SlideShare a Scribd company logo

Discover Zero Point Energy and Vacuum Fluctuations Effects

β€’
β€’
A
Ana_T

The document discusses several topics related to zero point energy and vacuum fluctuations: 1) It explains how the Heisenberg uncertainty principle leads to zero point energy, which is the lowest possible energy of a quantum system in its ground state. 2) It describes vacuum fluctuations as quantum fluctuations of fields even in their lowest energy state. These fluctuations can be thought of as virtual particles being created and destroyed in the vacuum. 3) Several phenomena are discussed that demonstrate the effects of zero point energy and vacuum fluctuations, including spontaneous emission, the Casimir effect, and the Lamb shift.

TechnologyBusiness
1 of 41
Zero Point Energy and Vacuum Fluctuations Effects Ana Trakhtman Department of Physics Ariel University Center of Samaria
Table of Content ,[object Object]
Zero Point Energy – a new friend or an old acquaintance?
Vacuum Fluctuations – what is it?
Spontaneous Emission and what it has to do with ZPE
Casimir Effect or Van der Waals Attraction
The Lamb Shift
The Beam Splitter
Science Fiction or is it?
Conclusion,[object Object]
Zero Point Energy The origin of zero-point energy is the Heisenberg uncertainty principle. It is the lowest possible energy that a quantum mechanical system may have; it is the energy of its ground state. The most famous such example of zero-point energy is 𝐸=12β„πœ” associated with the ground state of the quantum harmonic oscillator. It is the expectation value of the Hamiltonian of the system in the ground state. Β 
Zero Point Energy 𝐻=ℏ22π‘šΒ βˆ‡2+𝑉(π‘Ÿ,𝑑) 𝑍𝑃𝐸=𝐻=Ξ¨π‘”π‘Ÿπ‘œπ‘’π‘›π‘‘π»Ξ¨π‘”π‘Ÿπ‘œπ‘’π‘›π‘‘ Β 
Vacuum Fluctuations In quantum field theory, the fabric of space is visualized as consisting of fields, with the field at every point in space and time being a quantum harmonic oscillator. The zero-point energy is again the expectation value of the Hamiltonian; here, however, the phrase vacuum expectation value is more commonly used, and the energy is called the vacuum energy. Vacuum energy can also be thought of in terms of virtual particles (also known as vacuum fluctuations) which are created and destroyed out of the vacuum. The concept of vacuum energy was derived from energy-time uncertainty principle.
Vacuum Fluctuations The vacuum state |π‘£π‘Žπ‘> of the field is the state of the lowest energy. The expectations values of both π‘Žπ‘˜π‘  and π‘Žπ‘˜π‘ + vanish in the vacuum state, because: π‘Žπ‘˜π‘ |π‘£π‘Žπ‘>Β =0=<π‘£π‘Žπ‘|π‘Žπ‘˜π‘ + Vector 𝐹(π‘Ÿ,𝑑), which may be the electric or magnetic or the vector potential, having a mode expansion of the general form: πΉπ‘Ÿ,𝑑=1𝐿32π‘˜,π‘ π‘™πœ”π‘Žπ‘˜π‘ πœ€π‘˜π‘ π‘’π‘–π‘˜βˆ™π‘Ÿβˆ’πœ”π‘‘+h.𝑐 Β 
Vacuum Fluctuations Where π‘™πœ” is some slowly varying function of frequency which is different for each field vector. Expectation value of πΉπ‘Ÿ,𝑑 in the vacuum state: <π‘£π‘Žπ‘πΉπ‘Ÿ,π‘‘π‘£π‘Žπ‘>Β =0 However, the expectation of the square of the field operator does not vanish, as we will show soon. This implies that there are fluctuations of the em field, even in its lowest energy. Β 
Vacuum Fluctuations If we use the mode expansion and make use of the fact that: π‘£π‘Žπ‘π‘Žπ‘˜π‘ +π‘Žπ‘˜β€²π‘ β€²π‘£π‘Žπ‘=0 π‘£π‘Žπ‘π‘Žπ‘˜π‘ +π‘Žπ‘˜β€²π‘ β€²+π‘£π‘Žπ‘=0 π‘£π‘Žπ‘π‘Žπ‘˜π‘ π‘Žπ‘˜β€²π‘ β€²π‘£π‘Žπ‘=0 We find that: π‘£π‘Žπ‘πΉ2(π‘Ÿ,𝑑)π‘£π‘Žπ‘==1𝐿3π‘˜π‘ π‘˜β€²π‘ β€²π‘™πœ”π‘™βˆ—(πœ”β€²)π‘£π‘Žπ‘π‘Žπ‘˜π‘ π‘Žπ‘˜β€²π‘ β€²+π‘£π‘Žπ‘(πœ€π‘˜π‘ βˆ™πœ€π‘˜β€²π‘ β€²βˆ—)βˆ™π‘’π‘–[π‘˜βˆ’π‘˜β€²π‘Ÿβˆ’πœ”βˆ’πœ”β€²π‘‘] Β 
Vacuum Fluctuations π‘Žπ‘˜π‘ π‘‘,Β π‘Žπ‘˜β€²π‘ β€²+(𝑑)=π‘Žπ‘˜π‘ βˆ™π‘Žπ‘˜β€²π‘ β€²+βˆ’π‘Žπ‘˜β€²π‘ β€²+βˆ™π‘Žπ‘˜π‘ =π›Ώπ‘˜π‘˜β€²3𝛿𝑠𝑠′ With the help of the commutation relation we have: π‘£π‘Žπ‘π‘Žπ‘˜π‘ π‘Žπ‘˜β€²π‘ β€²+π‘£π‘Žπ‘=π‘£π‘Žπ‘(π‘Žπ‘˜β€²π‘ β€²+βˆ™π‘Žπ‘˜π‘ +π›Ώπ‘˜π‘˜β€²3𝛿𝑠𝑠′)π‘£π‘Žπ‘=π›Ώπ‘˜π‘˜β€²3𝛿𝑠𝑠′ Β 
Vacuum Fluctuations So that: π‘£π‘Žπ‘πΉ2(π‘Ÿ,𝑑)π‘£π‘Žπ‘=1𝐿3π‘˜,π‘ π‘™πœ”2=2𝐿3π‘˜π‘™πœ”2  ⟢ 22πœ‹3π‘™πœ”2𝑑3π‘˜ This is clearly non-zero, and indeed is infinite for an unbounded set of modes. As it is know: π‘£π‘Žπ‘βˆ†πΉ2π‘£π‘Žπ‘=π‘£π‘Žπ‘πΉ2π‘£π‘Žπ‘Β Β Β ,Β Β Β Β βˆ†πΉ=πΉβˆ’πΉ βˆ†πΉ – the deviation from the mean This shows us that the field fluctuates in the vacuum state. Β 
Vacuum Fluctuations The effects of vacuum energy can be observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales.
Spontaneous Emission Quantum electrodynamics shows that spontaneous emission takes place because there is always some electromagnetic field present in the vicinity of an atom, even when a field is not applied. Like any other system with discretely quantized energy, the electromagnetic field has a zero-point energy. Quantum electrodynamics shows that there will always be some electromagnetic field vibrations present, of whatever frequency is required to induce the charge oscillations that cause the atom to radiate 'spontaneously'.
The Casimir Effect One of the more striking examples is the attractive force between a pair of parallel, uncharged, conducting plates in vacuum. This force is also referred to as a Van der Waals attraction and has been calculated by Dutch physicists Hendrik B. G. Casimir and Dirk Polder (1948).
The Casimir Effect One can account for this force (also known as Casimir force), and obtain an approximate value of its magnitude, by assuming that the force is a consequence of the separation-dependent vacuum field energy trapped between the two plates. If the plats are squares of side L and are separated by a distance z, we may suppose that the system constitutes a β€œcavity” that supports modes with wave number k down to about 1/z. the vacuum field energy trapped between the plates may therefore be written approximately as: π‘ˆ=π‘˜,𝑠12β„πœ”β‰ˆπΏ2𝑧1π‘§πΎβ„π‘π‘˜Β π‘˜2π‘‘π‘˜β‰ˆ14𝐿2ℏ𝑐𝑧𝐾4βˆ’1𝑧3=π‘ˆπ‘’π‘π‘π‘’π‘Ÿβˆ’π‘ˆπ‘™π‘œπ‘€π‘’π‘Ÿ Β 
The Casimir Effect we have introduced a high frequency cut-off K to make the energy finite. We can think of the negative rate of change of the lower cut-off energy π‘ˆπ‘™π‘œπ‘€π‘’π‘Ÿ with separation z as constituting a force of attraction, whose magnitude F per unit are is given by: 𝐹=βˆ’1𝐿2π‘‘π‘ˆπ‘™π‘œπ‘€π‘’π‘Ÿπ‘‘π‘§~ℏ𝑐𝑧4 Β 
The Casimir Effect It is interesting to note from the structure of F that the force is proportional to ℏ and is therefore quantum mechanical. Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. On a submicrometre scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. Β 
The Casimir Effect At separations of 10 nmβ€”about 100 times the typical size of an atomβ€”the Casimir effect produces the equivalent of 1 atmosphere of pressure (101.325 kPa), the precise value depending on surface geometry and other factors. In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; and in applied physics, it is significant in some aspects of emerging micro technologies and nanotechnologies.
The Lamb Shift The Lamb shift, named after Willis Lamb (1913–2008), is a small difference in energy between two energy levels 2S1 / 2 and 2P1 / 2 of the hydrogen atom in quantum electrodynamics. According to Dirac, the 2S1 / 2 and 2P1 / 2 orbitals should have the same energies. However, the interaction between the electron and the vacuum causes a tiny energy shift on 2S1 / 2. Lamb and Robert Retherford measured this shift in 1947. Lamb won the Nobel Prize in Physics in 1955 for his discoveries related to the Lamb shift.
The Lamb Shift
The Lamb Shift In 1948 Welton succeeded in accounting for the Lamb shift between the s and p energy levels of atomic hydrogen in terms of the perturbation of the electronic orbit brought about by vacuum fluctuations. A perturbation π›Ώπ‘Ÿ in electronic position in general causes a change of potential energy 𝛿𝑉 given by: 𝛿𝑉=π‘‰π‘Ÿ+π›Ώπ‘Ÿβˆ’π‘‰π‘Ÿ=βˆ‡π‘‰βˆ™π›Ώπ‘Ÿ+12πœ•πœ•π‘Ÿπ‘–πœ•πœ•π‘Ÿπ‘—π‘‰π›Ώπ‘Ÿπ‘–π›Ώπ‘Ÿπ‘—+β‹― Β 
The Lamb Shift When we average this over the random displacements π‘Ÿ, the term in π›Ώπ‘Ÿ2 is the leading non-zero term and we find that: 𝛿𝑉=16βˆ‡2π‘‰Β π›Ώπ‘Ÿ2 In order to calculate the value of π›Ώπ‘Ÿ2 resulting from the fluctuations of the vacuum field, we observe that, under the influence of an electric field πΈπœ” of frequency πœ”, the electronic position r obeys the equation of motion: π‘šπ‘Ÿ=βˆ’π‘’πΈπœ”cosπœ”π‘‘ Β 
The Lamb Shift And this results in a mean squared displacement about its equilibrium value of: π›Ώπ‘Ÿπœ”2=12𝑒2π‘š2πœ”4Β πΈπœ”2π‘£π‘Žπ‘=ℏ𝑒22πœ‹3πœ€0π‘š2𝑑3π‘˜πœ”3=ℏ𝑒22πœ‹2πœ€0π‘š2𝑐3πœ”0Ξ©π‘‘πœ”πœ” Β 
The Lamb Shift The integral diverges logarithmically at the upper end, and had to be provided with a cut-off Ξ©, which is usually chosen to be of order π‘šπ‘2/ℏ. When this expression for π›Ώπ‘Ÿ2 is inserted in 𝛿𝑉, and we average βˆ‡2𝑉(π‘Ÿ) over the electronic orbit with the help of the wave function πœ“(π‘Ÿ), we obtain finally for the perturbation of the atomic energy level: 𝛿𝑉=ℏ𝑒212πœ‹2πœ€0π‘š2𝑐3 𝑑3π‘ŸΒ βˆ‡2π‘‰π‘Ÿπœ“π‘Ÿ2πœ”0Ξ©π‘‘πœ”πœ” Β 
The Lamb Shift If we take the potential energy 𝑉(π‘Ÿ) to be: π‘‰π‘Ÿ=βˆ’π‘’24πœ‹πœ€0π‘ŸΒ  then: βˆ‡2π‘‰π‘Ÿ=𝑒2πœ€0𝛿3(π‘Ÿ) and the volume integral reduces to: 𝑒2πœ€0πœ“02 Β 
The Lamb Shift This vanishes for a p-state but gives a finite value for an s-state. The difference between the s and p energy levels is therefore: βˆ†πΈ=ℏ𝑒412πœ‹2πœ€02π‘š2𝑐3πœ“π‘ 02lnπ‘šπ‘2β„πœ”0 Β 
The Lamb Shift This leads to: βˆ†πΈβ„~1040 𝑀𝐻𝑧 For the 2s-state of hydrogen, and is in reasonable agreement with measurements by Lamb and Retherford (1947). Β 
The Beam Splitter
The Beam Splitter After decomposing all fields into plane-wave modes in the usual way, we consider a single incident mode labeled 1, which gives rise to a reflected mode 2 and a transmitted mode 3. r, t are the complex amplitude reflectivity and transmissivity for light incident from one side. π‘Ÿβ€², 𝑑′ for light coming from the other side there are no losses in the beam splitter Β 
The Beam Splitter Then these parameters must obey the following reciprocity relations (due to Stokes, 1849): π‘Ÿ=π‘Ÿβ€²Β Β ,  𝑑=𝑑′ π‘Ÿ2+𝑑2=1 π‘Ÿπ‘‘βˆ—+π‘Ÿβˆ—π‘‘=0 Β 
The Beam Splitter It follows that an incoming classical wave of complex amplitude 𝜐1 gives rise to a reflected wave 𝜐2, and a transmitted wave 𝜐3 such that: 𝑣2=π‘Ÿπ‘£1Β Β Β ,   𝑣3=𝑑𝑣1 From these relations it follows immediately that: 𝑣22+𝑣32=𝑑2+π‘Ÿ2𝑣12 So that the incoming energy is conserved. Β 
The Beam Splitter Now suppose that we wish to apply a similar argument to the treatment of a quantum field. Then 𝑣1, 𝑣2, 𝑣3 have to be replaced by the complex amplitude operators π‘Ž1,Β π‘Ž2Β ,Β π‘Ž3 , which obey the commutation relations: π‘Žπ‘—,Β π‘Žπ‘—+=1,  𝑗=1,Β 2,Β 3 π‘Ž2,Β π‘Ž3+=0 Β 
The Beam Splitter if we simply replace 𝑣1, 𝑣2, 𝑣3 by the operators π‘Ž1,Β π‘Ž2Β ,Β π‘Ž3 , we readily find that the commutation equations do not hold for π‘Ž2Β ,Β π‘Ž3. Instead we obtain: π‘Ž2Β ,Β π‘Ž3+=π‘Ÿ2π‘Ž1Β ,Β π‘Ž1+=π‘Ÿ2 π‘Ž3Β ,Β π‘Ž3+=𝑑2π‘Ž1Β ,Β π‘Ž1+=𝑑2 π‘Ž2Β ,Β π‘Ž3+=π‘Ÿπ‘‘βˆ—π‘Ž1Β ,Β π‘Ž1+=π‘Ÿπ‘‘βˆ— Β 
The Beam Splitter The reason for the discrepancy is that we have ignored the fourth beam splitter input port, which is justifiably ignored in the classical treatment because no light enter that way. However, even if no energy is flowing through the mode labeled 0, in a quantized field treatment there is a vacuum field that enters here and contributes to the two output modes.

