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@kshegunov Quantum Mechanics

@kshegunov , and other physicists:
OK then. 2 initial quantum questions:
What does the empirical demonstration of Bell's Inequality Theorem thing tell me about the physical world I inhabit?

So what actually happened when they did the experiment on Schrödinger's cat?


@JNBarchan said in @kshegunov Quantum Mechanics:
 What does the empirical demonstration of Bell's Inequality Theorem thing tell me about the physical world I inhabit?
Not much as far as I know. Just that there can be no hidden variables in a quantumlike theory. Can't elaborate much on it as I'm not that familiar with the whole formalism.
 So what actually happened when they did the experiment on Schrödinger's cat?
As with any thought experiment  at the end of it they got a headache ;)
The cat is just an metaphor that tries to illustrate the principle of superposition in QM, but many people fundamentally misunderstand it and think it's bizarre and/or wrong. Basically it boils down to a very simple idea  you have a system with 2 pure states (i.e. the cat is alive, or the cat is dead, you could make the argument with the electron spin all the same). In the closed system where there's no interaction with the outside world the state is a superposition of the two with some probability. When you measure you're no longer dealing with a closed system, that is the person/instrument that measures influences the system, and since there's now determinism involved (i.e. the act of measurement) the state of the system collapses to one of the pure states  the cat is either dead or alive.

@kshegunov
Hi,I understand the Schrödinger cat idea, I don't think it's wrong. I just want to know which way it did actually turn out when opened the box on his cat?
For the Bell/EPR thing, it's the implication of the "can be no hidden variables" that's intriguing, don't you think? What could quantum entanglement be? Are you more of a "Mathematical Physicist" rather than a "Philosophical Physicist"? ;)

@JNBarchan said in @kshegunov Quantum Mechanics:
I just want to know which way it did actually turn out when opened the box on his cat?
Well, either one way or the other. :)
The point is you can't tell until you open the box.For the Bell/EPR thing, it's the implication of the "can be no hidden variables" that's intriguing, don't you think?
I guess. I wouldn't trust theories that depend on hidden variables anyway, though. The whole point of science is to learn things, if we argue there exist things that can be neither measured, known or are otherwise hidden, we might as well go to church instead.
What could quantum entanglement be?
State coupling, which is pretty common. The typical (and quite known) problem, however, is not with entanglement itself. It's with the fact the QM is nonlocal, this mean everything (every process in QM) happens instantaneously in the whole of space, which is bizarre and hard to reconcile with.
Are you more of a "Mathematical Physicist" rather than a "Philosophical Physicist"?
Nuclear theory. Probably you could say I'm more of a mathematical physicist, I enjoy philosophy but am ultimately a practical man.

It's with the fact the QM is nonlocal, this mean everything (every process in QM) happens instantaneously in the whole of space, which is bizarre and hard to reconcile with.
That's the bit I mean. And I assume a particle could in principle entangle with many others, and then any of them could influence it at the opposite side of The Universe. When they discover one day, I wonder what the "mechanism" will turn out to be....
Probably you could say I'm more of a mathematical physicist, I enjoy philosophy but am ultimately a practical man.
Yes I kind of guessed :) Being a layman, I am of course a purely philosophical amateur physicist!
Nuclear theory.
Ah ha! That's more like it! Right then: why haven't you figured practical nuclear fusion yet for the world's needs? You've had enough time now!

@JNBarchan said in @kshegunov Quantum Mechanics:
That's the bit I mean. And I assume a particle could in principle entangle with many others, and then any of them could influence it at the opposite side of The Universe. When they discover one day, I wonder what the "mechanism" will turn out to be....
Yes, in principle it could. A group of Chinese scientists farily recently entangled two ensembles (please don't ask me to dig up the article it's quite late). Probably they'd discover QM is just an approximation ... just like what happened with classical mechanics and the relativistic corrections.
Yes I kind of guessed :) Being a layman, I am of course a purely philosophical amateur physicist!
No harm in that. :)
Ah ha! That's more like it! Right then: why haven't you figured nuclear fission yet for the world's needs? You've had enough time now!
Well I had a colleague that was working on that, he went into the private sector  there's just little money in science. Also we have figured it out ages ago, the problem is an engineering one, not a physical. For this you can ask the engineers around ... @Wieland, don't hide, why haven't you built the damn reactor already?! ;)

Ah ha! That's more like it! Right then: why haven't you figured nuclear fission yet for the world's needs? You've had enough time now!
You quoted me before I had changed "fission" to "fusion", which is embarrassing! [Although it would be one way to solve all our needs :) ] I had also changed it to "practical nuclear fusion".
So once it's "practical" you hand over to engineers?! It's their problem. What about you come with some nuclear science physics which aids the practicalities? I don't know, find I way to make it work much closer to room temperature, or with less need for input power? :) We have been waiting for like 50 years for this promised physics + technology, and it's always "20odd years away".

