Physics, Chemistry, and Mathematics

Advances in the investigation of the physical universe we live in.
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Re: Physics, Chemistry, and Mathematics

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Please see above :wink:
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Re: Physics, Chemistry, and Mathematics

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Re: Physics, Chemistry, and Mathematics

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6yfWdb-JOA8
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Re: Physics, Chemistry, and Mathematics

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.
One of the most fundamental claims of quantum theory — that objects separated by great distance can instantaneously affect each other’s behaviour.

The finding is another blow to one of the bedrock principles of standard physics known as “locality,” which states that an object is directly influenced only by its immediate surroundings. The Delft study, published Wednesday in the journal Nature, lends further credence to an idea that Einstein famously rejected. He said quantum theory necessitated “spooky action at a distance,” and he refused to accept the notion that the universe could behave in such a strange and apparently random fashion.

In particular, Einstein derided the idea that separate particles could be “entangled” so completely that measuring one particle would instantaneously influence the other, regardless of the distance separating them.

.
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Re: Physics, Chemistry, and Mathematics

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And now for something completely different "Confuse a Cat"

http://www.nature.com/scitable/blog/pop ... eshire_cat
The Quantum Cheshire Cat In The Wonderland of Quantum Physics


"Well I've often seen a cat without a grin... but a grin without a cat is a most curious thing"

Can you have a ring without a bell? A bark without its dog? In the weird quantum world you can. The Quantum Cheshire Cat Experiment, named after the mischievously grinning feline Alice encounters in Wonderland, has turned from theory to reality the remarkable feat of separating particles from their properties. Physicists were able to separate neutrons from their spins, like the Cheshire cat and its grin, and in doing so further question our understanding of the world around us.

We are taught that the universe is made up of many different particles - light of photons, atoms of electrons and protons and neutrons - and that these all have specific properties such as charge and spin. The idea that somehow these particles could exist without their properties, and ever stranger that these properties could exist without their particles, is a notion that goes against our intuition though one that is permitted by quantum theory.

Quantum physics emerged a century ago, and whilst contrary at the time to our classical understanding, has proven to be hugely successful. No experiment has disagreed with its predictions. Though it provides an accurate description of the microscopic world, this is a strange world, where particles can be in different places at the same time, spin clockwise and anticlockwise at the same time, and instantaneously influence each other from across the universe. Quite why the behaviour in the microscopic and macroscopic worlds differs so much is yet to be fully explained, with physicists still lacking a deep understanding of QM. This has resulted in experiments that have, and continue to, reveal a wonderfully weird picture of our world.

One of the most fascinating theories was provided by Aharonov half a century ago, showing that time in quantum mechanics is, at least mathematically, two way - it does not have to flow from past to present. This let to the time-symmetric formulation of quantum mechanics in the 1960s, which showed that not only did time flow both ways, but that events in both the past and the future could affect the state of a quantum system in the present. In the 1990s Tollaksen and Aharonov found that these influences could lead to a particle and its properties being separated. The Quantum Cheshire Cat analogy was founded.

Tollaksen, in his PhD thesis in 2001, proposed an experiment to test this theory. The first step is called pre-selection, in which a large number of neutrons all with identical spins are gathered. These particles are then sent into a device called an interferometer, where a beamsplitter splits the beam of neutrons in two. Each of the neutrons is then in the state of superposition, where it is travelling along both paths at the same time. On both paths there is equipment capable of making measurements of the neutrons and their spins. The two beams are then brought back together, combining in such a way that the neutrons exit one of two ways. The neutrons exiting along one of the paths undergo a process called post-selection, where their spin is measured. Only some of the neutrons will have the desired spin value, the others are disregarded. These processes of pre-selection and post-selection relate respectively to affecting the past and future of the quantum state of the neutrons. Now here's the curious thing. The mathematics shows that all the neutrons with the desired spin observed in post-selection took the same path inside the interferometer, whereas their spins went along the other path. The Cheshire cat and its grin would be separated.

It was a nice thought experiment, but the real intrigue has been whether in reality it can occur. Testing any quantum theory though encounters a serious problem. In the quantum world particles can spin clockwise and anticlockwise at the same time, but we only ever see them spinning one way or the other, due to the act of measuring them destroying the delicate superposition of states. Aharonov and colleagues theorised however in the late 1980s that by measuring with a device that interacts extremely weakly with the particle, its quantum state is preserved, and information about it can be gathered. But this insight into the particle's quantum nature comes with a great uncertainty. So studying one particle is not really any use - but the trick is to make these weak measurements on numerous identical particles, thereby providing through averaging the data information on the quantum state with a reduced uncertainty.

