marlon
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Five "socalled" Easy Pieces !
Hey, guys and girls,
I have written a little and simple text in order to eliminate some common misconceptions of QFT (well QM too ofcourse).
NUMBER ONE:
Besides, i would like to add this : people always ask how do electrons orbiting the nucleus prevent from falling in ? Well, this question itself contains incorrect formulations. the electron does NOT orbit the nucleus. Just look at the lowest energy orbital : the s-orbital. It is a sphere around the nucleus. So , prior to any kind of measurement, the electron is basically everywhere around the nucleus.
Same goes for any other orbital (ofcourse the have another shape)
QM proves us that the kinetic energy is higher when being closer to the nucleus, but the potential energy is lower (more negative). The sum of these two really yields a stable equilibrium throughout all energy levels.
NUMBER TWO:
People always mix QFT with QM. A wave function that describes an electron is not a wave that IS an electron. It just contains the electron-properties. This is QM
In QFT, particles arise as fluctuations of fields but the fields themselves ARE NOT particles. Particles arise (and also forces) as actual vibrations of these fields. Just think of the mattress analogy that i have used throughout my entire journal
NUMBER THREE:
An electron has a spin (intrinsic angular momentum), but it does NOT actually rotate around its axis, guys. The 'rotational nature' of spin comes from the behavior of the Dirac wavefunction (this is a matrix that represents a physical state and arises when solving the Dirac equation. This equation describes a fermion : a particle with non-integer spin) under coordinate-transformations (which are called the rotations).
With behavior i mean : how does the physics change if we interchange the components of this Dirac spinor, if we change the parity, if we apply coordinate transformations to the wavefunction and so on...For example, if we rotate the wavefunction 360°, do we still get the same physical laws...You see the pattern ?
It is this specific behavior that yields the name SPINOR because if you rotate it 360°, you get the opposite value. Now, changing coordinates (represented by rotations) and looking how the physics changes or not, is NOT THE SAME as actually rotating. So, spin arises thanks to symmetries involved but there is no actual rotation.
ps : be sure that you know what 'intrinsic' means
NUMBER FOUR:
Finally : there ain't two ways of describing light : The particle wave-duality exists only because of our 'classical minds' ; we want to think in terms of either particles or waves. There is no problem with that but we do need to keep the correct perspective on things here. First of all 'particles' in this case does not mean little objects with finite boundaries. It means little finite pieces of energy (this is the actual quantization , right ?)
Secondly, in QM we have experiments that are better explained with the wave-like notion (eg the double slit experiment) and we have those experiments that are better described with the particle-like notion (eg photo-electric effect). However in the end both descriptions are just ONE SINGLE way of describing the physical properties of light...that is all.
NUMBER FIVE:
Another common misconception is the fact that the photo-electric effect proved the existence of photons. That is not true because this photo-electric effect can be described in terms of the wavelike-notion of the incident EM-radiation too. It is only the atoms of the target electrode that are treated with QM. However, the particle-like notion of light is suggested by this experiment. If you want to read more, check out my journal and find the article on creating an entangeled photon-state in an undergrad lab
Here's the article : Create entangled photons yourself in an undergrad laboratory :
http://marcus.whitman.edu/~beckmk/Q...r/Thorn_ajp.pdf
regards
marlon
Hey, guys and girls,
I have written a little and simple text in order to eliminate some common misconceptions of QFT (well QM too ofcourse).
NUMBER ONE:
Besides, i would like to add this : people always ask how do electrons orbiting the nucleus prevent from falling in ? Well, this question itself contains incorrect formulations. the electron does NOT orbit the nucleus. Just look at the lowest energy orbital : the s-orbital. It is a sphere around the nucleus. So , prior to any kind of measurement, the electron is basically everywhere around the nucleus.
Same goes for any other orbital (ofcourse the have another shape)
QM proves us that the kinetic energy is higher when being closer to the nucleus, but the potential energy is lower (more negative). The sum of these two really yields a stable equilibrium throughout all energy levels.
NUMBER TWO:
People always mix QFT with QM. A wave function that describes an electron is not a wave that IS an electron. It just contains the electron-properties. This is QM
In QFT, particles arise as fluctuations of fields but the fields themselves ARE NOT particles. Particles arise (and also forces) as actual vibrations of these fields. Just think of the mattress analogy that i have used throughout my entire journal
NUMBER THREE:
An electron has a spin (intrinsic angular momentum), but it does NOT actually rotate around its axis, guys. The 'rotational nature' of spin comes from the behavior of the Dirac wavefunction (this is a matrix that represents a physical state and arises when solving the Dirac equation. This equation describes a fermion : a particle with non-integer spin) under coordinate-transformations (which are called the rotations).
With behavior i mean : how does the physics change if we interchange the components of this Dirac spinor, if we change the parity, if we apply coordinate transformations to the wavefunction and so on...For example, if we rotate the wavefunction 360°, do we still get the same physical laws...You see the pattern ?
It is this specific behavior that yields the name SPINOR because if you rotate it 360°, you get the opposite value. Now, changing coordinates (represented by rotations) and looking how the physics changes or not, is NOT THE SAME as actually rotating. So, spin arises thanks to symmetries involved but there is no actual rotation.
ps : be sure that you know what 'intrinsic' means
NUMBER FOUR:
Finally : there ain't two ways of describing light : The particle wave-duality exists only because of our 'classical minds' ; we want to think in terms of either particles or waves. There is no problem with that but we do need to keep the correct perspective on things here. First of all 'particles' in this case does not mean little objects with finite boundaries. It means little finite pieces of energy (this is the actual quantization , right ?)
Secondly, in QM we have experiments that are better explained with the wave-like notion (eg the double slit experiment) and we have those experiments that are better described with the particle-like notion (eg photo-electric effect). However in the end both descriptions are just ONE SINGLE way of describing the physical properties of light...that is all.
NUMBER FIVE:
Another common misconception is the fact that the photo-electric effect proved the existence of photons. That is not true because this photo-electric effect can be described in terms of the wavelike-notion of the incident EM-radiation too. It is only the atoms of the target electrode that are treated with QM. However, the particle-like notion of light is suggested by this experiment. If you want to read more, check out my journal and find the article on creating an entangeled photon-state in an undergrad lab
Here's the article : Create entangled photons yourself in an undergrad laboratory :
http://marcus.whitman.edu/~beckmk/Q...r/Thorn_ajp.pdf
regards
marlon
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