Recommended

Quantum mechanics I
Quantum mechanics IQuantum mechanics I
Quantum mechanics ISaiva Bhanu Kshatriya College, Aruppukottai.
Β 
Introduction to quantum mechanics and schrodinger equation
Introduction to quantum mechanics and schrodinger equationIntroduction to quantum mechanics and schrodinger equation
Introduction to quantum mechanics and schrodinger equationGaurav Singh Gusain
Β 
Particle in a box- Application of Schrodinger wave equation
Particle in a box- Application of Schrodinger wave equationParticle in a box- Application of Schrodinger wave equation
Particle in a box- Application of Schrodinger wave equationRawat DA Greatt
Β 
Harmonic Oscillator
Harmonic OscillatorHarmonic Oscillator
Harmonic OscillatorMANISHSAHU106
Β 
Photochemistry PPT.pptx
Photochemistry PPT.pptxPhotochemistry PPT.pptx
Photochemistry PPT.pptxSATISH KOLA
Β 
FERROMAGNETIC AND ANTIFERROMAGNETIC MATERIALS.pptx
FERROMAGNETIC AND ANTIFERROMAGNETIC MATERIALS.pptxFERROMAGNETIC AND ANTIFERROMAGNETIC MATERIALS.pptx
FERROMAGNETIC AND ANTIFERROMAGNETIC MATERIALS.pptxTHE CREATORS ACADEMY
Β 
Schrodinger Equation of Hydrogen Atom
Schrodinger Equation of Hydrogen AtomSchrodinger Equation of Hydrogen Atom
Schrodinger Equation of Hydrogen AtomSaad Shaukat
Β 
quantum view of Harmonic oscillator
quantum view of Harmonic oscillator quantum view of Harmonic oscillator
quantum view of Harmonic oscillator Ahmed Haider
Β 