At the time this approach was met with disbelief and scepticism. But with the advancements in technology in the decades since, theory has become reality, and physicists have been able to study the quantum world in depth. To now investigate, Tollaksen and a team of researchers at Austria's Vienna University of Technology set about attempting to make such weak measurements on neutrons, a feat never previously achieved. They did so using an experimental setup involving weak magnetic fields and a weakly interacting neutron absorber to make the measurements. When the absorber was placed in one of the paths of the interferometer, there was an affect on the output, however placing it in the other path resulted in no such effect. This showed that the neutrons were travelling along only one of the two paths. Along each path of the interferometer, a weak magnetic field was established to interact with the spin of the neutrons. On one of the paths the magnetic field interacted with the neutron's spin and produced a change in the interferometer's output, however there was no such interaction on the other path. This therefore confirmed that the neutrons and their spin had taken different paths. The cat and its grin had been separated.

An amazing bit of experimental physics. But where do we go from here? Speculation has begun into the possibilities resulting from this ability to split particles from their properties, with particular intrigue into measuring the electric dipole moment of the neutron, which is crucial in theories explaining the matter-antimatter composition of the universe. Whilst the experiment involved neutrons and their spin, it isn't limited to this setup. In theory other particles such as photons and electrons, and other properties such as charge and magnetic moment, could all be studied. The only thing that can't be done is to separate particles from their mass. The Cheshire cat phenomenon could perhaps be best put to use in quantum computing, to overcome the major problem of shielding particles from external disturbances that destroy their important superposition of states that is key to the system. Another possibility is in high-precision metrology. Numerous other ways to take advantage of this physics are surely to be found.

It's important not to get too carried away with this new take on reality. The strangeness of the quantum world is clearly far from our everyday experience of the world around us. The post-selection process of the experiment is a neat trick to give an insight into the quantum nature of particles, but is not analogous to the sci-fi tales of future actions changing the past, such as squishing a bug today causing the extinction of the dinosaurs millions of years ago. This quantum take on the Cheshire cat and its grin only makes sense if you give physical meaning to these weak measurements and accept the conclusions based on averaging many results to reduce the high uncertainties. Furthermore, and fundamentally to the whole concept, it is unclear what it actually means for particles and their properties to be separated.

What is obvious is that the quantum Cheshire cat, the separation of particles and their properties, is a fascinating theory now become reality that is further proving insight into the bizarre quantum world and continuing to challenge our understanding of reality. Curiouser and curiouser indeed.
"I fancied myself as some kind of god....It is a sort of disease when you consider yourself some kind of god, the creator of everything, but I feel comfortable about it now since I began to live it out.” -- George Soros
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Re: Physics, Chemistry, and Mathematics

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Nautilus | Math’s Beautiful Monsters

Image
In mathematics, the Weierstrass function is an example of a pathological real-valued function on the real line. The function has the property of being continuous everywhere but differentiable nowhere. It is named after its discoverer Karl Weierstrass.
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Re: Physics, Chemistry, and Mathematics

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Re: Physics, Chemistry, and Mathematics

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Typhoon wrote:Closing the Door on Einstein and Bohr’s Quantum Debate

It is a quantum universe.
The next step is for quantum physicists to find a different language to communicate the theory to themselves and the public. Sentences like "an electron can be at two places at the same time" is not only linguistically an oxymoron but also misrepresents the quantum reality it describes.
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Re: Physics, Chemistry, and Mathematics

Post by Parodite »

Parodite wrote:
Typhoon wrote:Closing the Door on Einstein and Bohr’s Quantum Debate

It is a quantum universe.
The next step is for quantum physicists to find a different language to communicate the theory to themselves and the public. Sentences like "an electron can be at two places at the same time" is not only linguistically an oxymoron but also misrepresents the quantum reality it describes.
More of same language madness:
The strange fate of a person falling into a black hole

If you fell into a black hole, you might expect to die instantly. But in fact your fate would be far stranger than that

By Amanda Gefter

25 May 2015

This was the most-read story on BBC Earth in 2015. Here is another chance to read it.

