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swimfeeders
Chatterbox
swimfeeders is offline
Shropshire
Joined: Oct 2014
Posts: 24,056
swimfeeders is male  swimfeeders has posted at least 25 times and has been a member for 3 months or more 
 
13-07-2019, 03:36 PM
1

Amazing Photograph.

Hi

Einstein predicted a spooky outcome of his theories.

His words, not mine.

We have now managed to photograph it.

https://news.sky.com/story/quantum-e...-time-11762100

One particle reacting with another at the same instant in time even though they can be millions of miles apart.

We have so much to learn.
Kowhaigirl
Senior Member
Kowhaigirl is offline
New Zealand
Joined: Jul 2019
Posts: 77
Kowhaigirl is female 
 
13-07-2019, 03:44 PM
2

Re: Amazing Photograph.

Originally Posted by swimfeeders ->
Hi

Einstein predicted a spooky outcome of his theories.

His words, not mine.

We have now managed to photograph it.

https://news.sky.com/story/quantum-e...-time-11762100

One particle reacting with another at the same instant in time even though they can be millions of miles apart.

We have so much to learn.
Most of that made little or no sense to me, but was still, somehow, pretty cool
Donkeyman
Chatterbox
Donkeyman is offline
Melton,United Kingdom
Joined: Jan 2019
Posts: 9,088
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13-07-2019, 06:37 PM
3

Re: Amazing Photograph.

Originally Posted by swimfeeders ->
Hi

Einstein predicted a spooky outcome of his theories.

His words, not mine.

We have now managed to photograph it.

https://news.sky.com/story/quantum-e...-time-11762100

One particle reacting with another at the same instant in time even though they can be millions of miles apart.

We have so much to learn.
How is it possible to observe and record an event occuring
in two places a million miles apart at the same time unless
we have mastered time travel Swimmy?

Regards Donkeyman!
swimfeeders
Chatterbox
swimfeeders is offline
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13-07-2019, 07:09 PM
4

Re: Amazing Photograph.

Originally Posted by Donkeyman ->
How is it possible to observe and record an event occuring
in two places a million miles apart at the same time unless
we have mastered time travel Swimmy?

Regards Donkeyman!
Hi

Quantum Physics, Donkeyman.

Extremely small particles, much smaller than an atom, behave differently to our laws rules of physics.

The photo was not taken using particles a million miles apart, the thing is they interact with each other at the same time no matter how far they are apart.

Distance is not important in quantum physics.

It is the next big thing in computing.
realspeed
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13-07-2019, 07:25 PM
5

Re: Amazing Photograph.

he particle in a one-dimensional potential energy box is the most mathematically simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy everywhere inside a certain region, and therefore infinite potential energy everywhere outside that region. For the one-dimensional case in the {\displaystyle x} x direction, the time-independent Schrödinger equation may be written[90]

{\displaystyle -{\frac {\hbar ^{2}}{2m}}{\frac {d^{2}\psi }{dx^{2}}}=E\psi .} -{\frac {\hbar ^{2}}{2m}}{\frac {d^{2}\psi }{dx^{2}}}=E\psi .
With the differential operator defined by

{\displaystyle {\hat {p}}_{x}=-i\hbar {\frac {d}{dx}}} {\hat {p}}_{x}=-i\hbar {\frac {d}{dx}}
the previous equation is evocative of the classic kinetic energy analogue,

{\displaystyle {\frac {1}{2m}}{\hat {p}}_{x}^{2}=E,} {\frac {1}{2m}}{\hat {p}}_{x}^{2}=E,
with state {\displaystyle \psi } \psi in this case having energy {\displaystyle E} E coincident with the kinetic energy of the particle.

The general solutions of the Schrödinger equation for the particle in a box are

{\displaystyle \psi (x)=Ae^{ikx}+Be^{-ikx}\qquad \qquad E={\frac {\hbar ^{2}k^{2}}{2m}}} \psi (x)=Ae^{ikx}+Be^{-ikx}\qquad \qquad E={\frac {\hbar ^{2}k^{2}}{2m}}
or, from Euler's formula,

{\displaystyle \psi (x)=C\sin kx+D\cos kx.\!} \psi (x)=C\sin kx+D\cos kx.\!
The infinite potential walls of the box determine the values of C, D, and k at x = 0 and x = L where ψ must be zero. Thus, at x = 0,

{\displaystyle \psi (0)=0=C\sin 0+D\cos 0=D\!} \psi (0)=0=C\sin 0+D\cos 0=D\!
and D = 0. At x = L,

{\displaystyle \psi (L)=0=C\sin kL.\!} \psi (L)=0=C\sin kL.\!
in which C cannot be zero as this would conflict with the Born interpretation. Therefore, since sin(kL) = 0, kL must be an integer multiple of π,

{\displaystyle k={\frac {n\pi }{L}}\qquad \qquad n=1,2,3,\ldots .} k={\frac {n\pi }{L}}\qquad \qquad n=1,2,3,\ldots .
The quantization of energy levels follows from this constraint on k, since

