Gravitationsfält
Uppdaterad: 180112
[12]
Har jag använt någon bild som jag inte får använda? Låt mig veta så tar jag bort den.
christian.karlsson@ckfysik.se
[1] Gravitation – ett märkligt fenomen [2] Gravitationsfält
[3] Gravitationsfält
Läget idag
[x]
X
Läget idag
Partikelegenskaper Vågegenskaper
Materia
Strålning
Ja! (mekanik)
p = mv Wk = mv2 2
p =γmv Ek = (γ−1)mc2 R = p
Ja! (fotonmodellen)
light!waves and particles" are mutually exclusive because they appear independently in different experiments. To elimi- nate this conceptual difficulty we have designed an apparatus in which the particle and wave aspects can first be demon- strated individually. Then the same apparatus is used to vi- sualize the real-time evolution of individual quantum events to a classical wave pattern. The use of the same light source and the same interferometer is important to convince stu- dents that we can investigate the two aspects of light with the same apparatus.
Two-beam interference phenomena are often explained on the basis of Young’s double slit experiment by displaying the well known interference pattern on a distant screen. Al- though this example is well suited for a theoretical discus- sion and most easily realized using a laser pointer and a double slit, it is not practical for advanced demonstration experiments because it does not allow the variation of system parameters in a simple way. In the present experiment we have chosen a Mach-Zehnder interferometer in which a large spatial separation of the two interfering beams can be easily realized, permitting several manipulations, such as the ad- justment of the path length difference and the relative angle of the interfering beams, and, most importantly, the easy blocking of one of the two beams. The macroscopic dimen- sions of the Mach-Zehnder interferometer allow the observer to see all components from the light source via the genera- tion and recombination of the interfering beams up to their detection.
A green laser pointer was chosen as the light source be- cause it has a sufficiently long coherence length for the easy alignment of the interferometer. The intensity of the green beam and its wavelength near the vicinity of the eye’s maxi- mum sensitivity ensure that even expanded interference pat- terns are easily visible in a large auditorium.
Our main design criterion was to have the apparatus as simple and pedagogical as possible while also offering the flexibility to vary certain parameters to illustrate several as-
pects of the phenomena. The equipment is designed for dem- onstrations in a large auditorium. The interferometer is mounted on an aluminum plate tilted by 45°, so that all com- ponents can be easily seen. If necessary, a webcam can be used to project a close-up of the interferometer table. As mentioned, the expanded fringe pattern using the full laser intensity can easily be seen from a distance without addi- tional tools. Individual photon events can be seen as pulses on an oscilloscope, or heard as clicks using audio equipment.
All relevant electronic signals !photomultiplier pulses and photodiode signals" can easily be projected using equipment such as a digital oscilloscope equipped with a video port or a USB-based oscilloscope. Attention was paid to obtain stable pictures and good visibility of all the components and pro- jected signals. Last but not least, we have made an effort to reduce component cost as much as possible, and to give the apparatus a pleasant look.
III. EXPERIMENTAL SETUP
The scheme of the experimental apparatus is shown in Fig.
2 and a photo of its main components in Fig.3. The light source is a 5 mW green!!=537 nm" laser pointer. The bat- teries in the laser pointer were replaced by electrical contacts so that the laser could be driven by an external power supply.
We found that the spectral width of the laser radiation and hence its coherence length depends on the operating voltage and a randomly chosen pointer has its own optimal voltage for the highest fringe contrast. Once set correctly and after a warm-up time of several minutes this voltage gives repro- ducible results on daily basis.
The standard Mach-Zehnder interferometer has two beam splitters and two mirrors !all 1 in. optics" arranged in a 18
"18 cm2square !see Figs.2and3". One of the mirrors is mounted on a low-voltage piezotransducer that allows the voltage-controlled variation of the path length difference
!#5 V per fringe".
