Moving all the old Physics factlects to the same hashtag to make easier to find them. As Twitter does not allow me to edit my tweets, I need to repost all of them. Apologies if this floods your timeline.
#Physicsfactlet (1)
The uncertainty principle is not a principle, it is a theorem. Just like the Pauli exclusion principle and many others. It was a principle when it was first formulated, but we have since realised that it can be derived from first principles.
The uncertainty principle is not a principle, it is a theorem. Just like the Pauli exclusion principle and many others. It was a principle when it was first formulated, but we have since realised that it can be derived from first principles.
#Physicsfactlet (2)
There is nothing quantum in describing particles as waves. In fact one can rewrite the whole Newtonian mechanics as a wave theory without changing any result or prediction. (See Hamilton-Jacobi formalism)
There is nothing quantum in describing particles as waves. In fact one can rewrite the whole Newtonian mechanics as a wave theory without changing any result or prediction. (See Hamilton-Jacobi formalism)
#Physicsfactlet (3)
For statistical mechanics (a classical theory) to be consistent with thermodynamics (a classical theory) you need to consider particles to be indistinguishable from each other, a very quantum assumption. Otherwise you incur in Gibbs' paradox.
For statistical mechanics (a classical theory) to be consistent with thermodynamics (a classical theory) you need to consider particles to be indistinguishable from each other, a very quantum assumption. Otherwise you incur in Gibbs' paradox.
#Physicsfactlet (4)
Energy conservation is a direct consequence of the fact that the law of Physics do not change with time. In a universe where the law of nature (e.g. the value of some fundamental constant) change, energy would not be conserved.
Energy conservation is a direct consequence of the fact that the law of Physics do not change with time. In a universe where the law of nature (e.g. the value of some fundamental constant) change, energy would not be conserved.
#Physicsfactlet (5)
Bell's inequality experiments do NOT rule out nonlocal hidden variables interpretations of QM (e.g. Bohmian mechanics). The only real problem anyone ever found with hidden variable theories is that it is difficult to make a quantum field theory out of them.
Bell's inequality experiments do NOT rule out nonlocal hidden variables interpretations of QM (e.g. Bohmian mechanics). The only real problem anyone ever found with hidden variable theories is that it is difficult to make a quantum field theory out of them.
#Physicsfactlet (6)
The refractive index is an emergent property due to the scattering of light from each and every atom/molecule forming the material. All the scattered waves interfere destructively except for a forward (slower) one. (See the Ewald–Oseen extinction theorem)
The refractive index is an emergent property due to the scattering of light from each and every atom/molecule forming the material. All the scattered waves interfere destructively except for a forward (slower) one. (See the Ewald–Oseen extinction theorem)
#Physicsfactlet (7)
Perfect crystals are a thermodynamic impossibility. At finite temperature the Helmholtz free energy is minimised for a positive amount of entropy, resulting in a crystal with defects of some kind as soon as you are above zero Kelvin.
Perfect crystals are a thermodynamic impossibility. At finite temperature the Helmholtz free energy is minimised for a positive amount of entropy, resulting in a crystal with defects of some kind as soon as you are above zero Kelvin.
#Physicsfactlet (8)
In classical electrodynamics two different electric fields overlap without interacting, and the result is just the sum of the two. But in quantum electrodynamics two photon can scatter from each other via a fermion loop, withut any medium to mediate it.
In classical electrodynamics two different electric fields overlap without interacting, and the result is just the sum of the two. But in quantum electrodynamics two photon can scatter from each other via a fermion loop, withut any medium to mediate it.
#Physicsfactlet (9)
To see a rainbow you need the sun behind you and mist or clouds in front of you. If the condition are ok you can see a second rainbow around the first one. The third rainbow is the one you never see, because it is actually behind your back, toward the sun.
To see a rainbow you need the sun behind you and mist or clouds in front of you. If the condition are ok you can see a second rainbow around the first one. The third rainbow is the one you never see, because it is actually behind your back, toward the sun.
#Physicsfactlet (10)
#Photon is one of the most misused words in Physics. A photon is a quantum of excitation of a mode of the em field. A photon is NOT a little ball of energy zipping around. A more authoritative discussion on the topic can be found at link.springer.com/article/10.100…
#Photon is one of the most misused words in Physics. A photon is a quantum of excitation of a mode of the em field. A photon is NOT a little ball of energy zipping around. A more authoritative discussion on the topic can be found at link.springer.com/article/10.100…
#Physicsfactlet (11)
There is no good fundamental reason we know of why the inertial mass and the gravitational mass of a body should be the same. But all the empirical evidence we have tells us they are, and the direct consequence of this fact is General Relativity.
There is no good fundamental reason we know of why the inertial mass and the gravitational mass of a body should be the same. But all the empirical evidence we have tells us they are, and the direct consequence of this fact is General Relativity.
#Physicsfactlet (12)
There are only two central potentials that guarantee that all bound orbits are also closed: the harmonic and the 1/r potential (Bertrand's theorem). Which means that if gravity was even a bit different, the solar system would be a strange place indeed.