It could happen to anyone. Maybe you're out trying to find a new habitable planet for the human race, or maybe you're just on a long walk and you slip. Whatever the circumstances, at some point we all find ourselves confronted with the age-old question: what happens when you fall into a black hole?

You might expect to get crushed, or maybe torn to pieces. But the reality is stranger than that.

The instant you entered the black hole, reality would split in two. In one, you would be instantly incinerated, and in the other you would plunge on into the black hole utterly unharmed.

[...]
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Re: Physics, Chemistry, and Mathematics

Post by Simple Minded »

Parodite wrote:
More of same language madness:
The strange fate of a person falling into a black hole

If you fell into a black hole, you might expect to die instantly. But in fact your fate would be far stranger than that

By Amanda Gefter

25 May 2015

This was the most-read story on BBC Earth in 2015. Here is another chance to read it.

It could happen to anyone. Maybe you're out trying to find a new habitable planet for the human race, or maybe you're just on a long walk and you slip. Whatever the circumstances, at some point we all find ourselves confronted with the age-old question: what happens when you fall into a black hole?

You might expect to get crushed, or maybe torn to pieces. But the reality is stranger than that.

The instant you entered the black hole, reality would split in two. In one, you would be instantly incinerated, and in the other you would plunge on into the black hole utterly unharmed.

[...]
Life after death in the scientific realm as well as the religious realm..... the differences between those with exclusive "knowledge/data" blur. Probably intentionally.

Similar to the language madness of "social libertarian." A lefty or a righty?
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Re: Physics, Chemistry, and Mathematics

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Parodite wrote:
Typhoon wrote:Closing the Door on Einstein and Bohr’s Quantum Debate

It is a quantum universe.
The next step is for quantum physicists to find a different language to communicate the theory to themselves and the public. Sentences like "an electron can be at two places at the same time" is not only linguistically an oxymoron but also misrepresents the quantum reality it describes.
I reread the article and could not locate any reference to "an electron can be at two places at the same time".

Rather I found the article to be a clear exposition of the QM versus local reality issue and of the conceptual and technical challenges faced by the three recent tour de force experiments in testing Bell's Theorem.

Regarding "an electron can be at two places at the same time" the accurate statement is that what one calculates is the evolution of the probability amplitude of the electron.

http://www.feynmanlectures.caltech.edu/III_03.html
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Re: Physics, Chemistry, and Mathematics

Post by Parodite »

Typhoon wrote:
Parodite wrote:
Typhoon wrote:Closing the Door on Einstein and Bohr’s Quantum Debate

It is a quantum universe.
The next step is for quantum physicists to find a different language to communicate the theory to themselves and the public. Sentences like "an electron can be at two places at the same time" is not only linguistically an oxymoron but also misrepresents the quantum reality it describes.
I reread the article and could not locate any reference to "an electron can be at two places at the same time".
Not in this article, but in countless other articles where QM physicists or commentators use such language.
Rather I found the article to be a clear exposition of the QM versus local reality issue and of the conceptual and technical challenges faced by the three recent tour de force experiments in testing Bell's Theorem.
Which means that when expirement reveals new information or verifies an existing predictive theory, it is about time to consider its meaning for physical reality.
Regarding "an electron can be at two places at the same time" the accurate statement is that what one calculates is the evolution of the probability amplitude of the electron.

http://www.feynmanlectures.caltech.edu/III_03.html
What I get from that is not that an electron has a probability amplitude but that what will be measured follows these probabilities.
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Re: Physics, Chemistry, and Mathematics

Post by Typhoon »

Parodite wrote:
Typhoon wrote:
Parodite wrote:
Typhoon wrote:Closing the Door on Einstein and Bohr’s Quantum Debate

It is a quantum universe.
The next step is for quantum physicists to find a different language to communicate the theory to themselves and the public. Sentences like "an electron can be at two places at the same time" is not only linguistically an oxymoron but also misrepresents the quantum reality it describes.
I reread the article and could not locate any reference to "an electron can be at two places at the same time".
Not in this article, but in countless other articles where QM physicists or commentators use such language.
Don't know as I don't read popularizations of QM.
Parodite wrote:
Rather I found the article to be a clear exposition of the QM versus local reality issue and of the conceptual and technical challenges faced by the three recent tour de force experiments in testing Bell's Theorem.
Which means that when expirement reveals new information or verifies an existing predictive theory, it is about time to consider its meaning for physical reality.
It is not clear to me what you are trying to state here.

