I think the coolest fact that I didn't grok until undergrad is that gravity relates to the stress-energy tensor and is not just due to rest mass alone. Which means that anything that has energy associated with it (i.e., everything we've ever observed) affects the gravitational field.
Examples: A compressed spring weighs more than the same spring in an uncompressed state. A box of light (e.g., a box with perfectly reflective mirrored walls) weighs more than the same box without light, despite the fact that photons have zero rest mass. The bulk of a proton's "effective mass" is due to the kinetic energy of the quarks that comprise it. The joint earth + moon system weighs less than if you added up each component weighed in isolation.
The other interesting fact is that the Heisenberg Uncertainty Principle is commonly misunderstood to mean that you can't simultaneously measure the position and momentum of a particle. In fact, you can indeed obtain partial information on both properties at the same time, and there's quite a few papers out there describing how to perform joint measurements of incompatible observables.
What HUP more accurately entails is that, for a quantum state corresponding to a specific system, you cannot obtain complete information about the two properties — no matter what you do. This is because performing a position measurement destroys your ability to perform a subsequent momentum measurement (on the same system) and vice versa. One of the postulates of quantum mechanics is that measuring a system collapses it into an eigenstate of the observable corresponding to the type of measurement that was performed. Since the position and momentum operators don't commute, it's not possible to put the two into a joint eigenbasis (they can't be simultaneously diagonalized).
I'll temper your statement about uncertainty. You can measure whatever you want, but if your observables are incompatible, you can't say it's still in the eigenstate you measured it in afterward each measurement. Then again, people have to explain what it means when they say "measure at the same time" means. If it means "system A is in eigenstate |1> and eigenstate |a>" where |1> and |a> are eigenstates of different (non compatible) operators the answer is no.
> I think the coolest fact that I didn't grok until undergrad is that gravity relates to the stress-energy tensor and is not just due to rest mass alone. Which means that anything that has energy associated with it (i.e., everything we've ever observed) affects the gravitational field.
And not just energy, but tension. And tension is a signed quantity!
Imagine that you go out into deep (flat) space and build a large disk out of unobtanium, an extremely strong and rigid material. The ratio of the circumference to the disk to the radius is exactly pi. Now imagine trying to bring the disk to Earth's surface. Here space is curved by gravity, so the radius of a disk is just a bit longer relative to its circumference. So the disk has to flex! If it is rigid enough, it will want to spring back into flat space to minimize energy. You could imagine adding some gearing that would let you control this (anti-)gravity effect at will.
Calculating the material strength needed to make this effect usefully strong is left as an exercise to the reader.
(Disclaimer: this makes sense to me, but I am not a licensed antigravity engineer)
Since you obviously like this sort of thing, let me point out that quantum uncertainty isn't simply a factor of measurement/observer effects[1][2]. (The only part of what you said that I am addressing by this is the "this is because" section.)
It is offered but the student must elect to take the course, it is possible to pass through an American public school system without taking any advanced topics. Someone who does not enroll in courses of at least college prep level will arrive at university and be required to take some remedial credits to catch up with their peers.
It would be more accurate to say the wormholes are hypothetical than to say that they are fictional. They are an idea someone came up with of something that might really exist, we just don't have any evidence of them.
Wormholes could potentially exist; there is even a well-known non-crackpot theory called ER=EPR that roughly suggests entangled particles are connected by wormholes.
What is fiction is wormholes you can send information or people though.
I think it’s misleading to characterise Sabine Hossenfelder’s blog as “some blogspot blog”. She is a serious and respected theoretical physicist, not some random blogger.
She's a pop-science writer. She is a random blogger. She has a job as a physicist. It doesn't make her opinion a fact, just because she's a theoretical physicist with a job and a blog.
These are commonly accepted theories. It would be like citing Darwin every time you talked about evolution–nobody does this because you can easily do this yourself if you were in the unlikely event of being unaware of the science behind it.
I like the first part, entropy is essentially a measure of degeneracy for a state (the elementary definition is the log of the number of states multiplied by a unitful constant). Technically, if you're a supposed super-intelligence, that is good at remembering detail, every state of a system can be distinguishable and thus have small entropy. For example, consider a finite number of legos in a room. A computer could potentially remember where every lego is placed, while person can't do as well but could distinguish between a state where the legos are strewn about or built into a castle. So, the person would lump all the disordered states into just one state (the "mess" state) and give it a high entropy compared to the number of organized states (castles or ships made out of the legos).
