General Physics Thread

You know, I was expecting an inactive black hole to be a lot simpler than that.

It's much smaller than M87, so the gas of its accretion disc takes much less time to orbit it. This makes imaging it with radio interferometry a lot more challenging.

I'm watching the presentation. What is most remarkable about the image is that it exactly matches the predictions of general relativity. It's yet another triumphant validation of Einstein's theory and, even more importantly, a rejection of countering ideas.

Edited by Fighteer on May 12th 2022 at 9:29:30 AM

Black hole sun, won't you come? And wash away the rain~

Ok, joking aside, that's a pretty impressive image right there, I certainly didn't expect activity to be that visible.

I don't think it is. That's not like, light. That's a calculated image based on radiation patterns, I think? It's not a photo you can take with just a camera and a big ol telescope.

It is light, just not visible light. What we're measuring is radio emissions from the accretion disc. Infrared, visible, and ultraviolet light, which the disc is also emitting, is blocked by the gas and dust between us and the galactic center. We can also examine it in x-ray light, but with much lower resolution.

I had for some time in mind to explain the behaviours of superconductors, superfluids, white dwarfs and neutron stars using first-order quantum physics, so here goes nothing. Read from top to bottom as you need to rely on concepts laid out in previous sections:

Fermi-Dirac and Bose-Einstein statistics

In quantum mechanics, identical particles are present in different states, whereby a state is (roughly) a combination of a given particle's energy, location and other properties. A given state can (not: "will") host g/(x+e^((E-m)/(k*T))) particles; here e is the Euler constant, E is the state's energy in joules, m is the chemical potential^note Non-thermal energy of a particle that can be expended to occupy a state; unlike E this one's just an energy also in joules, T is temperature in kelvin, k is the Boltzmann constant and g is the so-called degeneracy of an energy level, that is the number of states with identical energy level.

x can be either +1 or -1, depending on the property of particles known as spin. According to the spin-statistic theorem, particles with half-integer spin have x=+1 and those with integer spin x=-1. We call the former fermions and the formula with x=+1 Fermi-Dirac statistic while the latter are called bosons and the formula with x=-1 Bose-Einstein statistic.

Most of the physically important particles (electrons, quarks, neutrinos, protons etc.) are fermions, while photons etc. are bosons. Compound particles like atomic nuclei can be either fermion or boson depending on the sum of the spins of the individual components. For example, the spin of the nucleus helium-4 is a sum of 4 and thus integer; hence it is a boson.

Two important notes:

1. In the case of bosons, E-m is always non-negative but can be 0. If m is greater than E then that means the particle will "overshoot" and go to a state with different value of E so that E-m remains non-negative.
2. The formula describes the capacity of each state; the actual amount of particles in a given state depends on the "distance" between particles' states (see below)
3. When you are discussing low particle densities or high temperatures, the capacity of a given state is small (since particles have to occupy a lot of energy levels to store the entire thermal energy) and that implies that the exponent in the denominator is much larger than 1. Thus you can disregard the 1 in the denominator of either the Fermi-Dirac or Bose-Einstein statistic and simply divide the degeneracy through the exponent: Boltzmann statistic which is important in a number of quantum or classical settings.

De Broglie wavelength and indistinguishable particles

Now as it's well-known, quantum objects are subject to the so-called wave-particle duality that is they can be described both as particles and as waves, whereby the "wave" is the probability to find a particle there. When we aren't talking of relativistic energies, this wavelength is the Planck constant divided through the momentum of the particle.

When the particles' mutual distances are less than the wavelengths, they begin to overlap and thus become indistinguishable (but see below). This is possible at very high pressures (which reduce distances) or very low temperatures (which decrease momentum and thus increase wavelengths)

For fermions: Pauli principle and degeneracy pressure

As one can see from above, since we aren't dealing with imaginary values of energy, exponents of e are always positive and thus the maximum number of fermions that can occupy a given state is identical with the degeneracy of said state (the denominator in the Fermi-Dirac statistic is always at least 1). This is what we call the Pauli principle.

What does that mean for fermionic matter under very high pressures, such as electrons in white dwarf stars and neutrons in neutron stars? Well, as the gravity pressure forces the particles to approach each other closer than the De Broglie wavelength, the Pauli principle means that they cannot actually occupy the same state. Rather, one of the electrons/neutrons gains some energy so that it can occupy a state with identical "location" but different "energy". This means that work has to be performed to squeeze them together, and vice versa that if they are allowed to relax they tend to move apart and can perform work. Mathematically, this is equivalent to a pressure, the degeneracy pressure, which opposes the gravitational pressure and prevents it from collapsing the body.

The particle does not necessarily stay the same as it rises in energy levels; electrons can become muons if they have enough energy, neutrons turn into hyperons or quark blobs. In fact, the neutrons are formed from protons through inverse beta decay; the energy consumed by this reaction is so small that this process happens before proton degeneracy can become relevant. The considerations here don't care about this.