Recommended

Quantum mechanics I
Quantum mechanics IQuantum mechanics I
Quantum mechanics ISaiva Bhanu Kshatriya College, Aruppukottai.
Β 
Introduction to quantum mechanics and schrodinger equation
Introduction to quantum mechanics and schrodinger equationIntroduction to quantum mechanics and schrodinger equation
Introduction to quantum mechanics and schrodinger equationGaurav Singh Gusain
Β 
Particle in a box- Application of Schrodinger wave equation
Particle in a box- Application of Schrodinger wave equationParticle in a box- Application of Schrodinger wave equation
Particle in a box- Application of Schrodinger wave equationRawat DA Greatt
Β 
Harmonic Oscillator
Harmonic OscillatorHarmonic Oscillator
Harmonic OscillatorMANISHSAHU106
Β 
Photochemistry PPT.pptx
Photochemistry PPT.pptxPhotochemistry PPT.pptx
Photochemistry PPT.pptxSATISH KOLA
Β 
FERROMAGNETIC AND ANTIFERROMAGNETIC MATERIALS.pptx
FERROMAGNETIC AND ANTIFERROMAGNETIC MATERIALS.pptxFERROMAGNETIC AND ANTIFERROMAGNETIC MATERIALS.pptx
FERROMAGNETIC AND ANTIFERROMAGNETIC MATERIALS.pptxTHE CREATORS ACADEMY
Β 
Schrodinger Equation of Hydrogen Atom
Schrodinger Equation of Hydrogen AtomSchrodinger Equation of Hydrogen Atom
Schrodinger Equation of Hydrogen AtomSaad Shaukat
Β 
quantum view of Harmonic oscillator
quantum view of Harmonic oscillator quantum view of Harmonic oscillator
quantum view of Harmonic oscillator Ahmed Haider
Β 
Quantum Mechanics Presentation
Quantum Mechanics PresentationQuantum Mechanics Presentation
Quantum Mechanics PresentationJasmine Wang
Β 
Quantum Chemistry
Quantum ChemistryQuantum Chemistry
Quantum Chemistrybaoilleach
Β 
The Variational Method
The Variational MethodThe Variational Method
The Variational MethodJames Salveo Olarve
Β 
POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...
POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...
POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...Saiva Bhanu Kshatriya College, Aruppukottai.
Β 
Born-Oppenheimer approximation.pptx
Born-Oppenheimer approximation.pptxBorn-Oppenheimer approximation.pptx
Born-Oppenheimer approximation.pptxNGokila1
Β 
Solid state physics (schottkey and frenkel)
Solid state physics (schottkey and frenkel)Solid state physics (schottkey and frenkel)
Solid state physics (schottkey and frenkel)abi sivaraj
Β 
Quantum mechanics
Quantum mechanicsQuantum mechanics
Quantum mechanicsPoojith Chowdhary
Β 
Classical mechanics vs quantum mechanics
Classical mechanics vs quantum mechanicsClassical mechanics vs quantum mechanics
Classical mechanics vs quantum mechanicsZahid Mehmood
Β 
Frankel and schottky defects
Frankel and schottky defectsFrankel and schottky defects
Frankel and schottky defectsGurpreet Singh
Β 
Mesons
Mesons Mesons
Mesons Samia Dogar
Β 
Engineering physics 2(Electron Theory of metals)
Engineering physics 2(Electron Theory of metals)Engineering physics 2(Electron Theory of metals)
Engineering physics 2(Electron Theory of metals)Nexus
Β 
Eigenvalues
EigenvaluesEigenvalues
EigenvaluesTarun Gehlot
Β 
Particle in a Box problem Quantum Chemistry
Particle in a Box problem Quantum ChemistryParticle in a Box problem Quantum Chemistry
Particle in a Box problem Quantum ChemistryNeel Kamal Kalita
Β 
5 introduction to quantum mechanics
5 introduction to quantum mechanics5 introduction to quantum mechanics
5 introduction to quantum mechanicsSolo Hermelin
Β 
Rasonance raman specroscopy
Rasonance raman specroscopyRasonance raman specroscopy
Rasonance raman specroscopytidke123
Β 
Classification of nuclei and properties of nucleus
Classification of nuclei and properties of nucleusClassification of nuclei and properties of nucleus
Classification of nuclei and properties of nucleushemalathasenthil
Β 
Origin of quantum mechanics
Origin of quantum mechanicsOrigin of quantum mechanics
Origin of quantum mechanicsMUHAMMED ABDURAHMAN
Β 
Rotational Spectra : Microwave Spectroscopy
Rotational Spectra : Microwave SpectroscopyRotational Spectra : Microwave Spectroscopy
Rotational Spectra : Microwave SpectroscopyKhemendra shukla
Β 
The Nuclear Shell Model
The Nuclear Shell ModelThe Nuclear Shell Model
The Nuclear Shell ModelMohammedFox
Β 
Non Rigid Rotator
Non Rigid RotatorNon Rigid Rotator
Non Rigid RotatorAnitaMalviya
Β 
Suppressed Inventions Water Disassociation Zero Point Energy
Suppressed Inventions Water Disassociation Zero Point EnergySuppressed Inventions Water Disassociation Zero Point Energy
Suppressed Inventions Water Disassociation Zero Point EnergyJohn Kuhles
Β 
zero point energy
zero point energyzero point energy
zero point energyJohn Hutchison
Β 

More Related Content

What's hot

Quantum Mechanics Presentation
Quantum Mechanics PresentationQuantum Mechanics Presentation
Quantum Mechanics PresentationJasmine Wang
Β 
Quantum Chemistry
Quantum ChemistryQuantum Chemistry
Quantum Chemistrybaoilleach
Β 
POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...
POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...
POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...Saiva Bhanu Kshatriya College, Aruppukottai.
Β 
Born-Oppenheimer approximation.pptx
Born-Oppenheimer approximation.pptxBorn-Oppenheimer approximation.pptx
Born-Oppenheimer approximation.pptxNGokila1
Β 
Solid state physics (schottkey and frenkel)
Solid state physics (schottkey and frenkel)Solid state physics (schottkey and frenkel)
Solid state physics (schottkey and frenkel)abi sivaraj
Β 
Classical mechanics vs quantum mechanics
Classical mechanics vs quantum mechanicsClassical mechanics vs quantum mechanics
Classical mechanics vs quantum mechanicsZahid Mehmood
Β 
Frankel and schottky defects
Frankel and schottky defectsFrankel and schottky defects
Frankel and schottky defectsGurpreet Singh
Β 
Engineering physics 2(Electron Theory of metals)
Engineering physics 2(Electron Theory of metals)Engineering physics 2(Electron Theory of metals)
Engineering physics 2(Electron Theory of metals)Nexus
Β 
Particle in a Box problem Quantum Chemistry
Particle in a Box problem Quantum ChemistryParticle in a Box problem Quantum Chemistry
Particle in a Box problem Quantum ChemistryNeel Kamal Kalita
Β 
5 introduction to quantum mechanics
5 introduction to quantum mechanics5 introduction to quantum mechanics
5 introduction to quantum mechanicsSolo Hermelin
Β 
Rasonance raman specroscopy
Rasonance raman specroscopyRasonance raman specroscopy
Rasonance raman specroscopytidke123
Β 
Classification of nuclei and properties of nucleus
Classification of nuclei and properties of nucleusClassification of nuclei and properties of nucleus
Classification of nuclei and properties of nucleushemalathasenthil
Β 
Origin of quantum mechanics
Origin of quantum mechanicsOrigin of quantum mechanics
Origin of quantum mechanicsMUHAMMED ABDURAHMAN
Β 
Rotational Spectra : Microwave Spectroscopy
Rotational Spectra : Microwave SpectroscopyRotational Spectra : Microwave Spectroscopy
Rotational Spectra : Microwave SpectroscopyKhemendra shukla
Β 
The Nuclear Shell Model
The Nuclear Shell ModelThe Nuclear Shell Model
The Nuclear Shell ModelMohammedFox
Β 
Non Rigid Rotator
Non Rigid RotatorNon Rigid Rotator
Non Rigid RotatorAnitaMalviya
Β 