I guess I always knew this, and this is sort of what we mean when we say "high entropy" but it's kind of fun to say it out explicitly like this. Most of the others seem like conflating the strict applicability of a theory vs. it's practical limits, like that QM doesn't really mean "small" or (equivalently) high energy, it just means when you're near the Heisenberg uncertainty limit for the observations you're making, which in most cases means small.
Allow me to add another one: "Special Relativity means when you go faster, time slows down for you!"
And another (controversial may be): "In Schrodinger's cat, the cat is both dead and alive at the same time!"
> every state of a system can be distinguishable and thus have small entropy
Which corresponds quite well to the fact that the entropy of a pure state is zero (since S=−tr[ρlnρ]). Entropy is better described as a property that arises between systems.
> For example, consider a finite number of legos in a room.
This works with legos, but not subatomic particles. No matter how smart you are, you can't distinguish between two states which differ only by having two electrons swapped.
Fair. This is mainly for macroscopic systems, not fundamental particles or other species that cannot be distinguished at all, then all you can do is lump the states together and give it a degeneracy.
There are variations on this that are more problematic (which I've never seen solutions to).
1) It looks like it takes forever, to an outside observer, for anything to reach the event horizon. So if no matter appears to reach event horizons, how can they (event horizons) form in the first place (i.e. exist in our universe)?
2) While it takes forever for matter to fall in (again to outside observers), it takes finite time for black holes to evaporate via Hawking radiation. So not only do black holes would take forever to form, they seem to have to extinguish before being able to exist (again in the sense of event horizons).
I'm not a physicist, but my speculation is that Black Holes don't really exist, they're just a limit of a process that approaches but doesn't converge to a singularity, which I think is unphysical.
I'm also not a physicist but I think I can guess a plausible answer to these?
1. Because if you don't have a black hole yet then there is no event horizon to prevent you from falling in and creating one. I think the event horizon wouldn't form at exactly the same point whose crossing would finally increase density enough to create it, so this shouldn't be a problem. (Although, again, since the event horizon doesn't exist yet, I think it might still not be a problem even in that case?) I would also expect that quantum fluctuations can also inject matter into a black hole, just as they can remove matter from it.
2. Again, they wouldn't take forever to form -- see above.
I'm pretty sure black holes have been observed indirectly, so the idea that they actually don't exist would require a pretty rock solid alternative explanation!
> There are variations on this that are more problematic (which I've never seen solutions to).
Then you haven't spent much time looking at actual textbooks on GR, since all of these issues are addressed there. (Not to mention in many peer-reviewed papers in the field.)
> if no matter appears to reach event horizons, how can they (event horizons) form in the first place (i.e. exist in our universe)?
This is the same fallacy as the fallacy that nothing can actually fall into a black hole because it looks like it takes forever from the outside. Oppenheimer and Snyder published a mathematical model way back in 1939 that shows how a black hole can form in a finite time from the gravitational collapse of a massive object, as seen by an observer falling inward on the surface of the object. The collapse appears to take forever as seen by a distant observer, but this is an optical illusion caused by the effect of spacetime curvature on the paths of light rays. This has been studied for decades and is thoroughly understood.
> While it takes forever for matter to fall in (again to outside observers), it takes finite time for black holes to evaporate via Hawking radiation.
Wrong. First, if matter is falling in, the hole is gaining mass, not losing it, so it will never evaporate even though, in principle, it is emitting Hawking radiation (in practice this radiation is many, many orders of magnitude too faint to detect for any black hole we can observe).
Second, if you include quantum effects, and therefore Hawking radiation in your model, you've changed the model, and it is no longer true that a distant observer will never see anyone falling into the hole. Instead, the distant observer will see light signals emitted by objects falling through the hole's horizon at the same time the distant observer sees the hole evaporate. (At least, that is the case in the simplest model, the one Hawking used when he first published his prediction of Hawking radiation. More complicated models have been developed since, and we won't know which, if any, of them is really correct until we have an experimentally confirmed theory of quantum gravity.)
> I'm not a physicist, but my speculation is that Black Holes don't really exist, they're just a limit of a process that approaches but doesn't converge to a singularity, which I think is unphysical.
Your speculation is uninformed and wrong. It is possible that an actual black hole, with an actual event horizon, is impossible when all of the laws of physics, including the laws of quantum gravity, are taken into account. This is an open area of research. But if it turns out that actual black holes cannot exist, it won't be for any of the reasons you give.