@JNBarchan said in @kshegunov Quantum Mechanics:
So once it's "practical" you hand over to engineers?!
It was just a jape.
What about you come with some nuclear science physics which aids the practicalities?
As far as I know, although it isn't my subspecialty, they're building a reactor currently in germany to test some ideas. They are hopeful, but you know ... we don't sell any guarantees ...
We have been waiting for like 50 years for this promised physics + technology, and it's always "20odd years away".
That's what I told my colleague while he was still working on it. He replied he doubts it'd be less than 50 years before we actually have a real and industry grade solution on that.

although it isn't my subspecialty
LOL :) So what exact area are you a physicist in, preferably in terms I can understand?

Nuclear structure, I'm trying to model out the internal structure of the nucleus ... not so successfully as I'd like if I may add ... :}

@kshegunov
Ah. Well I can help you there: Bunch of stuff in the centre. Sometimes it behaves oddly.
 Then lots & lots of empty space. Nothing there. Except maybe millions of virtual particles and dark energy.
 Then cloudy area sort of containing small stuff. Nothing's really where it seems to be.
There, that should help, if you wish to use this in your work you are welcome. :)

I promise to cite your contribution as any good scientist will do. :)
Now I have to go to sleep before I fall asleep on the keyboard. Night!

I way to make it work much closer to room temperature, or with less need for input power?

@MRen
I think that's the Holy Grail they are searching for but not achieving!

@MRen said in @kshegunov Quantum Mechanics:
I way to make it work much closer to room temperature, or with less need for input power?
What is that? Fusion? Doubtful, at least not in any meaningful way. Generating electricity is done by spinning steam turbines. No heat  no steam  no electricity.

@kshegunov
Well you know that news story a few years back about the scientist who claimed he was achieving fusion at room temperature, and all the world's energy problems were solved. Till nobody else could reproduce it....I've been waiting to see if you'd return. Happy Christmas!
Now I'd really like to ask a question I'd like answered  by you or the science community ppl here  about time dilation. I know it's OT from this topic's quantum mechanics, but should I just ask it here anyway?

@JonB said in @kshegunov Quantum Mechanics:
Well you know that news story a few years back about the scientist who claimed he was achieving fusion at room temperature
I've "achieved" it on a workshop in HIL in Warsaw. Any sufficiently powerful particle accelerator (in this case a cyclotron) will do the job. The point is we don't get energy out of that, only the fun. :)
I've been waiting to see if you'd return.
I'm like a nasty cold, I always return. :D
Belated merry Christmas!I know it's OT from this topic's quantum mechanics, but should I just ask it here anyway?
Shoot. This is THE Lounge, everything is OT here. :D

@kshegunov
I've heard about "cyclotrons". They do weird things.OK, my time dilation problem. So it's one part of the "Twin Paradox" (yes, we know it's not a paradox).
The story goes: Twins on Earth. One twin gets in rocket, travels very fast (close to the speed of light) and returns after, say, one year, and his brother has aged a hundred years.
Only one account I have read bothers to clarify the details. The issue is: why is it the twin in the rocket who ages less relative to the twin who stays on Earth? Through the principle of equivalence, we are just as entitled to view the rocket as stationary and the Earth which did the one year trip. Either twin's frame of reference should be valid. So is the situation actually symmetrical (in which case one twin can't age more than the other)?
The account which discusses this points out that it is not symmetrical: the rocket had to accelerate up to light speed, turn around after six months, and decelerate upon returning to Earth. Those are real effects applying only to the rocket twin, not the stationary one.
All of this I get. The bit I don't get is: most of the year the rocket is chugging along in a straight line at 99.9% the speed of light. This is constant speed relative to the twin on Earth, no acceleration. So, is this (majority) part of the journey irrelevant to the aging difference? Does all of the aging difference "occur during" (yes, I know...) the accelerative parts of the rocket journey? If we could accelerate the ship up to light speed very quickly, turn it around, and slow it back down in a very short period, skipping most of the year at constant speed, would the age difference be just the same? What relevance does the constant speed segment of the journey have at all??
I really would appreciate an answer/discussion from someone. It may seem odd, but I have worried over this for years :(