What's hot (20)

Quantum Mechanics Presentation
Quantum Mechanics PresentationQuantum Mechanics Presentation
Quantum Mechanics Presentation
Β 
Quantum Chemistry
Quantum ChemistryQuantum Chemistry
Quantum Chemistry
Β 
The Variational Method
The Variational MethodThe Variational Method
The Variational Method
Β 
POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...
POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...
POTENTIAL ENERGY SURFACE. KINETIC ISOTOPE EFFECT AND THEORIES OF UNI MOLECULA...
Β 
Born-Oppenheimer approximation.pptx
Born-Oppenheimer approximation.pptxBorn-Oppenheimer approximation.pptx
Born-Oppenheimer approximation.pptx
Β 
Solid state physics (schottkey and frenkel)
Solid state physics (schottkey and frenkel)Solid state physics (schottkey and frenkel)
Solid state physics (schottkey and frenkel)
Β 
Quantum mechanics
Quantum mechanicsQuantum mechanics
Quantum mechanics
Β 
Classical mechanics vs quantum mechanics
Classical mechanics vs quantum mechanicsClassical mechanics vs quantum mechanics
Classical mechanics vs quantum mechanics
Β 
Frankel and schottky defects
Frankel and schottky defectsFrankel and schottky defects
Frankel and schottky defects
Β 
Mesons
Mesons Mesons
Mesons
Β 
Engineering physics 2(Electron Theory of metals)
Engineering physics 2(Electron Theory of metals)Engineering physics 2(Electron Theory of metals)
Engineering physics 2(Electron Theory of metals)
Β 
Eigenvalues
EigenvaluesEigenvalues
Eigenvalues
Β 
Particle in a Box problem Quantum Chemistry
Particle in a Box problem Quantum ChemistryParticle in a Box problem Quantum Chemistry
Particle in a Box problem Quantum Chemistry
Β 
5 introduction to quantum mechanics
5 introduction to quantum mechanics5 introduction to quantum mechanics
5 introduction to quantum mechanics
Β 
Rasonance raman specroscopy
Rasonance raman specroscopyRasonance raman specroscopy
Rasonance raman specroscopy
Β 
Classification of nuclei and properties of nucleus
Classification of nuclei and properties of nucleusClassification of nuclei and properties of nucleus
Classification of nuclei and properties of nucleus
Β 
Origin of quantum mechanics
Origin of quantum mechanicsOrigin of quantum mechanics
Origin of quantum mechanics
Β 
Rotational Spectra : Microwave Spectroscopy
Rotational Spectra : Microwave SpectroscopyRotational Spectra : Microwave Spectroscopy
Rotational Spectra : Microwave Spectroscopy
Β 
The Nuclear Shell Model
The Nuclear Shell ModelThe Nuclear Shell Model
The Nuclear Shell Model
Β 
Non Rigid Rotator
Non Rigid RotatorNon Rigid Rotator
Non Rigid Rotator
Β 

Viewers also liked

Suppressed Inventions Water Disassociation Zero Point Energy
Suppressed Inventions Water Disassociation Zero Point EnergySuppressed Inventions Water Disassociation Zero Point Energy
Suppressed Inventions Water Disassociation Zero Point EnergyJohn Kuhles
Β 
zero point energy
zero point energyzero point energy
zero point energyJohn Hutchison
Β 
Pitch Deck Energy Floors - Zero Point Energy Pvt Ltd
Pitch Deck Energy Floors - Zero Point Energy Pvt Ltd Pitch Deck Energy Floors - Zero Point Energy Pvt Ltd
Pitch Deck Energy Floors - Zero Point Energy Pvt LtdMandar Tulankar
Β 
The Biophysical Effects of Heavy Water
The Biophysical Effects of Heavy WaterThe Biophysical Effects of Heavy Water
The Biophysical Effects of Heavy WaterAnthony Salvagno
Β 
Supercritical Fluid Chromatography
Supercritical Fluid ChromatographySupercritical Fluid Chromatography
Supercritical Fluid ChromatographyBHARATH_B
Β 
Heavy water production
Heavy water productionHeavy water production
Heavy water productionVasaru Gheorghe
Β 
Tritium isotope separation
Tritium isotope separationTritium isotope separation
Tritium isotope separationVasaru Gheorghe
Β 

Viewers also liked (7)

Suppressed Inventions Water Disassociation Zero Point Energy
Suppressed Inventions Water Disassociation Zero Point EnergySuppressed Inventions Water Disassociation Zero Point Energy
Suppressed Inventions Water Disassociation Zero Point Energy
Β 
zero point energy
zero point energyzero point energy
zero point energy
Β 
Pitch Deck Energy Floors - Zero Point Energy Pvt Ltd
Pitch Deck Energy Floors - Zero Point Energy Pvt Ltd Pitch Deck Energy Floors - Zero Point Energy Pvt Ltd
Pitch Deck Energy Floors - Zero Point Energy Pvt Ltd
Β 
The Biophysical Effects of Heavy Water
The Biophysical Effects of Heavy WaterThe Biophysical Effects of Heavy Water
The Biophysical Effects of Heavy Water
Β 
Supercritical Fluid Chromatography
Supercritical Fluid ChromatographySupercritical Fluid Chromatography
Supercritical Fluid Chromatography
Β 
Heavy water production
Heavy water productionHeavy water production
Heavy water production
Β 
Tritium isotope separation
Tritium isotope separationTritium isotope separation
Tritium isotope separation
Β 

Similar to Discover Zero Point Energy and Vacuum Fluctuations Effects

Electrodynamics ppt.pdfgjskysudfififkfkfififididhxdifififif
Electrodynamics ppt.pdfgjskysudfififkfkfififididhxdififififElectrodynamics ppt.pdfgjskysudfififkfkfififididhxdifififif
Electrodynamics ppt.pdfgjskysudfififkfkfififididhxdififififMAINAKGHOSH73
Β 
Lecture 14 on Blackbody Radiation.pptx
Lecture 14 on Blackbody Radiation.pptxLecture 14 on Blackbody Radiation.pptx
Lecture 14 on Blackbody Radiation.pptxTheObserver3
Β 
Fundamental Concepts on Electromagnetic Theory
Fundamental Concepts on Electromagnetic TheoryFundamental Concepts on Electromagnetic Theory
Fundamental Concepts on Electromagnetic TheoryAL- AMIN
Β 
Easy Plasma Theory BS Math helping notespdf
Easy Plasma Theory BS Math helping notespdfEasy Plasma Theory BS Math helping notespdf
Easy Plasma Theory BS Math helping notespdfAreeshaNoor9
Β 
Electricity Full lecture.pptx
Electricity Full lecture.pptxElectricity Full lecture.pptx
Electricity Full lecture.pptxAdnan al-emran
Β 
Class_12-Physics_ Alternating current and Electromagnetic Waves_ PPT-3 of 3.pdf
Class_12-Physics_ Alternating current and Electromagnetic Waves_ PPT-3 of 3.pdfClass_12-Physics_ Alternating current and Electromagnetic Waves_ PPT-3 of 3.pdf
Class_12-Physics_ Alternating current and Electromagnetic Waves_ PPT-3 of 3.pdfMuskanShrivastava15
Β 
Spin_Explained_As_Two_Rotating_Rings.pdf
Spin_Explained_As_Two_Rotating_Rings.pdfSpin_Explained_As_Two_Rotating_Rings.pdf
Spin_Explained_As_Two_Rotating_Rings.pdfSergio Prats
Β 
Elaborato Luca Rapacchiani
Elaborato Luca RapacchianiElaborato Luca Rapacchiani
Elaborato Luca RapacchianiLucaRapacchiani2
Β 
Superconductivity
SuperconductivitySuperconductivity
SuperconductivityParam Radadiya
Β 
An apologytodirac'sreactionforcetheory
An apologytodirac'sreactionforcetheoryAn apologytodirac'sreactionforcetheory
An apologytodirac'sreactionforcetheorySergio Prats
Β 
RADIATION OF AN ACCELERATED CHARGE
RADIATION OF AN ACCELERATED CHARGERADIATION OF AN ACCELERATED CHARGE
RADIATION OF AN ACCELERATED CHARGEijeljournal
Β 
RADIATION OF AN ACCELERATED CHARGE
RADIATION OF AN ACCELERATED CHARGERADIATION OF AN ACCELERATED CHARGE
RADIATION OF AN ACCELERATED CHARGEijeljournal
Β 
Field energy correction with discrete charges
Field energy correction with discrete chargesField energy correction with discrete charges
Field energy correction with discrete chargesSergio Prats
Β 
Radiation of an Accelerated Charge
Radiation of an Accelerated ChargeRadiation of an Accelerated Charge
Radiation of an Accelerated Chargeijeljournal
Β 
Radiation of an accelerated charge
Radiation of an accelerated chargeRadiation of an accelerated charge
Radiation of an accelerated chargeijeljournal
Β 
Radiation of an Accelerated Charge
Radiation of an Accelerated Charge Radiation of an Accelerated Charge
Radiation of an Accelerated Charge ijeljournal
Β 