Fig. 1.!Color online" From particles to waves: Detection of light diffracted from a double slit on a photon by photon basis using a single-photon imaging CCD camera. Although single frames show an apparently random distribution of photon impact points, their integration reveals the classical fringe pattern.
138 Am. J. Phys., Vol. 76, No. 2, February 2008 T. L. Dimitrova and A. Weis 138
light !waves and particles" are mutually exclusive because they appear independently in different experiments. To elimi- nate this conceptual difficulty we have designed an apparatus in which the particle and wave aspects can first be demon- strated individually. Then the same apparatus is used to vi- sualize the real-time evolution of individual quantum events to a classical wave pattern. The use of the same light source and the same interferometer is important to convince stu- dents that we can investigate the two aspects of light with the same apparatus.
Two-beam interference phenomena are often explained on the basis of Young’s double slit experiment by displaying the well known interference pattern on a distant screen. Al- though this example is well suited for a theoretical discus- sion and most easily realized using a laser pointer and a double slit, it is not practical for advanced demonstration experiments because it does not allow the variation of system parameters in a simple way. In the present experiment we have chosen a Mach-Zehnder interferometer in which a large spatial separation of the two interfering beams can be easily realized, permitting several manipulations, such as the ad- justment of the path length difference and the relative angle of the interfering beams, and, most importantly, the easy blocking of one of the two beams. The macroscopic dimen- sions of the Mach-Zehnder interferometer allow the observer to see all components from the light source via the genera- tion and recombination of the interfering beams up to their detection.
A green laser pointer was chosen as the light source be- cause it has a sufficiently long coherence length for the easy alignment of the interferometer. The intensity of the green beam and its wavelength near the vicinity of the eye’s maxi- mum sensitivity ensure that even expanded interference pat- terns are easily visible in a large auditorium.
Our main design criterion was to have the apparatus as simple and pedagogical as possible while also offering the flexibility to vary certain parameters to illustrate several as-
pects of the phenomena. The equipment is designed for dem- onstrations in a large auditorium. The interferometer is mounted on an aluminum plate tilted by 45°, so that all com- ponents can be easily seen. If necessary, a webcam can be used to project a close-up of the interferometer table. As mentioned, the expanded fringe pattern using the full laser intensity can easily be seen from a distance without addi- tional tools. Individual photon events can be seen as pulses on an oscilloscope, or heard as clicks using audio equipment.
All relevant electronic signals !photomultiplier pulses and photodiode signals" can easily be projected using equipment such as a digital oscilloscope equipped with a video port or a USB-based oscilloscope. Attention was paid to obtain stable pictures and good visibility of all the components and pro- jected signals. Last but not least, we have made an effort to reduce component cost as much as possible, and to give the apparatus a pleasant look.
III. EXPERIMENTAL SETUP
The scheme of the experimental apparatus is shown in Fig.
2 and a photo of its main components in Fig.3. The light source is a 5 mW green!!=537 nm" laser pointer. The bat- teries in the laser pointer were replaced by electrical contacts so that the laser could be driven by an external power supply.
We found that the spectral width of the laser radiation and hence its coherence length depends on the operating voltage and a randomly chosen pointer has its own optimal voltage for the highest fringe contrast. Once set correctly and after a warm-up time of several minutes this voltage gives repro- ducible results on daily basis.
The standard Mach-Zehnder interferometer has two beam splitters and two mirrors!all 1 in. optics" arranged in a 18
"18 cm2 square!see Figs.2 and3". One of the mirrors is mounted on a low-voltage piezotransducer that allows the voltage-controlled variation of the path length difference
!#5 V per fringe".
Fig. 1.!Color online" From particles to waves: Detection of light diffracted from a double slit on a photon by photon basis using a single-photon imaging CCD camera. Although single frames show an apparently random distribution of photon impact points, their integration reveals the classical fringe pattern.
