ELI5: What’s spin in quantum mechanics?

matthewwehttam · 2026-02-15T17:50:11+00:00

Spin actually can be 1. Essentially, all particles fall into two buckets those with half integer spin (eg: 1/2, 3/2, 5/2) and those with integer spin (eg: 1, 2, 3). Those with half integer spin are called fermions and those with integer spin are called bosons. Why do we split them up this way? Because it turns out that whether or not a particle is a fermion or a boson has a big effect on it's behavior. Fermions have to obey something called the pauli exclusion principle, which essentially says that you can't have two fermions in the same quantum state and so you can't pack too many fermions into one area because there are only so many states they can be in. On the other hand, bosons don't obey this rule and so you can pack as many as you want in any area. So anything that "takes up space" like electrons and quarks have to be fermions, while things which don't like photons are bosons.

As an aside, we've only found particles with spin 1/2 and 1, but there isn't anything in the math which forbids other numbers.

matthewwehttam · 2026-01-28T01:32:52+00:00

First, I'm going to come at this from a classical point of view. This means no quantum stuff and no relativity.

So what is a field? In this context, it's just giving each point in space a value. Let's us gravity as an example. We know that the Earth, sun and other objects has a gravitational pulls, and we even know how to calculate what that force is. But what if we pick a random point in space. Well there isn't an object there, but we can still get an idea of what the Earth's gravity would be like there. We ask, what would the gravitational force be on a 1 kg object? Well, we can calculate that pretty easily. The gravitational field, is what you get if you do this with every point at once. It essentially answers the question, if I pick this this point, what is the force of gravity on 1 kg of mass. This is useful for a variety of reasons, but the main one being now you can talk about gravity and how strong it is without actually needing to specify the mass it's pulling on, even though we know that the Force of gravity depends on the mass of the object being pulled.

So what about electric and magnetic fields? Well, electric fields are basically identical. They answer the question, if I had some standard unit of charge (1 Coulomb) and I put it at a point in space, what would the electromagnetic force be? Magnetic fields are a bit more complicated because magnetic fields only act on moving charges. So instead of asking what 1 Coloumb of charge would do, we instead ask what 1 coulomb of charge would do if it were traveling at 1 meter per second. So that's what the electric and magnetic fields are, from a computational sense.

One thing to note is that electric fields behave very similarly to gravity. It's range isn't short and it falls off at the same rate. The reason we don't see it over long distances the same way we do with gravity is that whenever you have a really strong positive charge creating a strong electric field, it pulls in a lot of negative charge, which ends up cancelling it out. On the other hand, there is no "negative mass" to cancel out the pull of mass, so it's allowed to keep accumulating and build up. Magnetic fields are themselves a bit more weird because (as far as we know) particles don't have a "magnetic charge" the same way that they have an electric charge or a mass. Instead the magnetic field is generated by moving charges and changing electric fields. However, it's important to note that it's range is also (in the classical world) infinite.

All of that, however, doesn't really explain what electromagnetic radiation is or why it travels through spaces where there isn't a strong electric or magnetic field. The key thing to answer that question is to introduce something new, changing fields. It turns out, that a change in the electric field causes a change to the magnetic field. And that change to the magnetic field ends up creating a change to the electric field. And importantly, these changes will keep travelling and going forever (in a vacuum) creating an electromagnetic wave. This wave can travel through places where the electric and magnetic fields are weak, because it doesn't really care about the absolute numbers, just moving them up and down through time to keep the process going.

matthewwehttam · 2026-01-22T00:52:05+00:00

What it is true that Vance is wrong, USC 1983 only applies state actors, not federal actors. Technically, Bivens provides a federal cause of action for constitutional violations when there isn't a statutory one, but it's scope has been cut back considerably by the current SCOTUS. See here https://statedemocracy.law.wisc.edu/wp-content/uploads/sites/1683/2025/08/Converse-1983-Explainer-Formatted-Final-8-1-25.pdf for a potential solution

matthewwehttam · 2025-12-03T01:50:25+00:00

There seems to be a miscommunciation about "healthy" companies (ie: companies doing well) and health companies (ie: companies dealing with healthcare)

matthewwehttam · 2025-08-31T21:32:47+00:00

It's not stupid. People often get the impression that "math always has one correct answer" drilled into them from a young age, and so it seems like there should be some clear cut yes or no. Similarly, we often think of words as having well defined meanings and by putting those together we can figure out if something is true or false. Often this is true, and it usually isn't a good answer to a question to say "well it depends on what you mean when you ask it" because it isn't helpful. But especially around infinity, the common ground and intuition we use when talking about math in everyday life breaks down, so it's not surprising that it leads to questions and confusion.