Oh, the infamous twins ... that's a rather common question, actually. :)
I'll try to break it down into manageable chunks, hopefully.
Firstly, the theory of special relativity is applicable only in inertial reference frames (no acceleration) and when there are no gravitational sources, everything else falls out of its scope. Secondly, it shows you that time flows differently in different reference frames, so as to keep the physical reality consistent. To elaborate on the second point, you'd need to consider how and why are the Lorentz transformations (the actual equations that give you time dilation) derived. To understand that, you need to accept two premises that the whole physics is based upon, though: Space (and spacetime) is homogeneous, meaning there is no preferred position. That is to say the physical laws are the same no matter if you are on Earth, on the Moon, or at the edge of the universe. Or to phrase it more "rigidly" there's translational invariance.
 Space (and spacetime, explained later in the text) is isotropic, meaning that there is no preferred direction. That is to say leftwards is no different than rightwards, nor upwards or any other direction. Or to phrase it more "rigidly" there's rotational invariance.
Due to Emmy Noether and her theorem (the actual math doesn't matter here), every symmetry "imposes" a conservation law. So 1) will give you the conservation of momentum law and 2) will give you the conservation of angular momentum. There's also few other symmetries (we have more conservation laws):
 the timereversal symmetry, which generates the energy conservation law
 parity symmetry, which generates "nochirality" (i.e. no preference to left or righthandedness)
 charge conjugation symmetry, which generates the charge symmetry.
However, these have been shown to be violated in some cases by the weak and/or strong interactions. As we are talking about the macro world they're not so interesting here, I've put them only for completeness.
Now back to the STR  it starts by introducing the Minkowski space (i.e. timespace), which means all vectors are now in 4dimensions, one for time and 3 for the physical space. As with every vector space one could (and should) introduce the notion of distance, but in this case the distance will include time also. The actual distance depends on the metric of the space (limiting the scope only to inertial frames of reference as travelling with acceleration involves derivatives of time), which in the case of STR is a diagonal matrix (i.e. there's no "mixing" between space axes and the time axis). After we have the notion of space, we can differentiate points in that space, or simply we can differentiate events (as time is already part of that space). Ultimately, the special theory of relativity's point is that we always want to have 1) and 2), so the Lorentz transformations are derived by making a rotation around the axis of time, thus obtaining the transformations one has to apply to the different quantities so 2) is true. That leads to a rather simple realization  two events are simultaneous when their distance in timespace is zero, which leads to your thought experiment.
The twins paradox is a consequence of the fact that one of twins is "staying still" on earth, while the other is traveling through space. You could identify two events that are common (simultaneous) for both twins  when one leaves, and when he returns, so by taking in mind what I've written so far to account for one's traveling through space his clock should tick more slowly, i.e. you get time dilation.
There are "peculiarities", however. For example there's no explanation of how one of the twins accelerates to relativistic speeds, as this is out of the scope of the special theory of relativity, nor the twins can be treated as point objects. In a sense the theory gives you only an indication of how the world "looks" from different points of view, but it doesn't explain how you arrive at that point of view. To have a realworld explanation one should account for travelling with acceleration, which is part of general relativity, and this isn't at all trivial. The thought experiment should be taken only as an illustration of the effect, although the effect is quite real, not as a realworld example.
A more realistic consideration would be the effects cosmic muons experience when they enter the atmosphere, which supports special relativity  their average lifetimes are predicted and observed to be longer than the ones they would have had if they were not moving with relativistic speeds. Similarly GPS systems could not operate without corrections reflecting the theory of special (and general) relativity.

@kshegunov
Firstly, thank you so much for your lovely, detailed response. I actually thought you might say "I'm a nuclear structure physicist, none of this is my area". But you didn't.I do understand what you have written, at least from a layman's POV.
However, and with the greatest respect, nothing you said addresses the question I am asking (at least as far as I understand it). You may have taken my question as a general one about the twin"paradox", but in fact I have a very specific query.
You wrote at one point about "special relativity" and "no acceleration". I concur totally with the distinction from general relativity. That is the nub of failure to understand and my question. I will state it again, in summary.

The question is: why does the travelling twin age relative to the stationary twin? What exactly in the traveller's journey causes this change?