138 Am. J. Phys., Vol. 76, No. 2, February 2008 T. L. Dimitrova and A. Weis 138
[x]
Ja! (elektromagnetism, optik) W = hf
p = h λ
(2005) E, B
Ja! (kvantmekanik) i∂ψ
∂t = − 2 2m
∂2ψ
∂x2 +Uψ
Kvantfältteorier
QED
QCD Partikelfysikens standardmodell
X
Läget idag
Partikelegenskaper Vågegenskaper
Materia
Strålning
Ja! (mekanik)
p = mv Wk = mv2 2
p =γmv Ek = (γ−1)mc2 R = p
Ja! (fotonmodellen)
light!waves and particles" are mutually exclusive because they appear independently in different experiments. To elimi- nate this conceptual difficulty we have designed an apparatus in which the particle and wave aspects can first be demon- strated individually. Then the same apparatus is used to vi- sualize the real-time evolution of individual quantum events to a classical wave pattern. The use of the same light source and the same interferometer is important to convince stu- dents that we can investigate the two aspects of light with the same apparatus.
Two-beam interference phenomena are often explained on the basis of Young’s double slit experiment by displaying the well known interference pattern on a distant screen. Al- though this example is well suited for a theoretical discus- sion and most easily realized using a laser pointer and a double slit, it is not practical for advanced demonstration experiments because it does not allow the variation of system parameters in a simple way. In the present experiment we have chosen a Mach-Zehnder interferometer in which a large spatial separation of the two interfering beams can be easily realized, permitting several manipulations, such as the ad- justment of the path length difference and the relative angle of the interfering beams, and, most importantly, the easy blocking of one of the two beams. The macroscopic dimen- sions of the Mach-Zehnder interferometer allow the observer to see all components from the light source via the genera- tion and recombination of the interfering beams up to their detection.
A green laser pointer was chosen as the light source be- cause it has a sufficiently long coherence length for the easy alignment of the interferometer. The intensity of the green beam and its wavelength near the vicinity of the eye’s maxi- mum sensitivity ensure that even expanded interference pat- terns are easily visible in a large auditorium.
Our main design criterion was to have the apparatus as simple and pedagogical as possible while also offering the flexibility to vary certain parameters to illustrate several as-
pects of the phenomena. The equipment is designed for dem- onstrations in a large auditorium. The interferometer is mounted on an aluminum plate tilted by 45°, so that all com- ponents can be easily seen. If necessary, a webcam can be used to project a close-up of the interferometer table. As mentioned, the expanded fringe pattern using the full laser intensity can easily be seen from a distance without addi- tional tools. Individual photon events can be seen as pulses on an oscilloscope, or heard as clicks using audio equipment.
All relevant electronic signals !photomultiplier pulses and photodiode signals" can easily be projected using equipment such as a digital oscilloscope equipped with a video port or a USB-based oscilloscope. Attention was paid to obtain stable pictures and good visibility of all the components and pro- jected signals. Last but not least, we have made an effort to reduce component cost as much as possible, and to give the apparatus a pleasant look.
III. EXPERIMENTAL SETUP
The scheme of the experimental apparatus is shown in Fig.
2 and a photo of its main components in Fig.3. The light source is a 5 mW green!!=537 nm" laser pointer. The bat- teries in the laser pointer were replaced by electrical contacts so that the laser could be driven by an external power supply.
We found that the spectral width of the laser radiation and hence its coherence length depends on the operating voltage and a randomly chosen pointer has its own optimal voltage for the highest fringe contrast. Once set correctly and after a warm-up time of several minutes this voltage gives repro- ducible results on daily basis.
The standard Mach-Zehnder interferometer has two beam splitters and two mirrors !all 1 in. optics" arranged in a 18
"18 cm2square !see Figs.2and3". One of the mirrors is mounted on a low-voltage piezotransducer that allows the voltage-controlled variation of the path length difference
!#5 V per fringe".
