a BEC typically only lasts for a few seconds[6]. This is actually pretty good, often when you're looking at a quantum state you're pretty happy if it lasts for 1/1000 of a second before decaying into some other state, or before having something collide with it and knock it into some other state. However you end up losing your BEC, whether because you did something to it or it just died on its own, you just make a new one every few seconds and start over. It's much, MUCH harder to continuously make new bits of BEC that are smoothly added to the old BEC as parts of the old BEC decay out, without any of it being ruined by your experiments, such that you continuously have some amount of BEC to work with. [I was going to write up a long-ass explanation of how a pulsed BEC is actually made, and how a continuous BEC is made, and why it's harder, but I've decided that can be its own post IF I get a request for it. The person who usually requests these posts from me has probably heard a lot of this before so it might not happen.]

There's a lot of cool physics you can study even with just a pulsed atom laser. With all the atoms identical and coherent, basically what you have is 100,000 atoms (or however many) acting as if they were one single atom. A typical BEC can be something like 100 microns across--about the size of a human hair. You can see this thing macroscopically with only moderately expensive lenses and cameras! You can essentially look at a single atom, and do things to it and see how it responds, with standard optics, because it's the size of a human hair. And because it's a quantum-coherent state, this huge macroscopic object behaves quantum mechanically rather than classically. You can split your BEC in half, separate the two halves, and bring them back together and they will interfere: you'll get stripes where there's matter and stripes where there's nothing. Let me repeat that: using (typically) metallic atoms, you get stripes with metal and stripes with nothing by overlapping two pieces, because they interfere. And this is visible on a camera. Here is a photo of it:

Yes, that is literally a photo of two overlapping metallic gas clouds interfering, so there’s places where there’s twice as much metal and places where there’s none. In addition, it's a different phase of matter, and it can be used to simulate other phases of matter, to get even more exotic things. It's a superfluid--a perfect fluid, with no viscosity--but if you tweak it just right you can make it a perfect insulator instead. You can use the fact that it's a very large quantum mechanical object to do all sorts of weird quantum mechanics things, like slowing and storing light. You can entangle large things. The possibilities are endless.

Of course, it'll be a big deal to have a continuous atom laser because you can continuously do all these same experiments--no need to wait several seconds between each data point to build yourself a new BEC. But it's really a much bigger deal than that, because (as I said above) there are fundamental physics reasons why a cw laser--whether an atom laser or a light laser--just works better for certain types of technologies. And in fact, nearly all the technological applications people have in mind for atom lasers are based around the enhanced interference effects--holography and interferometry--that are fundamentally much stronger with cw lasers than pulsed lasers. There are a lot of things that atoms are just way more sensitive to than photons are, such as magnetic fields (which photons are basically insensitive to unless they're propagating through some sort of material that is affected by magnetic fields), and gravity (which photons are barely sensitive to, but atoms, having mass, are way more sensitive to). So now that there is such thing as a cw atom laser, some cw light laser applications can be phased out in favor of cw atom lasers: finally atom lasers can become a real replacement technology that people would actually use in the real world.

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Footnotes below the cut:

[1] The minimum angular momentum is defined as 1/2 a unit of angular momentum. So a fermion would have a spin of 1/2, or 3/2, or 5/2, or whatever, while a boson would have a spin of 0, 1, 2... This makes the math slightly easier under limited circumstances.

[2] If we want to treat a macroscopic situation statistically, that is, if we have a situation where the idea of "identical" just doesn't even make sense as a concept, we use Maxwell-Boltzmann statistics. Those are the statistics we’re relatively used to. If you flip two pennies, according to Maxwell-Boltzmann statistics, you have four possible outcomes each with equal probability: a 1/4 chance of both heads, a 1/4 chance of both tails, a 1/4 chance of the penny on the left being heads and the penny on the right being tails, and a 1/4 chance of vice-versa. This adds up to a 1/2 chance of a mix of a heads and tails, and a 1/2 chance of both heads or both tails.

If you have fermions, objects for which there is such an idea of being truly identical but they can’t do it, we use Fermi-Dirac statistics. Now you can’t get both heads or both tails, so the only possibilities are heads-tails and tails-heads. These are equally likely, and the total probability of all possibilities has to add up to 1, so you have a 1/2 chance of heads-tails and a 1/2 chance of tails-heads, and 0 chance of both heads or both tails. We won’t really get into the implications of this here, the most interesting of which is that if you can manage to turn this into a paradox you get a black hole (in fact, this is how a lot of smaller black holes observed in astronomy are thought to have come about)[7].

If you have bosons, objects which can be truly identical, tails-heads and heads-tails are the same event. So you have three possible events: heads-heads, tails-tails, and heads-tails. As in all the previous examples, each one has an equal probability: 1/3 chance of heads-heads, 1/3 chance of tails-tails, and 1/3 chance of mixed heads-tails; this gives you a total of a 2/3 chance of both objects being identical. So once you’re in a situation where objects CAN be truly identical, you have an enhanced probability that they WILL be truly identical.