The journey consists of 2 distinct classes of motion:
a. the departure from Earth, turnaround at the halfway point, and return to Earth, all of which involve acceleration.
b. the long, "middle" phases of the outward & homeward journey, both of which involve constant velocity, no acceleration. 
The (best) account I read (seemed to) state:
 there must be a nonsymmetry about the twin's journey compared to the stationary twin for an age difference to arise.
 That difference can only lie because of 2.a., where acceleration is involved.
 During 2.b., where only constant velocity is involved, either twin can regard himself at rest with respect to the other. So no relative age difference can arise.
So my question is: if this account is correct, what relevance does the middle part of the twin's journey  the part of constant velocity  have to the final age difference when they are reunited at the end?
Let's say the journey is:
 1 day of acceleration out from Earth from 0% to reach 99.9% speed of light.
 6 months of constant velocity at that 99.9% speed of light.
 1 day of acceleration at the halfway point to turn round back to face Earth.
 6 months of constant velocity at that 99.9% speed of light.
 1 day of deceleration into Earth from 99.9% speed of light down to 0%.
The twin has been gone for 1 year in his time, but 100 years have passed on Earth. If we took out, or reduced to 1 day, specifically steps 2 & 4  the constant motion at 99.9% speed of light segments, leaving only the accelerative parts  so the whole journey only took the travelling twin 3 days, why wouldn't 100 years still have passed on Earth?
The way the twin paradox is phrased talks about him travelling for one year at 99.9% speed of light to give rise to the age difference upon return, but I don't get why any segment of constant motion would give rise to any age differing?
Thank you in advance for your answer to this specific issue!


@JonB said in @kshegunov Quantum Mechanics:
You may have taken my question as a general one about the twin"paradox"
Indeed, I have.
The question is: why does the travelling twin age relative to the stationary twin? What exactly in the traveller's journey causes this change?
As far as I understand it, it's due to the acceleration/deceleration, that is 2a.
what relevance does the middle part of the twin's journey  the part of constant velocity  have to the final age difference when they are reunited at the end?
If you mean relevance to the aging  none.
so the whole journey only took the travelling twin 3 days, why wouldn't 100 years still have passed on Earth?
The time the travelling twin would observe (i.e. how he'd perceive the time on Earth flowing) would practically slow to a halt, so much so that the total time that'd pass there would be the same as for the traveling twin. Or in other words the proper time of the traveling twin would be the same as the one stationary if there's no acceleration/deceleration.
I don't get why any segment of constant motion would give rise to any age differing?
It wouldn't. The special theory of relativity gives you a tool how to move from one frame of reference to the other, but the physical reality doesn't change  a journey from A to B will take the same amount of traveling in spacetime no matter what frame of reference you choose.

@kshegunov
Thank you!If I understand correctly, you seem to be concurring with my understanding that the final age difference when the traveller returns to Earth depends only on the acceleration he underwent and not on the phase(s) of constant motion.
Thus in my "thought experiment" we had:
 Total accelerative phases: 3 days.
 Total constant motion phases: 1 year.
 Travelling twin time passed: 1 year and 3 days
 Stationary Earth twin time passed: 100 years.
Now, if we play with #2 duration only:
 If #2 constant motion reduced to 0 days, time passed for traveller reduced from 1 year 3 days to 3 days, and time passed for stationary reduced from 100 years to 99 years.
 If #2 constant motion increased to 2 years, time passed for traveller increased from 1 year 3 days to 2 years 3 days, and time passed for stationary increased from 100 years to 101 years.
However, the popular accounts talk about "the length of the twin's journey and his fast speed affecting how long passes on Earth", with the implication being that if the journey is twice as long (2 years instead of 1) then the time passed for the observer would increase proportionally, i.e. 100 years to 200 years rather than 101 years.
You & I are claiming that is not correct, and that the time dilation occurs only as a result of General Relativity (acceleration) and not as a result of Special Relativity (constant motion). Is that right??!!

@JonB said in @kshegunov Quantum Mechanics:
If I understand correctly, you seem to be concurring with my understanding that the final age difference when the traveller returns to Earth depends only on the acceleration he underwent and not on the phase(s) of constant motion.
Yes.
Travelling twin time passed: 1 year and 3 days
From the point of view of the stationary twin, as the travelling twin's time will depend on the acceleration during the 3 days the stationary twin observes.
If #2 constant motion increased to 2 years, time passed for traveller increased from 1 year 3 days to 2 years 3 days, and time passed for stationary increased from 100 years to 101 years.
Again from the point of view of the stationary twin.
You & I are claiming that is not correct, and that the time dilation occurs only as a result of General Relativity (acceleration) and not as a result of Special Relativity (constant motion). Is that right??!!
Uhm, yes, I think I agree. However, time dilation is called the apparent difference in the speed with which the clock ticks no matter how you arrived at that particular reference frame (i.e. different speed). So in that sense you'd have time dilation in special relativity too.

@kshegunov
Hmmm.... I think we need to actually test this so I can verify my understanding ;)

@JonB, I stumbled upon this video and have remembered your questions ... so enjoy!

@kshegunov thanks for sharing, minutes Physics always worth a thumps up :)
But to be honest, I'm more excited about the moving dartboard mentioned in the video:
https://www.youtube.com/watch?v=MHTizZ_XcUM&feature=youtu.be