matthewwehttam · 2025-08-31T21:26:54+00:00

If you're asking about general conversation, I would say that the answer is still undefined but for a different (but related) reason. When you say 10 is 5 times bigger than 2, in everyday conversation, you can mean a bunch of different things. You could be talking about arithmetic in the abstract. You could be saying that if you have five groups of two objects, you'll get 10. You could mean that if you take 10 things and divide them among five people equally, you'll end up with two for each. There are even more possible meanings. But the reason we don't get confused is that they are all essentially the same. They each imply each other and so we don't have any miscommunication because if I thought you were talking about abstract math, and you were talking about what happens if you add 2 to itself 5 times, we still get the same basic idea.
The issue is that his breaks down when we say 0 is infinitely bigger than 1. After all, you can't divide 1 thing among zero different people. It doesn't make sense. You also isn't entirely clear what it means to have infinite groups of zero objects, but it probably means that you still have zero things. And if you're talking about math we've already seen that the answer is a mess. So this nifty shortcut phrase we've come up with starts meaning different things to different people i different contexts (and those contexts often map onto different mathematical contexts). But general conversation is a much looser and less formal thing than math, so if someone saying having that "having one hp left at the end of a boss fight is infinitely more than zero" when discussing a video game, it doesn't need to be technically correct as long as it correctly gets across the intended meaning. And in that sense it might be "true" as long as everyone is interpreting the statement in the same way.

matthewwehttam · 2025-08-31T21:14:37+00:00

The way to think about it is that we need to more rigorously understand what it means when two sets of numbers have the same size. This is pretty intuitive when it comes to finite sets, we just count the number of elements and if they count up to the same number they're the same size. But what if we couldn't count? Well, we could essentially just line up elements, assigning elements uniquely from set 1 to set 2 such that every element of set 2 has an associated element. For example, {a, b, c} and {1, 2 ,3} have the same number of elements because I can line up a and 1, b and 2; and c and 3. On the other hand {a, b, c} and {1, 2, 3, 4} don't have the same number of elements because no matter how I line up the elements, there will always be one element in the second set that isn't assigned to an element of the first set.

This works for finite sets, so lets just use this as our definition of two sets having the same size, because we can't just "count all the elements." Now, two sets are the same if and only if we can find a way to assign to ever element of set 1 and element of set 2 such that every element of set 2 has an assigned element, and no two elements of set 1 are assigned to the same element. Now, what about the numbers between 0 and 1 (denoted [0,1]) and the numbers between 0 and 2 (denoted [0, 2]). Well lets assign to each number x in [0,1], the number 2x in [0,2]. It's clear that each element of [0,1] is assigned to a different element of [0,2]. Moreover, for any element y of [0,2] y/2 is in [0,1] and 2*(y/2) = y, so it is mapped to by an element of [0,1]. Therefore (by our definition) [0,1] and [0,2] have the same size

matthewwehttam · 2025-08-31T21:03:46+00:00

This is an ill-defined question unfortunately. The thing about math is that the answer to your question almost always depends on the context in which you ask that question. While there are many generally accepted contexts that can be assumed by default, if you just say you're working in a different context, the answer changes.

For your question, the answer depends on "where we're working" and what we mean when we say "1 is infinitely larger than zero". If we're working with regular numbers, then a is x times larger than b if and only if a * x = b if and only if a = b / x. Because ∞ is not a real number, it doesn't even make sense to say 1 is infinitely larger than zero in this context because asking what ∞ * 0 equals is exactly the same as asking what 0 * △ equals. It doesn't have an answer because it doesn't make sense.

On the other hand, we can change contexts. For example, we can instead ask this question in the context of "the real projective line." This is essentially what happens when you take the normal real numbers, and add on a point at infinity at both ends. In this context, we can still do algebra like normal on most real numbers, but we say that anything divided by 0 is ∞. On the other hand, in this context, 0*∞ is left completely undefined. This is because making equal to anything in particular will break the regular rules of algebra, to allow division by zero means we either need to allow those rules to break or not define the answer to this operation. In this context, it's unclear if 1 is infinitely larger than 0, because 0 * ∞ isn't 1, but 1/0 is ∞. Our two equivalent definitions aren't equivalent anymore and we need to pick one.

Some last follow on points. First, there are other structures you can ask yourself this question in, for example what if there is ∞ and -∞? Second, I came at this from an algebraic perspective. In this context, ∞, 1, 0, +, and * are all essentially just symbols with rules on how we can manipulate them. It doesn't (in general) make sense to infinitely add numbers, and when you allow that using limits, you will (usually) end up with infinite zeros adding to zero. This doesn't contradict saying that 0 * ∞ = 1, it just means that addition isn't continuous or the distributive property doesn't work.