{\displaystyle E={\frac {\hbar ^{2}\pi ^{2}n^{2}}{2mL^{2}}}={\frac {n^{2}h^{2}}{8mL^{2}}}.} E={\frac {\hbar ^{2}\pi ^{2}n^{2}}{2mL^{2}}}={\frac {n^{2}h^{2}}{8mL^{2}}}.
The ground state energy of the particles is E1 for n=1.
Energy of particle in the nth state is En =n2E1, n=2,3,4,.....
Particle in a box with boundary condition V(x)=0 -a/2<x<+a/2

A particle in a box with a little change in the boundary condition.
In this condition the general solution will be same, there will a little change to the final result, since the boundary conditions are changed
{\displaystyle \psi (x)=C\sin kx+D\cos kx.\!} \psi (x)=C\sin kx+D\cos kx.\!
At x=0, the wave function is not actually zero at all value of n.
Clearly, from the wave function variation graph we have,
At n=1,3,4,...... the wave function follows a cosine curve with x=0 as origin
At n=2,4,6,...... the wave function follows a sine curve with x=0 as origin
Variation of wave function with x and n.
Wave Function Variation with x and n.
From this observation we can conclude that the wave function is alternatively sine and cosine.
So in this case the resultant wave equation is
ψn(x) = Acos(knx) n=1,3,5,.............
= Bsin(knx) n=2,4,6,.............


NoI don't understand it either
Lion Queen
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Lion Queen is offline
UK
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Posts: 9,592
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13-07-2019, 08:13 PM
6

Re: Amazing Photograph.

Originally Posted by realspeed ->
he particle in a one-dimensional potential energy box is the most mathematically simple example where restraints lead to the quantization of energy levels. The box is defined as having zero potential energy everywhere inside a certain region, and therefore infinite potential energy everywhere outside that region. For the one-dimensional case in the {\displaystyle x} x direction, the time-independent Schrödinger equation may be written[90]

{\displaystyle -{\frac {\hbar ^{2}}{2m}}{\frac {d^{2}\psi }{dx^{2}}}=E\psi .} -{\frac {\hbar ^{2}}{2m}}{\frac {d^{2}\psi }{dx^{2}}}=E\psi .
With the differential operator defined by

{\displaystyle {\hat {p}}_{x}=-i\hbar {\frac {d}{dx}}} {\hat {p}}_{x}=-i\hbar {\frac {d}{dx}}
the previous equation is evocative of the classic kinetic energy analogue,

{\displaystyle {\frac {1}{2m}}{\hat {p}}_{x}^{2}=E,} {\frac {1}{2m}}{\hat {p}}_{x}^{2}=E,
with state {\displaystyle \psi } \psi in this case having energy {\displaystyle E} E coincident with the kinetic energy of the particle.

The general solutions of the Schrödinger equation for the particle in a box are

{\displaystyle \psi (x)=Ae^{ikx}+Be^{-ikx}\qquad \qquad E={\frac {\hbar ^{2}k^{2}}{2m}}} \psi (x)=Ae^{ikx}+Be^{-ikx}\qquad \qquad E={\frac {\hbar ^{2}k^{2}}{2m}}
or, from Euler's formula,

{\displaystyle \psi (x)=C\sin kx+D\cos kx.\!} \psi (x)=C\sin kx+D\cos kx.\!
The infinite potential walls of the box determine the values of C, D, and k at x = 0 and x = L where ψ must be zero. Thus, at x = 0,

{\displaystyle \psi (0)=0=C\sin 0+D\cos 0=D\!} \psi (0)=0=C\sin 0+D\cos 0=D\!
and D = 0. At x = L,

{\displaystyle \psi (L)=0=C\sin kL.\!} \psi (L)=0=C\sin kL.\!
in which C cannot be zero as this would conflict with the Born interpretation. Therefore, since sin(kL) = 0, kL must be an integer multiple of π,

{\displaystyle k={\frac {n\pi }{L}}\qquad \qquad n=1,2,3,\ldots .} k={\frac {n\pi }{L}}\qquad \qquad n=1,2,3,\ldots .
The quantization of energy levels follows from this constraint on k, since

{\displaystyle E={\frac {\hbar ^{2}\pi ^{2}n^{2}}{2mL^{2}}}={\frac {n^{2}h^{2}}{8mL^{2}}}.} E={\frac {\hbar ^{2}\pi ^{2}n^{2}}{2mL^{2}}}={\frac {n^{2}h^{2}}{8mL^{2}}}.
The ground state energy of the particles is E1 for n=1.
Energy of particle in the nth state is En =n2E1, n=2,3,4,.....
Particle in a box with boundary condition V(x)=0 -a/2<x<+a/2

A particle in a box with a little change in the boundary condition.
In this condition the general solution will be same, there will a little change to the final result, since the boundary conditions are changed
{\displaystyle \psi (x)=C\sin kx+D\cos kx.\!} \psi (x)=C\sin kx+D\cos kx.\!
At x=0, the wave function is not actually zero at all value of n.
Clearly, from the wave function variation graph we have,
At n=1,3,4,...... the wave function follows a cosine curve with x=0 as origin
At n=2,4,6,...... the wave function follows a sine curve with x=0 as origin
Variation of wave function with x and n.
Wave Function Variation with x and n.
From this observation we can conclude that the wave function is alternatively sine and cosine.
So in this case the resultant wave equation is
ψn(x) = Acos(knx) n=1,3,5,.............
= Bsin(knx) n=2,4,6,.............