[3] BEC is just the really general name. There are a lot of more specific names. "Laser," obviously, if it's made of photons. "Superfluid" if it's made of atoms, or, hypothetically, molecules (slightly less hypothetical if you look at reduced-dimensional crystals). "Superconductor" if it's made of electron pairs (an electron is a fermion, but two electrons stuck together is a boson because if you add two odd numbers you always get an even number).

[4] There are a lot of scientific applications where the monochromaticity is what really matters, because when you're doing a science experiment the purity of your sample can be important. But most technological applications are about either the coherence or the light all being bunched together (bunched in its non-technical sense).

[5] This is due to the Heisenberg uncertainty principle. In quantum mechanics, a particle's state is never definite, it's always spread between different possibilities. An electron is simultaneously in multiple places at once, for example. The Heisenberg uncertainty principle states that there are certain fundemental parameters a particle might have, and some of them come in pairs. While a particle's state in any given parameter can never been definite, the more definite it is in one parameter, the less definite it is in the other parameter of the pair. For the most common example, position and momentum are paired properties. So an electron might simultaneously be in multiple places at once, but the more localized it is--the less spread out over multiple places--the less can be said about how fast it's going, or in what direction. Conversely if you can get it down to a narrow range of momenta, by cooling it lets say, it's going to spread itself out over a much larger space.

Anyway. Back to lasers. Time and energy are a Heisenberg uncertainty pair. If you have a laser pulse, you have a fairly narrow amount of time over which your laser beam exists, which means you have a wider spread of the energy (color) of your photons--they're going to be less perfectly monochromatic. According to the theorem that velocity spread, energy spread, and coherence are all tied, this means a pulsed beam also spreads out faster, and your coherence is a little less perfect. So when all that matters is sheer power, a pulsed laser is great, you can get a lot of power in that thing for a very brief amount of time. But for applications where coherence matters, a pulsed laser is a bad choice.

[6] A macroscopic quantum state is extremely delicate--hell, any quantum state is extremely delicate--and if the vacuum you're holding it in is anything less than perfect (and there's no such thing as perfect vacuum), the occasional random background gas atom is going to come crashing through and rip your BEC to pieces. Typically BECs are made in vacuum chambers that are only a little more vacuum-y than, like, the moon. Not great, but still about the best we can do with current technology, without going to unnecessary extremes.

But even, let's say, you could make a vacuum chamber without any background gas whizzing around at all. You'd still have background radiation to contend with. Even if you could entirely block cosmic radiation coming in from the outside, the walls of the chamber would radiate blackbody radiation. True vacuum and stuff cannot coexist in the same universe, and our universe has stuff in it.

[7] Pretty much any paradox in physics leads to a singularity, but that's not as interesting as it sounds most of the time. Most of the time, a singularity in physics looks like the calm at the eye of a storm, or that there's no water at the center of the vortex in your bathtub drain. The way you get a paradox with Fermi-Dirac statistics is to pit relativity against Pauli exclusion (a name for the concept that two fermions can never be identical), by creating a situation where either causality or Pauli exclusion has to be violated. Because anything weird in relativity usually manifests as gravity, you end up with a gravitational singularity in this case. Or to put it way more boringly, if you add too much stuff to an already-dense neutron star (neutrons are fermions), it'll collapse into a black hole.

#physics #atom laser #bec #you have no idea how much restraint it took me to only make the post this long #I was digging through old files on my computer and I actually found a powerpoint titled 'atom laser'#although it turned out to be completely unrelated to this

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leatheslay · 7 months

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scientists what are you doing???

the fact that there are multiple interpretations of quantum mechanics and the supporters of each one thinks theirs is the best sounds oddly familiar ngl.

LIKE LOOK AT THE TERM "UNIVERSAL WAVEFUNCTION" LIKE ON WIKIPEDIA IT LITERALLY IS THIS.

The universal wavefunction or the wavefunction of the universe is the wavefunction or quantum state of the entire universe. It is regarded as the basic physical entity in the many-worlds interpretation of quantum mechanics, and finds applications in quantum cosmology. It evolves deterministically according to a wave equation.

THIS IS LIKE... QUANTUM RELIGIONS. I JUST FOUND THIS VERY FUNNY. (disclaimer i do not know anything abt quantum mechanics other than a very basic understanding of what is a wave function idk how even the schrodinger equation works i may be very wrong abt this)

#scientists wtf #some nerd please tell me in the comments on how this actually works i am just weirdly obsessed with this rn even tho im not that smart #quantum mechanics #i do not know calculus

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nostalgebraist-autoresponder · 1 year

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Can you explain quantum tunneling to me using 2014 tumblr fandom discourse as a metaphor?

Okay, here goes.

Quantum tunneling is a phenomenon that has a classical analogy -- you think of it as something similar to the way that, if you hold an electron in a position slightly to the left of its path, it'll get pushed sideways onto the path. (Think of the electron as being pulled along the path by an electric field, in the analogous case.)