Similar to Discover Zero Point Energy and Vacuum Fluctuations Effects (20)

Electrodynamics ppt.pdfgjskysudfififkfkfififididhxdifififif
Electrodynamics ppt.pdfgjskysudfififkfkfififididhxdififififElectrodynamics ppt.pdfgjskysudfififkfkfififididhxdifififif
Electrodynamics ppt.pdfgjskysudfififkfkfififididhxdifififif
Β 
Lecture 14 on Blackbody Radiation.pptx
Lecture 14 on Blackbody Radiation.pptxLecture 14 on Blackbody Radiation.pptx
Lecture 14 on Blackbody Radiation.pptx
Β 
Fundamental Concepts on Electromagnetic Theory
Fundamental Concepts on Electromagnetic TheoryFundamental Concepts on Electromagnetic Theory
Fundamental Concepts on Electromagnetic Theory
Β 
Easy Plasma Theory BS Math helping notespdf
Easy Plasma Theory BS Math helping notespdfEasy Plasma Theory BS Math helping notespdf
Easy Plasma Theory BS Math helping notespdf
Β 
Electricity Full lecture.pptx
Electricity Full lecture.pptxElectricity Full lecture.pptx
Electricity Full lecture.pptx
Β 
Class_12-Physics_ Alternating current and Electromagnetic Waves_ PPT-3 of 3.pdf
Class_12-Physics_ Alternating current and Electromagnetic Waves_ PPT-3 of 3.pdfClass_12-Physics_ Alternating current and Electromagnetic Waves_ PPT-3 of 3.pdf
Class_12-Physics_ Alternating current and Electromagnetic Waves_ PPT-3 of 3.pdf
Β 
Physics
PhysicsPhysics
Physics
Β 
Electrostatics in vacuum
Electrostatics in vacuumElectrostatics in vacuum
Electrostatics in vacuum
Β 
L2 electric field, dipoles
L2 electric field, dipolesL2 electric field, dipoles
L2 electric field, dipoles
Β 
Spin_Explained_As_Two_Rotating_Rings.pdf
Spin_Explained_As_Two_Rotating_Rings.pdfSpin_Explained_As_Two_Rotating_Rings.pdf
Spin_Explained_As_Two_Rotating_Rings.pdf
Β 
Elaborato Luca Rapacchiani
Elaborato Luca RapacchianiElaborato Luca Rapacchiani
Elaborato Luca Rapacchiani
Β 
Superconductivity
SuperconductivitySuperconductivity
Superconductivity
Β 
An apologytodirac'sreactionforcetheory
An apologytodirac'sreactionforcetheoryAn apologytodirac'sreactionforcetheory
An apologytodirac'sreactionforcetheory
Β 
RADIATION OF AN ACCELERATED CHARGE
RADIATION OF AN ACCELERATED CHARGERADIATION OF AN ACCELERATED CHARGE
RADIATION OF AN ACCELERATED CHARGE
Β 
RADIATION OF AN ACCELERATED CHARGE
RADIATION OF AN ACCELERATED CHARGERADIATION OF AN ACCELERATED CHARGE
RADIATION OF AN ACCELERATED CHARGE
Β 
Field energy correction with discrete charges
Field energy correction with discrete chargesField energy correction with discrete charges
Field energy correction with discrete charges
Β 
B0330107
B0330107B0330107
B0330107
Β 
Radiation of an Accelerated Charge
Radiation of an Accelerated ChargeRadiation of an Accelerated Charge
Radiation of an Accelerated Charge
Β 
Radiation of an accelerated charge
Radiation of an accelerated chargeRadiation of an accelerated charge
Radiation of an accelerated charge
Β 
Radiation of an Accelerated Charge
Radiation of an Accelerated Charge Radiation of an Accelerated Charge
Radiation of an Accelerated Charge
Β 

Recently uploaded

Unblocking The Main Thread Solving ANRs and Frozen Frames
Unblocking The Main Thread Solving ANRs and Frozen FramesUnblocking The Main Thread Solving ANRs and Frozen Frames
Unblocking The Main Thread Solving ANRs and Frozen FramesSinan KOZAK
Β 
My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024The Digital Insurer
Β 
AI as an Interface for Commercial Buildings
AI as an Interface for Commercial BuildingsAI as an Interface for Commercial Buildings
AI as an Interface for Commercial BuildingsMemoori
Β 
Enhancing Worker Digital Experience: A Hands-on Workshop for Partners
Enhancing Worker Digital Experience: A Hands-on Workshop for PartnersEnhancing Worker Digital Experience: A Hands-on Workshop for Partners
Enhancing Worker Digital Experience: A Hands-on Workshop for PartnersThousandEyes
Β 
Key Features Of Token Development (1).pptx
Key Features Of Token Development (1).pptxKey Features Of Token Development (1).pptx
Key Features Of Token Development (1).pptxLBM Solutions
Β 
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024BookNet Canada
Β 
Are Multi-Cloud and Serverless Good or Bad?
Are Multi-Cloud and Serverless Good or Bad?Are Multi-Cloud and Serverless Good or Bad?
Are Multi-Cloud and Serverless Good or Bad?Mattias Andersson
Β 
APIForce Zurich 5 April Automation LPDG
APIForce Zurich 5 April Automation LPDGAPIForce Zurich 5 April Automation LPDG
APIForce Zurich 5 April Automation LPDGMarianaLemus7
Β 
Advanced Test Driven-Development @ php[tek] 2024
Advanced Test Driven-Development @ php[tek] 2024Advanced Test Driven-Development @ php[tek] 2024
Advanced Test Driven-Development @ php[tek] 2024Scott Keck-Warren
Β 
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024BookNet Canada
Β 
SQL Database Design For Developers at php[tek] 2024
SQL Database Design For Developers at php[tek] 2024SQL Database Design For Developers at php[tek] 2024
SQL Database Design For Developers at php[tek] 2024Scott Keck-Warren
Β 
Designing IA for AI - Information Architecture Conference 2024
Designing IA for AI - Information Architecture Conference 2024Designing IA for AI - Information Architecture Conference 2024
Designing IA for AI - Information Architecture Conference 2024Enterprise Knowledge
Β 
Unleash Your Potential - Namagunga Girls Coding Club
Unleash Your Potential - Namagunga Girls Coding ClubUnleash Your Potential - Namagunga Girls Coding Club
Unleash Your Potential - Namagunga Girls Coding ClubKalema Edgar
Β 
Benefits Of Flutter Compared To Other Frameworks
Benefits Of Flutter Compared To Other FrameworksBenefits Of Flutter Compared To Other Frameworks
Benefits Of Flutter Compared To Other FrameworksSoftradix Technologies
Β 
Making_way_through_DLL_hollowing_inspite_of_CFG_by_Debjeet Banerjee.pptx
Making_way_through_DLL_hollowing_inspite_of_CFG_by_Debjeet Banerjee.pptxMaking_way_through_DLL_hollowing_inspite_of_CFG_by_Debjeet Banerjee.pptx
Making_way_through_DLL_hollowing_inspite_of_CFG_by_Debjeet Banerjee.pptxnull - The Open Security Community
Β 
Streamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project SetupStreamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project SetupFlorian Wilhelm
Β 
Bun (KitWorks Team Study λ…Έλ³„λ§ˆλ£¨ λ°œν‘œ 2024.4.22)
Bun (KitWorks Team Study λ…Έλ³„λ§ˆλ£¨ λ°œν‘œ 2024.4.22)Bun (KitWorks Team Study λ…Έλ³„λ§ˆλ£¨ λ°œν‘œ 2024.4.22)
Bun (KitWorks Team Study λ…Έλ³„λ§ˆλ£¨ λ°œν‘œ 2024.4.22)Wonjun Hwang
Β 
New from BookNet Canada for 2024: BNC BiblioShare - Tech Forum 2024
New from BookNet Canada for 2024: BNC BiblioShare - Tech Forum 2024New from BookNet Canada for 2024: BNC BiblioShare - Tech Forum 2024
New from BookNet Canada for 2024: BNC BiblioShare - Tech Forum 2024BookNet Canada
Β 