There are only two central potentials that guarantee that all bound orbits are also closed: the harmonic and the 1/r potential (Bertrand's theorem). Which means that if gravity was even a bit different, the solar system would be a strange place indeed.
#Physicsfactlet (13)
Sound waves (at least in the audible range) are scalar waves.
Electromagnetic waves are vector waves.
But gravitational waves are tensor waves.
Sound waves (at least in the audible range) are scalar waves.
Electromagnetic waves are vector waves.
But gravitational waves are tensor waves.
#Physicsfactlet (14)
Charged black holes can have two horizons. An outer event horizon (like all other black holes), and another horizon inside, concentric with the first one.
Charged black holes can have two horizons. An outer event horizon (like all other black holes), and another horizon inside, concentric with the first one.
#Physicsfactlet (15)
In QM the standard way to insure an Hamiltonian has real eigenvalues (i.e. it describes a system with real energy) is to force it to be Hermitian. But technically also a PT-symmetric Hamiltonian would have the same property.
In QM the standard way to insure an Hamiltonian has real eigenvalues (i.e. it describes a system with real energy) is to force it to be Hermitian. But technically also a PT-symmetric Hamiltonian would have the same property.
#Physicsfactlet (16)
In QM there are potential barriers that actually do not reflect the wavefunction at all, independently from the energy of the particle (i.e. it is not a tunneling effect). The most famous is the Pöschl–Teller potential, but there are infinite others.
In QM there are potential barriers that actually do not reflect the wavefunction at all, independently from the energy of the particle (i.e. it is not a tunneling effect). The most famous is the Pöschl–Teller potential, but there are infinite others.
#Physicsfactlet (17)
There is such a thing as negative temperature (e.g. -10K). It happens when enough of the available energy levels are excited that increasing the system energy actually decreases its entropy. Interestingly -10K in not colder than +10K, but MUCH hotter.
There is such a thing as negative temperature (e.g. -10K). It happens when enough of the available energy levels are excited that increasing the system energy actually decreases its entropy. Interestingly -10K in not colder than +10K, but MUCH hotter.
#Physicsfactlet (18)
The human eye is more sensitive than any camera, and in the appropriate conditions, is able to detect single photons.
The human eye is more sensitive than any camera, and in the appropriate conditions, is able to detect single photons.
#Physicsfactlet (19)
Schrödinger equation is often presented as falling out of the blue sky to QM students, but it is easy to justify. Just take the dispersion relation of a free particle, make a Fourier transform and add the potential like you would for the Helmoltz equation.
Schrödinger equation is often presented as falling out of the blue sky to QM students, but it is easy to justify. Just take the dispersion relation of a free particle, make a Fourier transform and add the potential like you would for the Helmoltz equation.
#Physicsfactlet (20)
Noether's theorem connects symmetries and conserved quantities (e.g. translational invariance -> momentum conservation). There is no general equivalent for discrete symmetries, BUT for some of them the theorem works even if it shouldn't (e.g. parity).
Noether's theorem connects symmetries and conserved quantities (e.g. translational invariance -> momentum conservation). There is no general equivalent for discrete symmetries, BUT for some of them the theorem works even if it shouldn't (e.g. parity).
#Physicsfactlet (21)
(Math edition)
There is an uncountable infinity of real numbers, but only a countable infinity of algorithms to compute a number to an arbitrary precision in a finite time. Hence, there is an uncountable infinity of numbers that can not be computed.
(Math edition)
There is an uncountable infinity of real numbers, but only a countable infinity of algorithms to compute a number to an arbitrary precision in a finite time. Hence, there is an uncountable infinity of numbers that can not be computed.
#Physicsfactlet (22)
Usually you see only the upper half of a rainbow, but if you are on a plane or a tall mountain, sometimes you can see the full circle (known as a "glory halo")
Usually you see only the upper half of a rainbow, but if you are on a plane or a tall mountain, sometimes you can see the full circle (known as a "glory halo")
#Physicsfactlet (23)
Between classical correlations and entanglement, there is a huge family of correlations, known as "quantum discord", that are definitively not classical, but also not quantum enough to violate Bell's inequality.
Between classical correlations and entanglement, there is a huge family of correlations, known as "quantum discord", that are definitively not classical, but also not quantum enough to violate Bell's inequality.
#Physicsfactlet (24)
Special relativity imposes a limit on how fast information can propagate to satisfy causality, which means that wave energy velocity has to be equal or smaller than c. But both phase and group velocity can be as high as you want with no problem.
Special relativity imposes a limit on how fast information can propagate to satisfy causality, which means that wave energy velocity has to be equal or smaller than c. But both phase and group velocity can be as high as you want with no problem.
Obviously the real story of how Schrödinger arrived there is a lot less linear and full of false steps than this. For a discussion of the real story see e.g. mpiwg-berlin.mpg.de/Preprints/P437…
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