Nothing and uncertainty

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Introduction

My grandfathers first question in his German version book was “Did god create universe out of nothing”. Read more about his book in this page.  

When I found  a Youtube video where al-Khalili talks about “Nothing Everything and Nothing: What is Nothing?” I could not avoid to start looking at it. 

This video and the one one Walter levin (see below) became important in my search of a answer to my grandfathers question. 

I  created this page mainly with the help of these two videos.

During the work with this page, I discovered that I  wrote a post about nothing is something before. See at www.kinberg.net/wordpress/stellan/2018/01/26/nothing/
I added the content from that post at the end of this page.

Index

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The video

I begun looking at the beautiful documentary of Al-Khalili “Everything and nothing”

Aristotle

He said that there is no nothingness

a straw is always filled with substance.
If you empty it (suck the air out) the wall collapse. Why?

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Evangelista Torricelli

“Torricelli was an Italian physicist and mathematician, and a student of Galileo. He is best known for his invention of the barometer, but is also known for his advances in optics and work on the method of indivisibles.” ( wiki

Torricelli could create and capture empy space in a mecury glass tube for long time enough so nothingness/vakuum, could be studied.

He filled a glass tube with mercury to see if the mercury left the tube, like the water in a straw. (See picture below)

The he let the mercury  drain out but all the  mercury did not leave the glass tube as it was expected and seen with filled straws.

( Source: www.researchgate.net )

Pascal 

Blaise Pascal wanted to look closer at Torricellis discovery. He brought the Torricelli mercury tube to a top of a tower and saw that the air pressure changed with height.

Torricelli and Pascal understood that the level of vacuum in the mercury tube is a messure of the pressure of air. 

They discovered that air has a weight

Nothingness could now be captured and begin to be studied..

Torricelli wrote this:  “We live at the bottom of a ocean of air.”

Torricelli and Pascal research led us to understand that “The earth is cocooned by air.”

Vacuum is nature default state.

The Properties of nothingness/vakuum

A Bell inside vacuum jar can’t be heared but it can be seen.

I have done this experiment with all my  grade 8-9 science students. They learned that air is needed to hear sound. But I never thought about asking the students how we could still see the bell.

Maybe it was good I didn’t as I myself would not have been able to answer that question.

However, a vakuum contain a substance that can carry light.

The hypothesis came up among the scientists that there is a “luminipherous aether” in vakuum, a light carrying fluid.

Light is a wave so there must be something carrying it. There is no empty space.

But vacuum wasIntangible eluding all kind of attempt to study it until Michelsen made theMichelson–Morley experiment

Albert Michelsen 

“was an American physicist known for his work on measuring the speed of light and especially for the Michelson–Morley experiment. “ ( Wiki ) He was the first first American Nobel price winner 1907.

The properties ofluminipherous aether can be deduced studying the speed of light.

As earth moves around the sun, Michelsen thought that the “luminipherous aether” must  comes around the earth like a wind with different speed (like air around a wing as discovered by Daniel Bernouilli).

With Michelsen and Morleys experiment it was found that there is no “luminipherous aether” 

Einstein was able to proove that light can spread out in vakuum

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Heisenberg uncertainty principle

Heisenberg derived the uncertainty equation that can be written as below

(Image source: www.youtube.com/watch?v=a8FTr2qMutA 

This eaquation says that “It is impossible to find a state in which a particle had the definite position (x) and momentum (p x)”

A change in position (x) is indirectly proportional to the change in (dp)

Carlos S frenk, University of Durham in the video of above of al-Khalili says that:

  • x“Nature itself is based on uncertainty
  • The world of quantum physics is a world of uncertainty
  • You can never be sure what is going to happen.
  • On a very fundamental base nature is based on uncertainty”

Walter Levin tells us that despite a photon does not have a mass, it has a momentum.

Experimental demonstration

Heisenberg uncertainty principle is demontrated with the single split experiment as it is explained in this nice little video

Mathematical demonstration

The frequency of a photon is  expressed by the ratio h/λ where h represents Planck’s constant and λ represents the wavelength of the photon. The momentum of a photon of light (Δp) is known to simply be its frequency.  So we have the equation Δp=h/λ. 
As Δx=λ then we get 
Δp=h/Δx

and ΔxΔp=h or h=ΔxΔp

This lecture of Walter Levin is very good as it goes through the basics of quanta before coming to Heisenbergs equation.

 

Consider an arbitrary state |ψ>|ψ>, and a real number λRλ∈R. Now consider the position and momentum operators x^x^ and p^p^, which have commutation relations [x^,p^]=x^p^p^x^=i.[x^,p^]=x^p^−p^x^=iℏ.I’ll suppose that the average values of x^x^ and p^p^, are zero :<x^>=<p^>=<ψ|x^|ψ>=<ψ|p^|ψ>=0.:<x^>=<p^>=<ψ|x^|ψ>=<ψ|p^|ψ>=0. We don’t lose any generality in the proof, if the average values aren’t 0 then just replace x^x^ by x^<x^>x^−<x^> in the following proof. Same goes for momentum.

Now you have that x^+iλp^|ψ>2>0‖x^+iλp^|ψ>‖2>0, you’re just saying that the square norm of a vector is positive, this means that :

<ψ|(x^iλp^)(x^+iλp^)|ψ><ψ|(x^−iλp^)(x^+iλp^)|ψ>

Because the hilbert conjugate of (x^+iλp^(x^+iλp^ is (x^iλp^).(x^−iλp^).