Recently uploaded (20)

Unblocking The Main Thread Solving ANRs and Frozen Frames
Unblocking The Main Thread Solving ANRs and Frozen FramesUnblocking The Main Thread Solving ANRs and Frozen Frames
Unblocking The Main Thread Solving ANRs and Frozen Frames
Β 
My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024My INSURER PTE LTD - Insurtech Innovation Award 2024
My INSURER PTE LTD - Insurtech Innovation Award 2024
Β 
AI as an Interface for Commercial Buildings
AI as an Interface for Commercial BuildingsAI as an Interface for Commercial Buildings
AI as an Interface for Commercial Buildings
Β 
Hot Sexy call girls in Panjabi Bagh πŸ” 9953056974 πŸ” Delhi escort Service
Hot Sexy call girls in Panjabi Bagh πŸ” 9953056974 πŸ” Delhi escort ServiceHot Sexy call girls in Panjabi Bagh πŸ” 9953056974 πŸ” Delhi escort Service
Hot Sexy call girls in Panjabi Bagh πŸ” 9953056974 πŸ” Delhi escort Service
Β 
Enhancing Worker Digital Experience: A Hands-on Workshop for Partners
Enhancing Worker Digital Experience: A Hands-on Workshop for PartnersEnhancing Worker Digital Experience: A Hands-on Workshop for Partners
Enhancing Worker Digital Experience: A Hands-on Workshop for Partners
Β 
Key Features Of Token Development (1).pptx
Key Features Of Token Development (1).pptxKey Features Of Token Development (1).pptx
Key Features Of Token Development (1).pptx
Β 
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
#StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
Β 
Are Multi-Cloud and Serverless Good or Bad?
Are Multi-Cloud and Serverless Good or Bad?Are Multi-Cloud and Serverless Good or Bad?
Are Multi-Cloud and Serverless Good or Bad?
Β 
APIForce Zurich 5 April Automation LPDG
APIForce Zurich 5 April Automation LPDGAPIForce Zurich 5 April Automation LPDG
APIForce Zurich 5 April Automation LPDG
Β 
Advanced Test Driven-Development @ php[tek] 2024
Advanced Test Driven-Development @ php[tek] 2024Advanced Test Driven-Development @ php[tek] 2024
Advanced Test Driven-Development @ php[tek] 2024
Β 
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
Transcript: #StandardsGoals for 2024: What’s new for BISAC - Tech Forum 2024
Β 
SQL Database Design For Developers at php[tek] 2024
SQL Database Design For Developers at php[tek] 2024SQL Database Design For Developers at php[tek] 2024
SQL Database Design For Developers at php[tek] 2024
Β 
Designing IA for AI - Information Architecture Conference 2024
Designing IA for AI - Information Architecture Conference 2024Designing IA for AI - Information Architecture Conference 2024
Designing IA for AI - Information Architecture Conference 2024
Β 
Unleash Your Potential - Namagunga Girls Coding Club
Unleash Your Potential - Namagunga Girls Coding ClubUnleash Your Potential - Namagunga Girls Coding Club
Unleash Your Potential - Namagunga Girls Coding Club
Β 
Benefits Of Flutter Compared To Other Frameworks
Benefits Of Flutter Compared To Other FrameworksBenefits Of Flutter Compared To Other Frameworks
Benefits Of Flutter Compared To Other Frameworks
Β 
Making_way_through_DLL_hollowing_inspite_of_CFG_by_Debjeet Banerjee.pptx
Making_way_through_DLL_hollowing_inspite_of_CFG_by_Debjeet Banerjee.pptxMaking_way_through_DLL_hollowing_inspite_of_CFG_by_Debjeet Banerjee.pptx
Making_way_through_DLL_hollowing_inspite_of_CFG_by_Debjeet Banerjee.pptx
Β 
Streamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project SetupStreamlining Python Development: A Guide to a Modern Project Setup
Streamlining Python Development: A Guide to a Modern Project Setup
Β 
Bun (KitWorks Team Study λ…Έλ³„λ§ˆλ£¨ λ°œν‘œ 2024.4.22)
Bun (KitWorks Team Study λ…Έλ³„λ§ˆλ£¨ λ°œν‘œ 2024.4.22)Bun (KitWorks Team Study λ…Έλ³„λ§ˆλ£¨ λ°œν‘œ 2024.4.22)
Bun (KitWorks Team Study λ…Έλ³„λ§ˆλ£¨ λ°œν‘œ 2024.4.22)
Β 
E-Vehicle_Hacking_by_Parul Sharma_null_owasp.pptx
E-Vehicle_Hacking_by_Parul Sharma_null_owasp.pptxE-Vehicle_Hacking_by_Parul Sharma_null_owasp.pptx
E-Vehicle_Hacking_by_Parul Sharma_null_owasp.pptx
Β 
New from BookNet Canada for 2024: BNC BiblioShare - Tech Forum 2024
New from BookNet Canada for 2024: BNC BiblioShare - Tech Forum 2024New from BookNet Canada for 2024: BNC BiblioShare - Tech Forum 2024
New from BookNet Canada for 2024: BNC BiblioShare - Tech Forum 2024
Β 