Note that while I am discussing white dwarfs and neutron stars, electrons in everyday metals such as kitchen utensils also have a notable degeneracy pressure, which strongly influences the property of metals.

Relativistic corrections to degeneracy pressure: Chandrasekhar and Tolman-Oppenheimer-Volkoff mass limits

The above assumes that we aren't talking about relativistic systems. In reality, as the mass of the white dwarf and neutron star and thus its gravitational pressure increase, electrons/neutrons are occupying higher and higher energy levels. At some point, these energies become comparable to the rest mass of the electrons/neutrons and thus relativistic mass increase begins to matter. It disproportionally increases the momentum and thus decreases the wavelength and that in turn slows the increase of the degeneracy pressure. Eventually, at a certain mass of the star gravity can match degeneracy pressure and force the collapse of the star; thus such stars cannot exceed this limiting mass if they are supported solely by degeneracy pressure.

For bodies sustained by the degeneracy pressure of electrons, this mass is the Chandrasekhar mass and is about 1.4 solar masses for bodies with an even amount of neutrons and protons. For bodies sustained by the degeneracy pressure of neutrons, we call it the Tolman-Oppenheimer-Volkoff mass but the strong/nuclear force between neutrons is considerably stronger than the electromagnetic and weak forces between electrons and thus it adds to the degeneracy pressure. It is probably in the space of 2 or 3 solar masses but strongly depends on the exact properties of matter this dense.

Bosons: Superfluidity and friends

Bosons are not subject to the Pauli principle since the denominator can become arbitrarily small for physical values of E, mu and T; thus at low enough temperatures and high enough densities (when the inter-particle distance is smaller than the De Broglie wavelength, which at a given pressure happens at a given temperature), all particles can overlap - that is, become part of the same state - and become indistinguishable. We call this a Bose-Einstein condensate.

The most important property of such a condensate is that since its constituent particles aren't distinguishable, it cannot behave like a cloud of particles. Thus for example it cannot experience drag when it's fluid (superfluidity), electric resistance if it's fluid and electrically charged (superconductivity) or undergo particle-derived physical or chemical processes such as absorbing or expelling heat (it loses its heat capacity).

In practice, helium-4 at very low temperatures is the most important compound with these properties.

From fermions to bosons: Spin and Cooper pairs

The processes above cannot occur for fermions because the Pauli principle disallows the formation of indistinguishable states. There is a loophole, though: Two identical fermions with spins of a different sign can occupy the same state if there is some kind of attractive force between the fermions; this generates a couple called a Cooper pair that behaves like a boson.

You see, just like a clock turns counterclockwise when seen from behind but clockwise when seen from the front, the sign of a particle's spin depends on the frame of reference and thus isn't an intrinsic property. And since a particle with no spin isn't a fermion (0 is an integer), any fermion can exist in both states and thus each energy level has a degeneracy of 2.

In metals, electromagnetic interactions between electrons and metal atoms can generate electric fields which draw atoms to an electron, and further electrons to these atoms. These fields are the attractive force that triggers the formation of Cooper pairs of electrons. However, in a metal above the superconductor temperature the atoms move themselves and tend to shatter the Cooper pairs, thus the metal needs to be cold enough. Physically, the temperatures at which Cooper pairs break apart are considerably lower than these required to make them evaporate; thus Cooper pairs form Bose-Einstein condensates by default.

A metal where the electrons have formed Cooper pairs is a superconductor, since these Cooper pairs are a Bose-Einstein condensate and thus don't display particle-like properties; without these properties electric resistance does not exist.

Edited by SeptimusHeap on Sep 4th 2022 at 3:56:32 PM

Welp, this is a pretty long term necro, but I think this question is relevant and productive enough to warrant that.

So, recently I've been very interested and fascinated by science in general. I initially was interested in astronomy, but that required strong basis on physics, and that in turn also required mathematical knowledge.

That brought me to learn just enough math so I can use it as a base for other scientific fields, both natural and social, with special emphasis on physics. Now, the question is, what kind of math is essential to actually understand (undergraduate level of) physics?

From google search and reading up on mathematical literature, I know that I need to learn at the very least algebra, geometry & trigonometry, calculus^note  Apparently different branches and level of physics require specific subsets of calculus, but I will just say calculus broadly for the sake of (mostly my) convenience, and also bits of statistics & probability.

Would that be enough or are there additional fields that I might have to learn?

Edited by dRoy on Apr 12th 2023 at 9:37:05 PM

For undergrad freshman level physics, calculus, trigonometry, and (high-school level) geometry and algebra would be sufficient. If you want to learn about as much as mechanical/aerospace/electrical engineers, add vector calculus, differential equations, and linear algebra. For more advanced physics, you might need more advanced math and probability theory/statistics.

Ayyy, thank you kindly!

linear algebra

Oh man.