Fig. 1.!Color online" From particles to waves: Detection of light diffracted from a double slit on a photon by photon basis using a single-photon imaging CCD camera. Although single frames show an apparently random distribution of photon impact points, their integration reveals the classical fringe pattern.
138 Am. J. Phys., Vol. 76, No. 2, February 2008 T. L. Dimitrova and A. Weis 138
light !waves and particles" are mutually exclusive because they appear independently in different experiments. To elimi- nate this conceptual difficulty we have designed an apparatus in which the particle and wave aspects can first be demon- strated individually. Then the same apparatus is used to vi- sualize the real-time evolution of individual quantum events to a classical wave pattern. The use of the same light source and the same interferometer is important to convince stu- dents that we can investigate the two aspects of light with the same apparatus.
Two-beam interference phenomena are often explained on the basis of Young’s double slit experiment by displaying the well known interference pattern on a distant screen. Al- though this example is well suited for a theoretical discus- sion and most easily realized using a laser pointer and a double slit, it is not practical for advanced demonstration experiments because it does not allow the variation of system parameters in a simple way. In the present experiment we have chosen a Mach-Zehnder interferometer in which a large spatial separation of the two interfering beams can be easily realized, permitting several manipulations, such as the ad- justment of the path length difference and the relative angle of the interfering beams, and, most importantly, the easy blocking of one of the two beams. The macroscopic dimen- sions of the Mach-Zehnder interferometer allow the observer to see all components from the light source via the genera- tion and recombination of the interfering beams up to their detection.
A green laser pointer was chosen as the light source be- cause it has a sufficiently long coherence length for the easy alignment of the interferometer. The intensity of the green beam and its wavelength near the vicinity of the eye’s maxi- mum sensitivity ensure that even expanded interference pat- terns are easily visible in a large auditorium.
Our main design criterion was to have the apparatus as simple and pedagogical as possible while also offering the flexibility to vary certain parameters to illustrate several as-
pects of the phenomena. The equipment is designed for dem- onstrations in a large auditorium. The interferometer is mounted on an aluminum plate tilted by 45°, so that all com- ponents can be easily seen. If necessary, a webcam can be used to project a close-up of the interferometer table. As mentioned, the expanded fringe pattern using the full laser intensity can easily be seen from a distance without addi- tional tools. Individual photon events can be seen as pulses on an oscilloscope, or heard as clicks using audio equipment.
All relevant electronic signals !photomultiplier pulses and photodiode signals" can easily be projected using equipment such as a digital oscilloscope equipped with a video port or a USB-based oscilloscope. Attention was paid to obtain stable pictures and good visibility of all the components and pro- jected signals. Last but not least, we have made an effort to reduce component cost as much as possible, and to give the apparatus a pleasant look.
III. EXPERIMENTAL SETUP
The scheme of the experimental apparatus is shown in Fig.
2 and a photo of its main components in Fig.3. The light source is a 5 mW green!!=537 nm" laser pointer. The bat- teries in the laser pointer were replaced by electrical contacts so that the laser could be driven by an external power supply.
We found that the spectral width of the laser radiation and hence its coherence length depends on the operating voltage and a randomly chosen pointer has its own optimal voltage for the highest fringe contrast. Once set correctly and after a warm-up time of several minutes this voltage gives repro- ducible results on daily basis.
The standard Mach-Zehnder interferometer has two beam splitters and two mirrors!all 1 in. optics" arranged in a 18
"18 cm2 square!see Figs.2 and3". One of the mirrors is mounted on a low-voltage piezotransducer that allows the voltage-controlled variation of the path length difference
!#5 V per fringe".
Fig. 1.!Color online" From particles to waves: Detection of light diffracted from a double slit on a photon by photon basis using a single-photon imaging CCD camera. Although single frames show an apparently random distribution of photon impact points, their integration reveals the classical fringe pattern.