Discover Zero Point Energy and Vacuum Fluctuations Effects

  • 1. Zero Point Energy and Vacuum Fluctuations Effects Ana Trakhtman Department of Physics Ariel University Center of Samaria
  • 2.
  • 3. Zero Point Energy – a new friend or an old acquaintance?
  • 4. Vacuum Fluctuations – what is it?
  • 5. Spontaneous Emission and what it has to do with ZPE
  • 6. Casimir Effect or Van der Waals Attraction
  • 7. The Lamb Shift
  • 8. The Beam Splitter
  • 10.
  • 11. Zero Point Energy The origin of zero-point energy is the Heisenberg uncertainty principle. It is the lowest possible energy that a quantum mechanical system may have; it is the energy of its ground state. The most famous such example of zero-point energy is 𝐸=12β„πœ” associated with the ground state of the quantum harmonic oscillator. It is the expectation value of the Hamiltonian of the system in the ground state. Β 
  • 12. Zero Point Energy 𝐻=ℏ22π‘šΒ βˆ‡2+𝑉(π‘Ÿ,𝑑) 𝑍𝑃𝐸=𝐻=Ξ¨π‘”π‘Ÿπ‘œπ‘’π‘›π‘‘π»Ξ¨π‘”π‘Ÿπ‘œπ‘’π‘›π‘‘ Β 
  • 13. Vacuum Fluctuations In quantum field theory, the fabric of space is visualized as consisting of fields, with the field at every point in space and time being a quantum harmonic oscillator. The zero-point energy is again the expectation value of the Hamiltonian; here, however, the phrase vacuum expectation value is more commonly used, and the energy is called the vacuum energy. Vacuum energy can also be thought of in terms of virtual particles (also known as vacuum fluctuations) which are created and destroyed out of the vacuum. The concept of vacuum energy was derived from energy-time uncertainty principle.
  • 14. Vacuum Fluctuations The vacuum state |π‘£π‘Žπ‘> of the field is the state of the lowest energy. The expectations values of both π‘Žπ‘˜π‘  and π‘Žπ‘˜π‘ + vanish in the vacuum state, because: π‘Žπ‘˜π‘ |π‘£π‘Žπ‘>Β =0=<π‘£π‘Žπ‘|π‘Žπ‘˜π‘ + Vector 𝐹(π‘Ÿ,𝑑), which may be the electric or magnetic or the vector potential, having a mode expansion of the general form: πΉπ‘Ÿ,𝑑=1𝐿32π‘˜,π‘ π‘™πœ”π‘Žπ‘˜π‘ πœ€π‘˜π‘ π‘’π‘–π‘˜βˆ™π‘Ÿβˆ’πœ”π‘‘+h.𝑐 Β 
  • 15. Vacuum Fluctuations Where π‘™πœ” is some slowly varying function of frequency which is different for each field vector. Expectation value of πΉπ‘Ÿ,𝑑 in the vacuum state: <π‘£π‘Žπ‘πΉπ‘Ÿ,π‘‘π‘£π‘Žπ‘>Β =0 However, the expectation of the square of the field operator does not vanish, as we will show soon. This implies that there are fluctuations of the em field, even in its lowest energy. Β 
  • 16. Vacuum Fluctuations If we use the mode expansion and make use of the fact that: π‘£π‘Žπ‘π‘Žπ‘˜π‘ +π‘Žπ‘˜β€²π‘ β€²π‘£π‘Žπ‘=0 π‘£π‘Žπ‘π‘Žπ‘˜π‘ +π‘Žπ‘˜β€²π‘ β€²+π‘£π‘Žπ‘=0 π‘£π‘Žπ‘π‘Žπ‘˜π‘ π‘Žπ‘˜β€²π‘ β€²π‘£π‘Žπ‘=0 We find that: π‘£π‘Žπ‘πΉ2(π‘Ÿ,𝑑)π‘£π‘Žπ‘==1𝐿3π‘˜π‘ π‘˜β€²π‘ β€²π‘™πœ”π‘™βˆ—(πœ”β€²)π‘£π‘Žπ‘π‘Žπ‘˜π‘ π‘Žπ‘˜β€²π‘ β€²+π‘£π‘Žπ‘(πœ€π‘˜π‘ βˆ™πœ€π‘˜β€²π‘ β€²βˆ—)βˆ™π‘’π‘–[π‘˜βˆ’π‘˜β€²π‘Ÿβˆ’πœ”βˆ’πœ”β€²π‘‘] Β 
  • 17. Vacuum Fluctuations π‘Žπ‘˜π‘ π‘‘,Β π‘Žπ‘˜β€²π‘ β€²+(𝑑)=π‘Žπ‘˜π‘ βˆ™π‘Žπ‘˜β€²π‘ β€²+βˆ’π‘Žπ‘˜β€²π‘ β€²+βˆ™π‘Žπ‘˜π‘ =π›Ώπ‘˜π‘˜β€²3𝛿𝑠𝑠′ With the help of the commutation relation we have: π‘£π‘Žπ‘π‘Žπ‘˜π‘ π‘Žπ‘˜β€²π‘ β€²+π‘£π‘Žπ‘=π‘£π‘Žπ‘(π‘Žπ‘˜β€²π‘ β€²+βˆ™π‘Žπ‘˜π‘ +π›Ώπ‘˜π‘˜β€²3𝛿𝑠𝑠′)π‘£π‘Žπ‘=π›Ώπ‘˜π‘˜β€²3𝛿𝑠𝑠′ Β 
  • 18. Vacuum Fluctuations So that: π‘£π‘Žπ‘πΉ2(π‘Ÿ,𝑑)π‘£π‘Žπ‘=1𝐿3π‘˜,π‘ π‘™πœ”2=2𝐿3π‘˜π‘™πœ”2  ⟢ 22πœ‹3π‘™πœ”2𝑑3π‘˜ This is clearly non-zero, and indeed is infinite for an unbounded set of modes. As it is know: π‘£π‘Žπ‘βˆ†πΉ2π‘£π‘Žπ‘=π‘£π‘Žπ‘πΉ2π‘£π‘Žπ‘Β Β Β ,Β Β Β Β βˆ†πΉ=πΉβˆ’πΉ βˆ†πΉ – the deviation from the mean This shows us that the field fluctuates in the vacuum state. Β 
  • 19. Vacuum Fluctuations The effects of vacuum energy can be observed in various phenomena such as spontaneous emission, the Casimir effect and the Lamb shift, and are thought to influence the behavior of the Universe on cosmological scales.
  • 20. Spontaneous Emission Quantum electrodynamics shows that spontaneous emission takes place because there is always some electromagnetic field present in the vicinity of an atom, even when a field is not applied. Like any other system with discretely quantized energy, the electromagnetic field has a zero-point energy. Quantum electrodynamics shows that there will always be some electromagnetic field vibrations present, of whatever frequency is required to induce the charge oscillations that cause the atom to radiate 'spontaneously'.
  • 21. The Casimir Effect One of the more striking examples is the attractive force between a pair of parallel, uncharged, conducting plates in vacuum. This force is also referred to as a Van der Waals attraction and has been calculated by Dutch physicists Hendrik B. G. Casimir and Dirk Polder (1948).
  • 22. The Casimir Effect One can account for this force (also known as Casimir force), and obtain an approximate value of its magnitude, by assuming that the force is a consequence of the separation-dependent vacuum field energy trapped between the two plates. If the plats are squares of side L and are separated by a distance z, we may suppose that the system constitutes a β€œcavity” that supports modes with wave number k down to about 1/z. the vacuum field energy trapped between the plates may therefore be written approximately as: π‘ˆ=π‘˜,𝑠12β„πœ”β‰ˆπΏ2𝑧1π‘§πΎβ„π‘π‘˜Β π‘˜2π‘‘π‘˜β‰ˆ14𝐿2ℏ𝑐𝑧𝐾4βˆ’1𝑧3=π‘ˆπ‘’π‘π‘π‘’π‘Ÿβˆ’π‘ˆπ‘™π‘œπ‘€π‘’π‘Ÿ Β 
  • 23. The Casimir Effect we have introduced a high frequency cut-off K to make the energy finite. We can think of the negative rate of change of the lower cut-off energy π‘ˆπ‘™π‘œπ‘€π‘’π‘Ÿ with separation z as constituting a force of attraction, whose magnitude F per unit are is given by: 𝐹=βˆ’1𝐿2π‘‘π‘ˆπ‘™π‘œπ‘€π‘’π‘Ÿπ‘‘π‘§~ℏ𝑐𝑧4 Β 
  • 24. The Casimir Effect It is interesting to note from the structure of F that the force is proportional to ℏ and is therefore quantum mechanical. Because the strength of the force falls off rapidly with distance, it is only measurable when the distance between the objects is extremely small. On a submicrometre scale, this force becomes so strong that it becomes the dominant force between uncharged conductors. Β 
  • 25. The Casimir Effect At separations of 10 nmβ€”about 100 times the typical size of an atomβ€”the Casimir effect produces the equivalent of 1 atmosphere of pressure (101.325 kPa), the precise value depending on surface geometry and other factors. In modern theoretical physics, the Casimir effect plays an important role in the chiral bag model of the nucleon; and in applied physics, it is significant in some aspects of emerging micro technologies and nanotechnologies.
  • 26. The Lamb Shift The Lamb shift, named after Willis Lamb (1913–2008), is a small difference in energy between two energy levels 2S1 / 2 and 2P1 / 2 of the hydrogen atom in quantum electrodynamics. According to Dirac, the 2S1 / 2 and 2P1 / 2 orbitals should have the same energies. However, the interaction between the electron and the vacuum causes a tiny energy shift on 2S1 / 2. Lamb and Robert Retherford measured this shift in 1947. Lamb won the Nobel Prize in Physics in 1955 for his discoveries related to the Lamb shift.