The experiments have ruled out local reality theories and provided strong evidence that QM as described by it's mathematics is how nature works.
Parodite wrote:
Regarding "an electron can be at two places at the same time" the accurate statement is that what one calculates is the evolution of the probability amplitude of the electron.

http://www.feynmanlectures.caltech.edu/III_03.html
What I get from that is not that an electron has a probability amplitude but that what will be measured follows these probabilities.
From the point of view of the QM math, the distinction is not meaningful.
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Re: Physics, Chemistry, and Mathematics

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Parodite wrote:
Rather I found the article to be a clear exposition of the QM versus local reality issue and of the conceptual and technical challenges faced by the three recent tour de force experiments in testing Bell's Theorem.
Which means that when expirement reveals new information or verifies an existing predictive theory, it is about time to consider its meaning for physical reality.
It is not clear to me what you are trying to state here.
Well, the article does mention some ideas where future technology, if it works, would prove non-local instanteneous causation (or, to stay on the safe side, call it correlation) [my bold]:
The schemes demonstrated by the Vienna, NIST, and Delft groups have important consequences for quantum information. For instance, a loophole-free Bell’s inequality test is needed to guarantee the security of some device-independent quantum cryptography schemes [27]. Moreover, the experiment by the Delft group, in particular, shows it is possible to entangle static quantum bits, offering a basis for long distance quantum networks [28, 29].
It seems to me that this would truly be a revolution.
The experiments have ruled out local reality theories and provided strong evidence that QM as described by it's mathematics is how nature works.
But the experiments do not solve the problem of qm-gravity? at least not before the 2-spin graviton has been detected for starters.

Another thing that is mentioned in the article (and that appears to be down played a bit) that could spoil the fun is this [my bold]:
Of course we must remember that these experiments were primarily meant to settle the conflict between Einstein’s and Bohr’s points of view. Can we say that the debate over local realism is resolved? There is no doubt that these are the most ideal experimental tests of Bell’s inequalities to date. Yet no experiment, as ideal as it is, can be said to be totally loophole-free. In the experiments with entangled photons, for example, one could imagine that the photons’ properties are determined in the crystal before their emission, in contradiction with the reasonable hypothesis explained in the note in Ref. [18]. The random number generators could then be influenced by the properties of the photons, without violating relativistic causality. Far fetched as it is, this residual loophole cannot be ignored, but there are proposals for how to address it [30].
In your understanding, is this [the bold] a relevant possibility that can explain long distant non-local instantaneous/faster than light correlation? Of course Einstein maintained, up to his death bed, that faster than light causation or information transfer is impossible. He never liked "spooky action at a distance" for that reason. Did this experiment in Delft prove he was wrong there too?
Parodite wrote:
Regarding "an electron can be at two places at the same time" the accurate statement is that what one calculates is the evolution of the probability amplitude of the electron.
What I get from that is not that an electron has a probability amplitude but that what will be measured follows these probabilities.
From the point of view of the QM math, the distinction is not meaningful.
But Bohr, in his 30 years debates with Einstein, claimed that really nothing to very little can be said about the nature of physical reality such as "an electron" as it exists, may exist, independent from measurements in quantum experiments. The phrase "an eletron has a probability amplitude" is more how Einstein would say it. But then of course, he rejected the idea that electrons have probability amplitudes. He didn't like the idea of God playing dice. So they both would agree that probability amplitudes say very little about the nature of reality independent from scientific experiment, measurement and human observation in general.

But I understand your view on causal and/or ontological interpretations of QM. None of them ever added anything, changed anything; standard QM theory and application work like a breeze. Can't recall Feynman's exact words, but somewhere he says that it doesn't really bother him that QM is kinda weird, intuitively difficult/impossible to grasp. That also in Newtonian physics there is endless ontological mystery remaining. That all that matters in the end is what theory works and predicts best. "Shut up and do the calc". It seems to me he was an agnostic when it comes to interpreting QM beyond the math. I doubt he would claim that reality is probabilistic in nature.
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Quantum weirdness

Post by Parodite »

Following this I thought a separate thread is justified.

If closing the loopholes in Bell's inequality experiments is indeed coming to a close.. it would totally revolutionize science and technology. Instantaneous communication between very far apart quantum devices, light years even, would be possible. Telepathic connections throughout the universe so to speak. Or this whole thing would still fall flat on its face in the end... as Einstein "told you so". No faster than light energy/information transfer is possible.