1. Because an 'event horizon' is not a physical boundary, it's more like a boundary that separates events that we can observe and events that we will never see in this universe, ever - that is, in this universe we can't know anything about events that happen beyond this horizon.
I mean, if you're a single point this is true. The more realistic situation is you're torn apart first.
The point (and this is the main point behind SR, see my comment elsewhere in this thread) is that in your rest-frame, you are, well, at rest. In some ways, it's sort of like an extension of the classical mechanical view that the easiest frame to do physics in is an inertial frame, while in moving frames, you have to add a velocity or a non-inertial frame, you have pseudo-forces. Newton still contented that there was some universal rest frame, somewhere, out there. Einstein essentially made the "inertial frame" a general thing: the best place to do physics is the rest frame for a system, but there is no "universal rest frame" and every observer lives in their own rest frame.
Technically, in GR, space time is also flat where you are, you only notice curvature when you look across distances, so, if you're dilly-dallying in your own rest frame as you fall into a black hole, well, you notice nothing because you're in your rest frame. You already experience this in free fall (which was Einstein's insight), you're just at rest. It's just other observers accelerating with respect to you (say, people on the ground, or the ground itself) measure you as accelerating with respect to them. When you hit the ground is when you are essentially violently accelerated into the ground's frame.
Of course, it's complicated in real life, because people aren't points, and if the scale of curvature is smaller than you're body's height, well, different parts will accelerate differently from each other (say, your eyes observing your feet), so you'll be torn apart.
I, for one, thought that conservation of energy was iron clad. It turns out that "except for the expansion of the universe" proviso, it is. As a religious adherent of the conservation laws this makes me unhappy. And brings up new questions. I'll have to sleep on this one.
While it is true that a system doesn't minimize the energy of the entire system, as energy IS conserved, except apparently for a miniscule amount due to the universe expanding, it is also true that locally it often looks like minimizing energy in some sense.
If you have a vibrating spring on a table, after a while it will have stopped because it has created motions in the air and in the table, spreading out at the speed of sound in whatever material it encounters, and some of it also at the speed of light in the form of thermal radiation.
So, looking only at the spring, it is minimizing it's energy by returning to a stable quiscent state. In the same way, if we look at a sphere with radius as "the speed of light times the time from the start of the experiment", all energy can still be accounted for within that volume.
One system, several perspectives.
I think the minimization model is often used because the statistical model of entropy can be hard to explain, as it simultaneously allows complex relatively ordered systems like us humans to exist, while at the same time explains the almost complete disorder of thermal energy and how it disperses.
Thus, since the energy minimization of the local state can be used as a relatively truthful proxy, we learn that model first. With the possible bonus that it also allows one to temporarily avoiding some rather (afaict) gnarly math until you actually have the tools you need to understand it.
I don’t know if it’s always true in the context he mentions - particle physics - but I’m pretty sure it is not always true in e.g. chemical physics. Both entropy and enthalpy matter. The reaction of potassium vapor with bromine vapor is spontaneous even though the solid crystalline potassium bromide product has lower entropy than the gas phase reactants. In the comments on the article Milkshake also gives an example of an entropically driven spontaneous reaction: ammonium nitrate dissolving in water. You need enthalpic and entropic terms to predict if a reaction is thermodynamically spontaneous.
And if you want to calculate if a thermodynamically spontaneous reaction will appreciably take place, you also need to understand the actual intermediates between A + B -> C, and find reaction barrier heights for all of them, and weight them appropriately. This is still very hard to do so information of this sort is mostly determined by experiment rather than calculation.
In a closed physical system energy is conserved.
For example, if you have container that has Helium on one side and Oxygen on the other. Both gases will mix, i.e. maximize entropy.
Minimizing energy would mean, the gas would reach absolute zero.
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Examples: A compressed spring weighs more than the same spring in an uncompressed state. A box of light (e.g., a box with perfectly reflective mirrored walls) weighs more than the same box without light, despite the fact that photons have zero rest mass. The bulk of a proton's "effective mass" is due to the kinetic energy of the quarks that comprise it. The joint earth + moon system weighs less than if you added up each component weighed in isolation.
The other interesting fact is that the Heisenberg Uncertainty Principle is commonly misunderstood to mean that you can't simultaneously measure the position and momentum of a particle. In fact, you can indeed obtain partial information on both properties at the same time, and there's quite a few papers out there describing how to perform joint measurements of incompatible observables.