  • 28. The Lamb Shift In 1948 Welton succeeded in accounting for the Lamb shift between the s and p energy levels of atomic hydrogen in terms of the perturbation of the electronic orbit brought about by vacuum fluctuations. A perturbation π›Ώπ‘Ÿ in electronic position in general causes a change of potential energy 𝛿𝑉 given by: 𝛿𝑉=π‘‰π‘Ÿ+π›Ώπ‘Ÿβˆ’π‘‰π‘Ÿ=βˆ‡π‘‰βˆ™π›Ώπ‘Ÿ+12πœ•πœ•π‘Ÿπ‘–πœ•πœ•π‘Ÿπ‘—π‘‰π›Ώπ‘Ÿπ‘–π›Ώπ‘Ÿπ‘—+β‹― Β 
  • 29. The Lamb Shift When we average this over the random displacements π‘Ÿ, the term in π›Ώπ‘Ÿ2 is the leading non-zero term and we find that: 𝛿𝑉=16βˆ‡2π‘‰Β π›Ώπ‘Ÿ2 In order to calculate the value of π›Ώπ‘Ÿ2 resulting from the fluctuations of the vacuum field, we observe that, under the influence of an electric field πΈπœ” of frequency πœ”, the electronic position r obeys the equation of motion: π‘šπ‘Ÿ=βˆ’π‘’πΈπœ”cosπœ”π‘‘ Β 
  • 30. The Lamb Shift And this results in a mean squared displacement about its equilibrium value of: π›Ώπ‘Ÿπœ”2=12𝑒2π‘š2πœ”4Β πΈπœ”2π‘£π‘Žπ‘=ℏ𝑒22πœ‹3πœ€0π‘š2𝑑3π‘˜πœ”3=ℏ𝑒22πœ‹2πœ€0π‘š2𝑐3πœ”0Ξ©π‘‘πœ”πœ” Β 
  • 31. The Lamb Shift The integral diverges logarithmically at the upper end, and had to be provided with a cut-off Ξ©, which is usually chosen to be of order π‘šπ‘2/ℏ. When this expression for π›Ώπ‘Ÿ2 is inserted in 𝛿𝑉, and we average βˆ‡2𝑉(π‘Ÿ) over the electronic orbit with the help of the wave function πœ“(π‘Ÿ), we obtain finally for the perturbation of the atomic energy level: 𝛿𝑉=ℏ𝑒212πœ‹2πœ€0π‘š2𝑐3 𝑑3π‘ŸΒ βˆ‡2π‘‰π‘Ÿπœ“π‘Ÿ2πœ”0Ξ©π‘‘πœ”πœ” Β 
  • 32. The Lamb Shift If we take the potential energy 𝑉(π‘Ÿ) to be: π‘‰π‘Ÿ=βˆ’π‘’24πœ‹πœ€0π‘ŸΒ  then: βˆ‡2π‘‰π‘Ÿ=𝑒2πœ€0𝛿3(π‘Ÿ) and the volume integral reduces to: 𝑒2πœ€0πœ“02 Β 
  • 33. The Lamb Shift This vanishes for a p-state but gives a finite value for an s-state. The difference between the s and p energy levels is therefore: βˆ†πΈ=ℏ𝑒412πœ‹2πœ€02π‘š2𝑐3πœ“π‘ 02lnπ‘šπ‘2β„πœ”0 Β 
  • 34. The Lamb Shift This leads to: βˆ†πΈβ„~1040 𝑀𝐻𝑧 For the 2s-state of hydrogen, and is in reasonable agreement with measurements by Lamb and Retherford (1947). Β 
  • 36. The Beam Splitter After decomposing all fields into plane-wave modes in the usual way, we consider a single incident mode labeled 1, which gives rise to a reflected mode 2 and a transmitted mode 3. r, t are the complex amplitude reflectivity and transmissivity for light incident from one side. π‘Ÿβ€², 𝑑′ for light coming from the other side there are no losses in the beam splitter Β 
  • 37. The Beam Splitter Then these parameters must obey the following reciprocity relations (due to Stokes, 1849): π‘Ÿ=π‘Ÿβ€²Β Β ,  𝑑=𝑑′ π‘Ÿ2+𝑑2=1 π‘Ÿπ‘‘βˆ—+π‘Ÿβˆ—π‘‘=0 Β 
  • 38. The Beam Splitter It follows that an incoming classical wave of complex amplitude 𝜐1 gives rise to a reflected wave 𝜐2, and a transmitted wave 𝜐3 such that: 𝑣2=π‘Ÿπ‘£1Β Β Β ,   𝑣3=𝑑𝑣1 From these relations it follows immediately that: 𝑣22+𝑣32=𝑑2+π‘Ÿ2𝑣12 So that the incoming energy is conserved. Β 
  • 39. The Beam Splitter Now suppose that we wish to apply a similar argument to the treatment of a quantum field. Then 𝑣1, 𝑣2, 𝑣3 have to be replaced by the complex amplitude operators π‘Ž1,Β π‘Ž2Β ,Β π‘Ž3 , which obey the commutation relations: π‘Žπ‘—,Β π‘Žπ‘—+=1,  𝑗=1,Β 2,Β 3 π‘Ž2,Β π‘Ž3+=0 Β 
  • 40. The Beam Splitter if we simply replace 𝑣1, 𝑣2, 𝑣3 by the operators π‘Ž1,Β π‘Ž2Β ,Β π‘Ž3 , we readily find that the commutation equations do not hold for π‘Ž2Β ,Β π‘Ž3. Instead we obtain: π‘Ž2Β ,Β π‘Ž3+=π‘Ÿ2π‘Ž1Β ,Β π‘Ž1+=π‘Ÿ2 π‘Ž3Β ,Β π‘Ž3+=𝑑2π‘Ž1Β ,Β π‘Ž1+=𝑑2 π‘Ž2Β ,Β π‘Ž3+=π‘Ÿπ‘‘βˆ—π‘Ž1Β ,Β π‘Ž1+=π‘Ÿπ‘‘βˆ— Β 
  • 41. The Beam Splitter The reason for the discrepancy is that we have ignored the fourth beam splitter input port, which is justifiably ignored in the classical treatment because no light enter that way. However, even if no energy is flowing through the mode labeled 0, in a quantized field treatment there is a vacuum field that enters here and contributes to the two output modes.
  • 42. The Beam Splitter Accordingly, we need to rewrite the commutation relations: π‘Ž2=π‘Ÿπ‘Ž1+π‘‘β€²π‘Ž0Β Β Β ;Β Β Β π‘Ž3=π‘‘π‘Ž1+π‘Ÿβ€²π‘Ž0 π‘Ž2Β ,Β π‘Ž2+=π‘Ÿ2π‘Ž1Β ,Β π‘Ž1++𝑑2π‘Ž0Β ,Β π‘Ž0+=π‘Ÿ2+𝑑2=1 π‘Ž2Β ,Β π‘Ž3+=π‘Ÿπ‘‘βˆ—π‘Ž1Β ,Β π‘Ž1+π‘Ÿβ€²βˆ—π‘‘β€²π‘Ž0Β ,Β π‘Ž0+=π‘Ÿπ‘‘βˆ—+π‘Ÿβ€²βˆ—π‘‘β€²=0 Β 
  • 43. Science Fiction or is it? As a scientific concept, the existence of zero point energy is not controversial although the ability to harness it is. Many claims exist of ''over unity devices'' (gadgets yielding a greater output than the required input for operation) driven by zero-point energy. Zero-point energy is not a thermal reservoir, and therefore does not suffer from the thermodynamic injunction against extracting energy from a lower temperature reservoir.
  • 44. Science Fiction or is it? In 1993 Cole and Puthoff published a thermodynamic analysis, ''Extracting energy and heat from the vacuum'' (see below), in which they concluded that ''extracting energy and heat from electromagnetic zero-point radiation via the use of the Casimir force'' is in principle possible without violating the laws of thermodynamics.
  • 45. Science Fiction or is it? A thought experiment for a device that readily demonstrates how the Casimir force could be put to use in principle was proposed by physicist Robert Forward in 1984 . A ''vacuum fluctuation battery'' could be constructed consisting of stacked conducting plates. Applying the same polarity charge to all the plates would yield a repulsive force between plates, thereby opposing the Casimir force which is acting to push the plates together. Adjusting the electrostatic force so as to permit the Casimir force to dominate will result in adding energy to the electric field between the plates, thereby converting zero-point energy to electric energy.
  • 46. Science Fiction or is it? In spite of the dubious nature of these claims (to date no such device has passed a rigorous, objective test), the concept of converting some amount of zero-point energy to usable energy cannot be ruled out in principle.
  • 47. Conclusion In all the examples above (not the science fiction part of course) we see that the vacuum field plays a fundamental role and is required for internal consistency. The vacuum has certain consequences in quantum electrodynamics that have no counterpart in the classical domain and it cannot be ignored.
  • 48. Bibliography β€œOptical Coherence and Quantum Optics” by Leonard Mandel and Emil Wolf β€œZero Point Energy and Zero Point Field” – Calphysics Institute Zero Point Energy and Vacuum Energy – Wikipedia General Interest Articles by Matt Visser, Victoria University of Wellington