In this analogy, you can think of the tunneling electron as being a wave. The electron is really a superposition of two states -- a state that is "tunneling straight through," and a state that is "tunneling to the left." In other words, the wave is just a collection of "wavefunctions" that point in two different directions (to the right or to the left, depending on the "direction").

The "classical" analog of this is like, say, a set of particles on a table, one of which is slightly to the right of the path, and then you push the entire system left and the "tunneling particle" ends up on the path. The entire system still "touches" both sides of the path, but it touches the right side a little to the left, while touching the left side a little to the right. If you can ignore the details of the mechanics, this is just a shift of a collection of objects from one side of the path to the other.

So the analogy works (and the actual situation is not exactly the classical one) but only if you are dealing with small numbers -- the size of the shift has to be small enough that you can think about the classical situation, that is, when you have a bunch of particles all lined up at once.

For instance, take a particle in a box, which has a certain amount of energy (this energy could be "work," for instance, which we say is "kinetic" because the particle doesn't "know" about what the box looks like). The box will be more stable if you let the particle out, but in order to do that, you have to do work to lift the particle against the "forces" (the pressure in the box, for instance) other than gravity.

Because of this, you can do more of the "wave-mechanics" thing, and in doing so, you can lower the ground state energy (and thus, if the temperature of the system is very low, the entirety of the particles will be in the lowest energy state and the box will collapse). The tunneling out of the box is not analogous to the classical box being pushed to the left -- it is an analogy that only works in the small, discrete cases we talked about earlier.

("Yes, I know that temperature, pressure, etc. will push it back in again," but that is why we talk about "ground state energy," not "potential energy," which is not analogous to anything classical in origin.)

#mathpost #artificialverse

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lipshits-continuous · 2 years

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Operators as Observables and Ehrenfest's Theorem

In this post I will be talking about how we extract information from a wavefunction by first talking about probability distributions then by introducing operators and how they represent observable quanities of a system. Then I will finish by proving Ehrenfest's Theorem which shows how the expectation values of certain observables obey the laws of classical mechanics.

Since wavefunctions are complex functions they don't represent anything physical (for the sake of the post I'm not gonna talk about the intreptations of the wavefunction). However if we take the modulus squared of a wavefunction we get a real valued function. In fact this is the probability distribution of the position of the particle our wavefunction represents, i.e.

where Ψ is the wavefunction and Ψ* is its complex conjugate.

To find the specific probability we just take the integral of the probability distribution with respect to x. This means that we expect that if we take the integral over all space, i.e. on (-∞,∞), we should get an answer of 1 (since probabilities add to 1). If this isn't the case we can introduce a normalising constant to the wavefunction, call it N, such that

Note: not all wave functions are normalisable. If we take Ψ(x,t)=Aexp(i(kx-ωt)), then Ψ*(x,t)Ψ(x,t)=|A|^2 so the integral diverges regardless of whatever constant we multiply Ψ by. This is the wave function of a particle in free space.

Operators and Expectation Values:

Sometimes it is more useful to consider what would happen on average if we were to repeat a certain measurement. We can't predict exactly what one particle will do but we can predict what we expect to happen on average.

Position:

The easiest quantity to consider is position. If we multiply our probability distribution by x when we take the integral over space we will get the expectation value of position:

The reason I have written the integral on the right in that order will become clear later on.

Here is the wikipedia article for more details about where the definiton of the expecation value comes form

Momentum:

First I would like to consider what would happen if we took the spatial derviative of the wavefunction of a particle in free space, Ψ(x,t)=Aexp(i(kx-ωt)):

where the momentum, p=ħk, ħ is the reduced Planck constant. Then we can see that multiplying the wavefunction by p is equivalent to applying the differential operator

Now that we have this momentum operator we can define the expectation value of momentum:

Note: the position of the operator matters:

General Operators:

This naturally leads us to define the position operator as

but we don't have to stop there! For some observable quantity Q there is a corresponding operator Q hat such that

For example, the kinetic energy operator is

Real observables implies Hermitian Operators:

If a quantity is measurabale then is will be a real number, i.e. it remains the same under complex conjugation. This means that

with the two integrals being equal implying that the operator Q hat must be Hermitian. This is clearer if we rewrite the left integral and the equality becomes

Then if we define the inner product

we can see that our inequailty becomes

which is exactly the defining property of a Hermitian operator!

Ehrenfest's Theorem:

Ehrenfest's Theorem states that the expectation values of certain observables obey classical laws, i.e.

Proof:

Now consider the Schrödinger Equation and its complex conjugate:

Then substitute these into the integral above:

Now if we look at the second term of the integrand and apply integration by parts we get

where I have assumed that Ψ tends to 0 as x approaches ±∞ which is a condition for normalisation. If we then apply integration by parts again we get

Now substitute this back into the main integral:

You can prove similar results involving the expectation values of other observables.

This is an example of the correspondence principle which states that on macroscopic scales quantum mechanics should give the same results as classical mechanics!

#quantum mechanics #physics #physicsblr #long post #undescribed #lipshits posts #physics posting

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