What HUP more accurately entails is that, for a quantum state corresponding to a specific system, you cannot obtain complete information about the two properties — no matter what you do. This is because performing a position measurement destroys your ability to perform a subsequent momentum measurement (on the same system) and vice versa. One of the postulates of quantum mechanics is that measuring a system collapses it into an eigenstate of the observable corresponding to the type of measurement that was performed. Since the position and momentum operators don't commute, it's not possible to put the two into a joint eigenbasis (they can't be simultaneously diagonalized).
And not just energy, but tension. And tension is a signed quantity!
Imagine that you go out into deep (flat) space and build a large disk out of unobtanium, an extremely strong and rigid material. The ratio of the circumference to the disk to the radius is exactly pi. Now imagine trying to bring the disk to Earth's surface. Here space is curved by gravity, so the radius of a disk is just a bit longer relative to its circumference. So the disk has to flex! If it is rigid enough, it will want to spring back into flat space to minimize energy. You could imagine adding some gearing that would let you control this (anti-)gravity effect at will.
Calculating the material strength needed to make this effect usefully strong is left as an exercise to the reader.
(Disclaimer: this makes sense to me, but I am not a licensed antigravity engineer)
[1] https://www.nature.com/news/quantum-uncertainty-not-all-in-t... [2] https://en.wikipedia.org/wiki/Uncertainty_principle
Quantum mechanics and Feynman diagrams in first year of highschool?
I did all biology and chemistry in highschool, I didn't have my first physics class until college.
Like "School of Engineering and Mathematical Sciences" etc.
It would be more accurate to say the wormholes are hypothetical than to say that they are fictional. They are an idea someone came up with of something that might really exist, we just don't have any evidence of them.
What is fiction is wormholes you can send information or people though.
"Aspects of theoretical physics not always taught in school" would be more appropriate.
I guess I always knew this, and this is sort of what we mean when we say "high entropy" but it's kind of fun to say it out explicitly like this. Most of the others seem like conflating the strict applicability of a theory vs. it's practical limits, like that QM doesn't really mean "small" or (equivalently) high energy, it just means when you're near the Heisenberg uncertainty limit for the observations you're making, which in most cases means small.
Allow me to add another one: "Special Relativity means when you go faster, time slows down for you!"
And another (controversial may be): "In Schrodinger's cat, the cat is both dead and alive at the same time!"
A macroscopic state is not a physical object. The same microscopic state may correspond to different macroscopic states for different observers.
Which corresponds quite well to the fact that the entropy of a pure state is zero (since S=−tr[ρlnρ]). Entropy is better described as a property that arises between systems.
This works with legos, but not subatomic particles. No matter how smart you are, you can't distinguish between two states which differ only by having two electrons swapped.
This one is really interesting! I've definitely never seen anyone emphasize this before.
1) It looks like it takes forever, to an outside observer, for anything to reach the event horizon. So if no matter appears to reach event horizons, how can they (event horizons) form in the first place (i.e. exist in our universe)?
2) While it takes forever for matter to fall in (again to outside observers), it takes finite time for black holes to evaporate via Hawking radiation. So not only do black holes would take forever to form, they seem to have to extinguish before being able to exist (again in the sense of event horizons).
I'm not a physicist, but my speculation is that Black Holes don't really exist, they're just a limit of a process that approaches but doesn't converge to a singularity, which I think is unphysical.
1. Because if you don't have a black hole yet then there is no event horizon to prevent you from falling in and creating one. I think the event horizon wouldn't form at exactly the same point whose crossing would finally increase density enough to create it, so this shouldn't be a problem. (Although, again, since the event horizon doesn't exist yet, I think it might still not be a problem even in that case?) I would also expect that quantum fluctuations can also inject matter into a black hole, just as they can remove matter from it.
2. Again, they wouldn't take forever to form -- see above.
I'm pretty sure black holes have been observed indirectly, so the idea that they actually don't exist would require a pretty rock solid alternative explanation!
Then you haven't spent much time looking at actual textbooks on GR, since all of these issues are addressed there. (Not to mention in many peer-reviewed papers in the field.)
> if no matter appears to reach event horizons, how can they (event horizons) form in the first place (i.e. exist in our universe)?