Of course to outsmart Einstein is a noble and legitimate desire, but the old bard may not be defeated that easily and only nature has the final answer, i.e. in experiment and with new technology that works.

I'm just a layman, but totally fascinated by these things. In my next life I hope to have more talent for mathematics and physics and promise to get at least a PhD first. I claim nothing, just like to make shots in the dark and understand things better in the process. When all great physicists agree that no one should try to understand quantum mechanics beyond the math...that is when I get really interested. It is possible though for laymen to understand these issues conceptually and with a high school level of mathematics+physics you can still get pretty far.

There is way too much about quantum weirdness on the Internet available. Just Google any of these: quantum entanglement, quantum superposition, double-slit experiment, Bell's Theorem, Bell's inequalities, particle-wave duality, Einstein-Bohr debate, quantum consciousness. Will keep you busy for years. Not only what is taught on universities on the subjects, but also mushrooming amounts of speculation, wild theorizing, philosophical cathedrals filled the goodies on what-not like "quantum consciousness".

This Church of Uncertainty and Speculation makes the MMGW Church look a small village pool club. Been there done that. Especially in the philosophy departments there is so much word salad you could feed the world 10 years with it. But it helps to be somewhat acquainted with this mess. In the end it is back to physics, experimental and theoretical, as it stands now. Which is why the latest experiments, notably Bell's inequality tests by Delft University, are so important.

Later I hope to throw some notes here, shots in the dark, ideas, questions, observations.
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Re: Quantum weirdness

Post by noddy »

i only did a year and a bit of this at uni and didnt find it interesting so let it drop - it was possibly a hissy fit as i found out that all the electron shell nonsense i was taught in high school was lies.

all i can say is that probability/statistical approach reeeks of failure to understand the system properly - to me its like ignoring all the actual reasons a car has an accident and then saying their is a 5% chance the car will not get round the corner.

however!

the recent advances and quantum experiments are really interesting and make me wish i had several brains and several lifetimes to use them.
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Re: Quantum weirdness

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noddy wrote:all i can say is that probability/statistical approach reeeks of failure to understand the system properly - to me its like ignoring all the actual reasons a car has an accident and then saying their is a 5% chance the car will not get round the corner.
Yes, this was also Einsteins position. You are in good company. He argued that if the quantum formula accurately predicts what will be measured it is still incomplete , "something is missing".

The usual lingo that describes what happens before the measurement occurs of say a photon or electron in a quantum experiment, is that it is in a "superposition", that the physical wave before it is measured is "in all possible states at the same time" and that only after measurement it "collapses" to one of the states as governed by the probability distribution.

An analogy would be that a dice is swirling randomly in the air while nobody is measuring/observing it yet, and only when "measured" it collapses to a value of 1-6, say when it comes to rest on a table. Our intuition would be to reject the idea that while swirling around before measurement the dice would be "in all 6 states at the same time", just that it is still undecided which value will show up during measurement. Yet this classical common sense explanation is rejected in standard quantum mechanics. That it can't have this common sense explanation is one of the things I try to figure out. Found nothing yet. Just the claim that it is so. That an outcome is still undecided before a measurement sounds..well, more normal and honest.

And if, as in standard qm lingo, it is considered impossible to know much about anything before "it" is observed/measured.. then why sin against this home brew principle by making claims like: "before measurement a particle-wave can be in more than one state at the same time.. and even in different places at the same time"? That is a huge claim about physical stuff before it is measured! Maybe qm is weird... but how some physicists think or "explain" what happens.. is even weirder. There are plenty more examples of weird qm thinking to the point of madness.
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Re: Quantum weirdness

Post by noddy »

i understand that differently - this is about the measuring and not in the thing being measured - our tools at atomic and sub atomic level and their crude limitations.

it was explained to me as being a clumsy blind man trying to find a soccer ball in a large stadium - you run around randomly and sometimes bump into the ball, which then knocks it somewhere else.

keep a record of where you found it, bingo - you have statistical probabilities of soccer ball location in a field.

before you found it you had no idea where it was, and after you found it, you now have no idea where it moved to!

this is the language of qm.

statistical understanding of things is better than no understanding, it provides *some* information.

im definately way out of date on all this, havent even looked like studying it for 25 years .. or more .. shudder.
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Re: Quantum weirdness

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That the physical universe operates according QM at the fundamental level has now been established by experiments.