138 Am. J. Phys., Vol. 76, No. 2, February 2008 T. L. Dimitrova and A. Weis 138
[x]
Ja! (elektromagnetism, optik) W = hf
p = h λ
(2005) E, B
Ja! (kvantmekanik) i∂ψ
∂t = − 2 2m
∂2ψ
∂x2 +Uψ
X
Hur kan ett föremål här ute
“känna av” jorden?
Gravitation – ett märkligt fenomen
1
Gravitation – ett märkligt fenomen
1
Hur kan ett föremål här ute
“känna av” jorden?
[1]
Gravitation – ett märkligt fenomen
1
Hur kan ett föremål här ute
“känna av” jorden?
F = Gm1m2 r2
[1]
[2] [3]
Gravitation – ett märkligt fenomen
1
Hur kan ett föremål här ute
“känna av” jorden?
”But hitherto I have not been able to discover the cause of those properties of gravity from phænomena, and I frame no hypotheses.
…
And to us it is enough, that gravity does really exist, and act according to the laws which we have
explained, and abundantly serves to account for all the motions of the celestial bodies, and of our sea.”
F = Gm1m2 r2
[1]
[2] [3]
[4]
Gravitationsfält
2
Ett sätt att förstå beskriva gravitationsväxelverkan:
Gravitationsfält
Ett sätt att förstå beskriva gravitationsväxelverkan:
2
Gravitationsfält
Ett sätt att förstå beskriva gravitationsväxelverkan:
1) Ett föremål med massa ger upphov till och omges av ett gravitationsfält.
2
• Gravitationsfält kan åskådliggöras genom att rita fältlinjer.
Gravitationsfält
Ett sätt att förstå beskriva gravitationsväxelverkan:
1) Ett föremål med massa ger upphov till och omges av ett gravitationsfält.
2
• Gravitationsfält kan åskådliggöras genom att rita fältlinjer.
Gravitationsfält
Ett sätt att förstå beskriva gravitationsväxelverkan:
1) Ett föremål med massa ger upphov till och omges av ett gravitationsfält.
2) Ett annat föremål med massa i fältet
2
• Gravitationsfält kan åskådliggöras genom att rita fältlinjer.
Gravitationsfält
Ett sätt att förstå beskriva gravitationsväxelverkan:
1) Ett föremål med massa ger upphov till och omges av ett gravitationsfält.
2) Ett annat föremål med massa i fältet påverkas av en gravitationskraft.
2
• Gravitationsfält kan åskådliggöras genom att rita fältlinjer.
• Gravitationsfältlinjer anger riktningen för gravitationskraften på e en partikel.
Gravitationsfält
Ett sätt att förstå beskriva gravitationsväxelverkan:
1) Ett föremål med massa ger upphov till och omges av ett gravitationsfält.
2) Ett annat föremål med massa i fältet påverkas av en gravitationskraft.
2
• Gravitationsfält kan åskådliggöras genom att rita fältlinjer.
• Gravitationsfältlinjer anger riktningen för gravitationskraften på e en partikel.
Gravitationsfält
kraft på litet föremål med massan m
2
Gravitationsfältstyrkan i en punkt:
storhet som beskriver fältet
g = Fg
m ⇒ Fg = mg
SI-enhet: 1 N/kg
(
Egentligen: g! = F"!"g)
m
Fg m
Gravitationsfält
kraft på litet föremål med massan m
Ett sätt att förstå beskriva gravitationsväxelverkan:
1) Ett föremål med massa ger upphov till och omges av ett gravitationsfält.
2) Ett annat föremål med massa i fältet påverkas av en gravitationskraft.
2
Gravitationsfältstyrkan i en punkt:
storhet som beskriver fältet
g = Fg
m ⇒ Fg = mg
SI-enhet: 1 N/kg
(
Egentligen: g! = F"!"g)
m
Fg m
• Gravitationsfält kan åskådliggöras genom att rita fältlinjer.
• Gravitationsfältlinjer anger riktningen för gravitationskraften på e en partikel
för gravitationsfältstyrkan (g).