NoI don't understand it either
I do but I can't be arsed explaining it to you realsy
Donkeyman
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Donkeyman is offline
Melton,United Kingdom
Joined: Jan 2019
Posts: 9,088
Donkeyman is male  Donkeyman has posted at least 25 times and has been a member for 3 months or more 
 
13-07-2019, 09:09 PM
7

Re: Amazing Photograph.

Originally Posted by swimfeeders ->
Hi

Quantum Physics, Donkeyman.

Extremely small particles, much smaller than an atom, behave differently to our laws rules of physics.

The photo was not taken using particles a million miles apart, the thing is they interact with each other at the same time no matter how far they are apart.

Distance is not important in quantum physics.

It is the next big thing in computing.
But, supposing the particles ARE a million miles apart
Swimmy, unless you use two cameras amillion miles apart
syncronised to do the neccassary imaging you can never
prove it happened? So how can you state that this interaction
between them actually took place!
Quantum physics sounds more like telapathy or teleporting
to me!

Regards Donkeyman!
Donkeyman
Chatterbox
Donkeyman is offline
Melton,United Kingdom
Joined: Jan 2019
Posts: 9,088
Donkeyman is male  Donkeyman has posted at least 25 times and has been a member for 3 months or more 
 
13-07-2019, 09:30 PM
8

Re: Amazing Photograph.

Originally Posted by swimfeeders ->
Hi

Einstein predicted a spooky outcome of his theories.

His words, not mine.

We have now managed to photograph it.

https://news.sky.com/story/quantum-e...-time-11762100

One particle reacting with another at the same instant in time even though they can be millions of miles apart.

We have so much to learn.
Were'nt Einsteins equations based on the speed of light being
constant Swimmy? But the discovery of black holes has cast
doubt on this belief, as light cannot escape the gravity field
of a black hole, its speed can obviously stopped, therefore
you would think its speed could vary from zero up to the
speed of light as we know it!
Surely this means that his theories also will vary?
Can you ( excuse the pun ) throw some light on this?

Regards Donkeyman!
swimfeeders
Chatterbox
swimfeeders is offline
Shropshire
Joined: Oct 2014
Posts: 24,056
swimfeeders is male  swimfeeders has posted at least 25 times and has been a member for 3 months or more 
 
14-07-2019, 03:46 AM
9

Re: Amazing Photograph.

Originally Posted by Donkeyman ->
Were'nt Einsteins equations based on the speed of light being
constant Swimmy? But the discovery of black holes has cast
doubt on this belief, as light cannot escape the gravity field
of a black hole, its speed can obviously stopped, therefore
you would think its speed could vary from zero up to the
speed of light as we know it!
Surely this means that his theories also will vary?
Can you ( excuse the pun ) throw some light on this?

Regards Donkeyman!
Hi

Light is made of photons.

Even though photons have no mass, they are still affected by gravity. That's how we can see black holes - by the way they distort the light going near them. The reason nothing can escape a black hole is because within the event horizon, space is curved to the point where all directions are actually pointing inside.


Hope this helps.
Donkeyman
Chatterbox
Donkeyman is offline
Melton,United Kingdom
Joined: Jan 2019
Posts: 9,088
Donkeyman is male  Donkeyman has posted at least 25 times and has been a member for 3 months or more 
 
14-07-2019, 09:35 AM
10

Re: Amazing Photograph.

Originally Posted by swimfeeders ->
Hi

Light is made of photons.

Even though photons have no mass, they are still affected by gravity. That's how we can see black holes - by the way they distort the light going near them. The reason nothing can escape a black hole is because within the event horizon, space is curved to the point where all directions are actually pointing inside.


Hope this helps.
Something like a vortex then, Swimmy!
Yes, l understand light can be deflected by a gravitational
field because we can observe it happening, but this only
supports my view that the speed of light is NOT constant
as Einstein believed? Which brings his theories into question,
as they are based on speed of light being constant?
Not so?
By the way, we cannot see black holes, what we observe is
the space they occupy, as a black space, because anything
on the far side of it are invisible due to the light they project
being sucked in by the black holes gravitational field before
it can reach us?
Anything between us and the black hole, providing it is not too
close to it, will still be able to be seen by us.
I would be interested to hear any observations you may have
on my views?

Regards Donkeyman!
 
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