This is the same fallacy as the fallacy that nothing can actually fall into a black hole because it looks like it takes forever from the outside. Oppenheimer and Snyder published a mathematical model way back in 1939 that shows how a black hole can form in a finite time from the gravitational collapse of a massive object, as seen by an observer falling inward on the surface of the object. The collapse appears to take forever as seen by a distant observer, but this is an optical illusion caused by the effect of spacetime curvature on the paths of light rays. This has been studied for decades and is thoroughly understood.
> While it takes forever for matter to fall in (again to outside observers), it takes finite time for black holes to evaporate via Hawking radiation.
Wrong. First, if matter is falling in, the hole is gaining mass, not losing it, so it will never evaporate even though, in principle, it is emitting Hawking radiation (in practice this radiation is many, many orders of magnitude too faint to detect for any black hole we can observe).
Second, if you include quantum effects, and therefore Hawking radiation in your model, you've changed the model, and it is no longer true that a distant observer will never see anyone falling into the hole. Instead, the distant observer will see light signals emitted by objects falling through the hole's horizon at the same time the distant observer sees the hole evaporate. (At least, that is the case in the simplest model, the one Hawking used when he first published his prediction of Hawking radiation. More complicated models have been developed since, and we won't know which, if any, of them is really correct until we have an experimentally confirmed theory of quantum gravity.)
> I'm not a physicist, but my speculation is that Black Holes don't really exist, they're just a limit of a process that approaches but doesn't converge to a singularity, which I think is unphysical.
Your speculation is uninformed and wrong. It is possible that an actual black hole, with an actual event horizon, is impossible when all of the laws of physics, including the laws of quantum gravity, are taken into account. This is an open area of research. But if it turns out that actual black holes cannot exist, it won't be for any of the reasons you give.
The point (and this is the main point behind SR, see my comment elsewhere in this thread) is that in your rest-frame, you are, well, at rest. In some ways, it's sort of like an extension of the classical mechanical view that the easiest frame to do physics in is an inertial frame, while in moving frames, you have to add a velocity or a non-inertial frame, you have pseudo-forces. Newton still contented that there was some universal rest frame, somewhere, out there. Einstein essentially made the "inertial frame" a general thing: the best place to do physics is the rest frame for a system, but there is no "universal rest frame" and every observer lives in their own rest frame.
Technically, in GR, space time is also flat where you are, you only notice curvature when you look across distances, so, if you're dilly-dallying in your own rest frame as you fall into a black hole, well, you notice nothing because you're in your rest frame. You already experience this in free fall (which was Einstein's insight), you're just at rest. It's just other observers accelerating with respect to you (say, people on the ground, or the ground itself) measure you as accelerating with respect to them. When you hit the ground is when you are essentially violently accelerated into the ground's frame.
Of course, it's complicated in real life, because people aren't points, and if the scale of curvature is smaller than you're body's height, well, different parts will accelerate differently from each other (say, your eyes observing your feet), so you'll be torn apart.
Very interesting, I feel somewhat misled if this is true.
While it is true that a system doesn't minimize the energy of the entire system, as energy IS conserved, except apparently for a miniscule amount due to the universe expanding, it is also true that locally it often looks like minimizing energy in some sense.
If you have a vibrating spring on a table, after a while it will have stopped because it has created motions in the air and in the table, spreading out at the speed of sound in whatever material it encounters, and some of it also at the speed of light in the form of thermal radiation.
So, looking only at the spring, it is minimizing it's energy by returning to a stable quiscent state. In the same way, if we look at a sphere with radius as "the speed of light times the time from the start of the experiment", all energy can still be accounted for within that volume.
One system, several perspectives.
I think the minimization model is often used because the statistical model of entropy can be hard to explain, as it simultaneously allows complex relatively ordered systems like us humans to exist, while at the same time explains the almost complete disorder of thermal energy and how it disperses.
Thus, since the energy minimization of the local state can be used as a relatively truthful proxy, we learn that model first. With the possible bonus that it also allows one to temporarily avoiding some rather (afaict) gnarly math until you actually have the tools you need to understand it.
And if you want to calculate if a thermodynamically spontaneous reaction will appreciably take place, you also need to understand the actual intermediates between A + B -> C, and find reaction barrier heights for all of them, and weight them appropriately. This is still very hard to do so information of this sort is mostly determined by experiment rather than calculation.
https://en.wikipedia.org/wiki/Minimum_total_potential_energy...
https://en.wikipedia.org/wiki/Principle_of_minimum_energy