It's amusing because I actually found a linear algebra college textbook in my house during house cleaning.

It's clearly a destiny!

Edited by dRoy on Apr 12th 2023 at 10:37:54 PM

I feel you on loving the concepts in Physics but being super intimidated by the Math.

Like whenever my old highschool physics class had discussions, I was the guy asking questions about the concepts.

Then when the math stuff hit, I lost interest.

My teacher always said I had a lot of potential energy I never use. Ha.

That tangentially reminds me of this YT vid and one hilarious comment:

Sorry, I'm just having a minor breakdown at losing my last years in highschool due to COVID.

I'll just lie down. All the Physics discussion gave me high school flashbacks.

EDIT: Okay, I'm feeling better.

Edited by RedHunter543 on Apr 12th 2023 at 10:31:21 PM

Quoting a passing aside in another thread because now that I remember this joke it demands spreading.

Refraction conserves n times the sine of the theta
If the n gets lower then the theta will get greater
If the n gets greater, then the light will get there later
Hey, n sin(θ)!

So, I just finished Infinite Powers: How Calculus Reveals the Secrets of the Universe, by Steven Strogatz.

I never thought I would ever buy AND finish reading a book very specifically about calculus. But hey, I need to know this if I want to actually understand physics.

On one hand, finishing this book made me realize just how little I know about geometry and how important it was in the history of both math and physics.

On the other hand, holy shit, I have a deeper understanding on the subject and I can see why this is so fundamental to physics.

Also, it's really morbidly ironic how Isaac Newton, co-creator of calculus, died from...urinatry tract calculi.

This is for a fictional concept, but I wish to know what terms exist in the field of physics that could be used to describe it.

Imagine that you have a planet. There's a huge mountain somewhere on it, at whose base you will find a natural tunnel. When you look through the tunnel, you find that it opens up to the other side of the mountain... except that you've already looked at the other side of the mountain, and you found nothing but solid rock!

You walk through the tunnel, and once you exit, you find that not only is the terrain on the other side looks very different from what should be there based on your previous exploration, the mountain side that you're looking at looks different from that which you've previously seen.

Then your radio bursts into life, with your colleagues in the spaceship high in orbit panickedly asking where you are; turns out that your radio tracking signal started to go inceasingly spotty the further you went through the tunnel, until it fizzled out entirely by the time you exited through the other side. Then you notice that there's other radio traffic, and once you tune in you manage to connect to another spaceship in orbit; long story short, you are being told that you are on a wholly different planet that's on the other side of the galaxy!

Later investigation then reveals that what you're perceiving as "two planets" are actually a single contiguous planet that seems to have "punched" through spacetime so that it exists in two different locations at the same time!

So... How would you concisely describe this in a scientific manner that isn't too complicated?

The planet's wedged halfway into a wormhole. That'd basically cover it.

Edited by Zendervai on May 17th 2023 at 12:34:14 PM

I believe folks call that a topological defect. That word also means we don't need to justify an unusual gravity in the tunnel.

Topological defect, you say? I suppose descriptions like "warped topology" also work?

Also, how would you describe the fact that the planet appears to outside observes to be physically discontinuous, giving the false impression that it's two different planets? Would you say that the planet exhibits a form of multipresence?

"Warped" is a problem- warped spacetime features intense gravitational fields. Hence "topological defects" instead.

The article does use "topological soliton" as an alternate name, which sounds more neutral. What does "soliton" mean in this context?

Also, would such a phenomenon imply that there's a fourth spatial dimension involved?

Soliton, but it's a wave so it has the same gravity issue. I don't think that a fourth spatial dimension is implicit in the existence of a topological effect.

Damn. Is there any alternative to "defect" that is more or less neutral-sounding?

So I just found and bought a copy of Classical Mechanics: The Theoretical Minimum, by Leonard Susskind ^note  Professor of theoretical physics at Stanford University and founding director of the Stanford Institute for Theoretical Physics from my local used bookstore.

...It happened to be a mistake because even this minimum was far too complicated for my level. Like, Jesus, nearly half of the whole book is nothing but math equations.

I guess I gotta get my math level up more.

A bit of Googling shows that there are a series of free lecture videos by the author. I don't know if they'll help. Looking at the table of contents, maybe the author overestimated the knowledge of the general public. Though, it does seem interesting to people in STEM but not pure physics. I guess I should give the videos a try; Hamiltonian mechanics was very difficult to understand when I saw it in class, so I wonder if the videos explain it in a more intuitive way.

Edited by minseok42 on Aug 28th 2023 at 9:41:58 AM

-looks at the list -

Aaaaaaand of course it includes quantum physics.

One of the most devastating revelations I had about physics is that apparently quantum physics IS pretty much the modern physics.

Honestly, I'm still on the level of scientific literacy where the very word "quantum" scares me. And I don't think I will ever grow beyond that point.