=<ψ|x^2|ψ>+iλ<ψ|x^p^p^x^|ψ>+λ2<ψ|p^2|ψ>=<ψ|x^2|ψ>+iλ<ψ|x^p^−p^x^|ψ>+λ2<ψ|p^2|ψ>

=λ2<p^2>+iλ<[x^,p^]>+<x^2>=λ2Δp2λ+Δx2>0=λ2<p^2>+iλ<[x^,p^]>+<x^2>=λ2Δp2−λℏ+Δx2>0

We have of course that <x^2>=Δx2<x^2>=Δx2 because the average value is 0. In general you have Δx2=<x^2><x^>2.Δx2=<x^2>−<x^>2.

Now we have there a polynomial in λλ that is always positive. This means that the discriminator is negative (if it’s always positive then there is at most one root, it means the parabola never crosses the x-axis). So we have that 24Δx2Δp2<0ΔxΔp>2ℏ2−4Δx2Δp2<0⟺ΔxΔp>ℏ2

And voilà ! A proof for quantum mechanics using algebra and polynomials. Essentially, the uncertainty principle exists here because the commutator between the two operators x^,p^x^,p^ isn’t zero. It’s a very general result, and it’s not restricted to operators that are a bit like “Fourier transforms” of the other, like it is the case with those two we used. ( Source: Jose Moran in a answer in www.quora)

he Schroedinger equation

This equation dveloped byErwin Schrödinger defines the state of the system at each spatial position, and time. And that is valid also for electrons around the nucleus.

Heisenbergs uncertainty principle can be described using the quantum wave function ψ (psi). What is ψ  and how is it used in a equation?

Psi- the quantum wave function 

Schroedinger gave us a description of the wave function he used in the Schroedinger equation.

“The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation.” ( Source: Wiki )

In the video at www.youtube.com ) I learn that
“Position and momentum of a particle does not have defined values until it is observed. The quantum wave function psi describes the probability of each Position and momentum does not have defined values until it is observerd. The quantum wave function psi describes the probability of each observation.”
and
“The probability of the particle being at a particular position is given by the square of the amplitude  of the wave function at that location.”

(Source: www.youtube.com )

Wave function

So Ihave to understand the math of a wave function in the visible world (inclassical physics ) like for water waves. Jean le Rond d’Alembert, discovered 1746 the one dimension equation of waves 

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and within ten years Euler discovered the three-dimensional wave equation.

Eulers three dimensional equation of waves

Euler used knowledge of differential Equations.

Where the heat equation is a partial differential equation. Look at la Place equation.

 

 

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Sacred book about nothing

As it is said in the Bible:

In the beginning was the Word, and the Word was with God, and the Word was God. He was with God in the beginning. Through him all things were made; without him nothing was made that has been made. (John 1:1-3 )

n Spanish “Word” has been translated to “Verb” like the tetragrammaton (JHWH) is translated to “To be” by the Witnesses of Jehovah.

Nothing is something?

Here follows a copy of post 26/1 2018 with title Nothing is something?

 
“In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters.” ( Bible Genesis 1:1-2 )

“Formless and empty “and “darkness” before the Creation of the heavens and earth. I think it is quite a remarkable observation about the time  before the Creation, remarcable as it was written down maybe 4000 years ago. What does the Scientific world say about nothng and about “before Big Bang”?

I  wrote about Big Bang in http://www.kinberg.net/cosmology/the-origins-of-the-universe/  and in http://www.kinberg.net/?s=big+bang

 Now I found a new video about nothing from the Science festival. These are my notes for the video.

Content

Someone may think that we have almost vacuum in between the galaxies where we have almost absolute zero (0 Kelvin = -273.15 C).  But not. There is plasma everywhere, even there. I wrote about it  some time ago in http://www.kinberg.net/?s=plasmasphere . This video doesnt mention plasmasphere but it is intresting anyway.

John Barrow

Some notes I made looking at this video.

How can nothing be something?

The history of nothing

The greeks didnt allow zero as a number in their counting system as it would be in contradiction with their philosophy.

450bc atomists like Democritos “Univese – a infinite void filled with small particles”

350 bc Aristoteles “there could not be void” “All motions was possible with contacts between things” Vacuum could not really be realized” “nothing could come from nothing” “There is never vacuum”

Stoic view “extracosmic void beyond the boundary of Universe”

Teologians. Vacuum is undesirable, rejected by God where God is not.

Modern Physics vacuum

Source: ( https://youtu.be/BCUmeE8sIVo?t=18m52s  ) 

So vacuum is not absolutely nothing.  Vacuum can change with time have have different energy states of particle interactions, of radiation or magnetism.

“a landscape of possible energies a system (vacuum) could reside in “

Source: ( https://youtu.be/BCUmeE8sIVo?t=19m51s )

Quantum picture of vacuum

(Source: https://youtu.be/BCUmeE8sIVo?t=20m59s

Only some frequencies can reside in between the plates

Like in between two boats that are  less than 70 meters away fom each other and slowly crash with each other due of the wave forces from outside.

casimir plates effect

the relative plus force outside the plates makes the plates approach each other. Read more in https://www.scientificamerican.com/article/what-is-the-casimir-effec/

Nothing before the Big Bang?

George Ellis said something like this in the video linked below: Even if there is no before Big Bang as there was no time, one could say that there were rules  and structure before the Big Bang happened.
(SOurce: https://youtu.be/BCUmeE8sIVo?t=30m20s )

 

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Conclusions

 

 

 

A agnostic pluralist seeker

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