The local reality objections of Einstein and others are now D.O.A.

Whether people are comfortable, or not, with this empirical reality is frankly irrelevant.
The problem for many people it that QM is different from their everyday macroscopic experience.

Anyways, to understand QM, one should as a minimum understand the double-slit experiment.
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Re: Quantum weirdness

Post by noddy »

of course reality doesnt care about opinions, however if eople only spoke when correct against reality the world would resemble a trappist monastery.
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Re: Quantum weirdness

Post by Simple Minded »

Typhoon wrote:That the physical universe operates according QM at the fundamental level has now been established by experiments.

The local reality objections of Einstein and others are now D.O.A.

Whether people are comfortable, or not, with this empirical reality is frankly irrelevant.
The problem for many people it that QM is different from their everyday macroscopic experience.

Anyways, to understand QM, one should as a minimum understand the double-slit experiment.
A very sensible explanation, yet also very religious sounding. Perhaps reality is determined primarily by one's faith. :?

Which mountain are you climbing or descending...... right now? ;)
Simple Minded

Re: Quantum weirdness

Post by Simple Minded »

noddy wrote:of course reality doesnt care about opinions, however if eople only spoke when correct against reality the world would resemble a trappist monastery.
wot's a normal bloke to do when the (religious/political/scientific) experts disagree..... but take matters into one's own hands (perception)? :P
Simple Minded

Re: Quantum weirdness

Post by Simple Minded »

noddy wrote:
it was explained to me as being a clumsy blind man trying to find a soccer ball in a large stadium - you run around randomly and sometimes bump into the ball, which then knocks it somewhere else.
better analogy: yer in your bedroom having sex with Charlize Theron, yer wife walks in and turns on the light.

yer all alone!

QM? or.... is Charlize Theron is a kind caring, compassionate, giving...... selfless person? :P
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Re: Quantum weirdness

Post by Typhoon »

Simple Minded wrote:
Typhoon wrote:That the physical universe operates according QM at the fundamental level has now been established by experiments.

The local reality objections of Einstein and others are now D.O.A.

Whether people are comfortable, or not, with this empirical reality is frankly irrelevant.
The problem for many people it that QM is different from their everyday macroscopic experience.

Anyways, to understand QM, one should as a minimum understand the double-slit experiment.
A very sensible explanation, yet also very religious sounding. Perhaps reality is determined primarily by one's faith. :?

Which mountain are you climbing or descending...... right now? ;)
Not sure how it is "very religious sounding".

I'm not aware of any religion based on statistically significant empirical evidence acquired under reproducible conditions.

Rather all religions that I can think of are based on metaphysicals claim that require belief, or in my case, a suspension of disbelief.
A set of historical irreproducible results.

One might argue that one had to believe in something. That the physical universe exists and may be investigated through the use of our senses is a minimum.
The empirical argument in favour of this minimal belief is the material scientific and technical progress made to-date since the start of the scientific and industrial revolutions, as compared to spending one's time debating, say, as to whether or not Jesus took a dump.

Anyways, one problem with QM [ and the standard model and special relativity and general relativity and statistical mechanics and . . . ] is that it takes most of us, myself included, significant time and effort to understand.

When I read an article on a new physics result at, for example, Physics Today which targets physicists, the comments section is invariably flooded by people claiming that it, be that it QM or the SM or SR or GR or . . ., is all wrong and that their pet hypothesis is correct. Alternative theories are very important. However, one must first understand the physical phenomenon in question and associated theory of, otherwise, one's score goes too high. What quickly becomes painfully obvious is that such commentators have not bothered to do so and have absolutely no intention of doing so.

It's a problem as old as civilization. Euclid is said to have replied to King Ptolemy's request for an easier way of learning mathematics that
there is no Royal Road to geometry.
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Nonc Hilaire
Posts: 6168
Joined: Sat Dec 17, 2011 1:28 am

Re: Quantum weirdness

Post by Nonc Hilaire »

I keep watching the 'Beautiful Women' and 'Sex' threads for evidence from Typhoon's double slit experiments, but I am starting to have my doubts regarding the existence of this phenomenon.
“Christ has no body now but yours. Yours are the eyes through which he looks with compassion on this world. Yours are the feet with which he walks among His people to do good. Yours are the hands through which he blesses His creation.”

Teresa of Ávila
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