Gravitationsfält
Genom att rita gravitationsfältstyrka-vektorer Genom att rita (gravitations)fält-linjer
J/C J/C
3
Två olika sätt att åskådliggöra gravitationsfält:
Rymdstationen MIR
X
[5]
Rymdstationen MIR
X
[5]
[6]
[7]
[8] [7]
[8] [7]
Rymdstationen MIR
X
[8]
[9]
[10]
[11] [12]
Rymdstationen MIR
[13]
Källor
[1] http://commons.wikimedia.org/wiki/File:The_Earth_seen_from_Apollo_17.jpg [2] https://en.wikipedia.org/wiki/Isaac_Newton
Porträtt målat 1689, då Newton var 47 år gammal. Principia gavs ut två år tidigare, 1687.
[3] https://en.wikipedia.org/wiki/Philosophiæ_Naturalis_Principia_Mathematica
[4] https://newtonprojectca.files.wordpress.com/2013/06/newton-general-scholium-1729-english-text-by-motte-a4.pdf [5] https://en.wikipedia.org/wiki/Mir
Wikipedia-bildtext: Russian Space Station Mir, backdropped against Earth, taken from the Space Shuttle Atlantis following undocking from the station at the end of STS-71 on the 4th of July, 1995. On the 29th of June, 1995, STS-71 became the first Shuttle mission ever to dock with the station.
[6] http://en.wikipedia.org/wiki/Mir [7] https://en.wikipedia.org/wiki/Mir
Wikipedia-bildtext: Approach view of the Mir Space Station viewed from Space Shuttle Endeavour during the STS-89 rendezvous.
A Progress cargo ship is attached on the left, a Soyuz manned spacecraft attached on the right.
[8] https://en.wikipedia.org/wiki/Mir
Core module – Kvant-1: 19 m, Priroda – docking module: 31 m, Kvant-2 – Spektr: 27,5 m (från Wikipedia)
[9] https://spaceflight.nasa.gov/gallery/images/shuttle/sts-76/html/sts076-461-014.html
Kosmonauten Yury V. Usachev. Utanför fönstret skymtar nosen på rymdfärjan Atlantis (STS-76).
[10] https://en.wikipedia.org/wiki/Mir_Core_Module [11] https://en.wikipedia.org/wiki/Mir_Core_Module Julen 1997 på MIR.
[12] https://www.flickr.com/photos/nasacommons/9461048636/in/album-72157649059305918/
MIR och rymdfärjan Atlantis den 4 juli 1995 (STS-71). Bilden är tagen av två kosmonauter som tog en flygtur i Soyuz-farkosten. Rymdfärjan verkar ha dockat på olika ställen på MIR vid olika tillfällen.
[13] https://spaceflight.nasa.gov/gallery/images/shuttle/sts-79/html/s79e5180.html
STS-79- och MIR-22-besättningarna den 20 september 1996.
[3] http://en.wikipedia.org/wiki/Dachshund [4] http://sv.wikipedia.org/wiki/Ullevi
[5] http://www.hakanpettersson.se/blogg.php?id=2260 [6] http://en.wikipedia.org/wiki/Wind_wave
[7] http://en.wikipedia.org/wiki/Electromagnetic_wave [8] http://en.wikipedia.org/wiki/Thurso
[9] http://en.wikipedia.org/wiki/Christiaan_Huygens [10] http://en.wikipedia.org/wiki/Breakwater_(structure) [11] http://academics.wellesley.edu/Physics/Tbauer/Poisson/
[12] http://de.wikipedia.org/wiki/Interferenz_(Physik) [13] http://en.wikipedia.org/wiki/Mark_knopfler
[14] http://researcher.ibm.com/researcher/view_project_subpage.php?id=4252 Fe-atomer på Cu(111).
[15] http://de.wikipedia.org/wiki/Liste_der_Berliner_Fußgängertunnel