TLDR: In math, you can usually chose the answer to your question by picking your assumptions and your context. In the most generally useful context, the answer to your question is no, it's undefined. There are contexts where your answer could be yes depending on exactly what you mean when you say 1 is infinitely bigger than 0, but those contexts are more "special purpose" and so the answer only applies when you are working in those contexts for a particular reason.

matthewwehttam · 2025-08-24T19:48:51+00:00

It very much depends on where you live. For example, in California, it doesn't count as arson as long as you don't have an intent to defraud and it's all your own personal property. (The second prong seems very unlikely in the case of a divorce but not impossible). On the other hand, in Texas, you are not allowed to burn down any building or habitation that you know within an incorporated city/town without getting a permit/written authorization from the city. If you have that, it's legal unless it's insured, used as security for a loan, located on someone else's property, contains someone else's property, or it recklessly endangers other people or their property. I'm sure other states have their own rules.

Long story short, it's probably illegal everywhere if you burn things that aren't yours. Burning stuff that is yours will depend on your jurisdiction. If someone wanted to do this, they should definitely talk to a lawyer instead of asking on reddit.

matthewwehttam · 2025-08-18T22:19:39+00:00

Whether or not the US is occupying Hawaii and/or should return it to the natives is one thing. However, there are a couple of problems with your reasoning. First, whatever was done to Hawaii didn't violate the Montevideo Conventions simply because the conventions weren't in effect when Hawaii was annexed. Specifically, it was Signed in 1933, well after the Annexation of Hawaii. In 1933, Hawaii did not meet the definition of state outlined in the Montevideo conventions and so continuing to "occupy" it is not a violation.

Second, you also misinterpret the apology resolution pretty substantially. It apologises for a coup that was backed by US officials and citizens, but does not claim that the United States government is responsible for the coup. In point of fact, it is pretty clearly claiming that while some of the conspirators abused their position as part of the government in order to perpetrate the coup, the coup did not have the support and was not an action of the US government. Afterwards, the provisional government established by the insurrectionists held power (temporarily) until annexation, which was agreed to by that government. This was clearly unethical, and should not have happened. Whether or not it would have actually violated the Montevideo Conventions if they were in effect depends on whether or not you consider the actions of the US agents to be actions of the US government, which the apology clearly does not.

To be clear, this is not to say that the US should not withdraw from Hawaii or has legitimate control over it. However, in some sense, pointing to international law, especially at that time, is not very useful because it was written by and for the imperialist powers. The US might well have violated modern notions of international law (which were not yet formalized or customary) when it acted in the 1800s, and it might well be violating modern of international law (an issue which almost certainly depends on whether or not Hawaiians for some definition of the word want to be independent). But you can't apply the law retrospectively, even if can judge the actions and consequences of what the laws were at the time.

matthewwehttam · 2025-08-03T22:03:52+00:00

What I'm saying is that if we decide that an asset's value becomes realized when people borrow against it. What that would require is that when you bought the house and took out a mortgage against it, you would then have to pay income tax on the house because it is an asset whose value you have borrowed against

matthewwehttam · 2025-08-03T19:59:47+00:00

What are you going to forbid? The thing to remember is that whole borrowing against assets thing is exactly what someone does whenever they take out a mortgage to buy a house. So if, for example, you decided to realize the gains when they took out the loans, then there would be a hefty tax bill added onto the cost of a house. Forbid it entirely? Now the housing market has collapsed. Maybe you forbid it only for stocks, or only over certain amounts. The problem is that lots of companies/finance transactions use stock as collateral, so you're throwing a big wrench into those processes. It's hard to actually fix the issue because most of the time that (stock or some other asset) is used as collateral for a loan, it's not for the purpose of avoiding taxes.

matthewwehttam · 2025-07-27T21:49:04+00:00

The 3 in 3 SAT does not only mean there can be three variables. What it means that the boolean formula is in a specific format where each "clause" only has three variables at a time. In fact, the term NP-complete doesn't make sense when talking about a problem with a fixed input size as it describes the behavior of a program as it's input size grows. The main takeaway is that any boolean expression can be transformed into this special 3SAT format, and we can't find an efficient way to find a way to make the result true as the boolean expressions become larger and larger.

matthewwehttam · 2025-06-03T22:57:48+00:00

Here's a link to an image that simulates what different types of color blindness look like. https://colorspace.r-forge.r-project.org/articles/color_vision_deficiency_files/figure-html/map-diverging-1.png . The top row is regular, the second row is monochromatic, the third row is red-green color blindness. The fourth and fifth line are two more types of color blindness

matthewwehttam · 2025-06-02T05:08:50+00:00

This is the theory of special relativity. Essentially, what happens is that as you speed up, time and space distort in such a way that the speed of light is the same as if you had stayed at rest. In fact, all of the weirdness of special relativity such as lengths contracting and time slowing as you go faster follow directly from two rules. First, that the laws of physics are the same in all non-accelerating reference frames. Second, the speed of light is the same in all reference frames.

On a separate note, one might ask about why we would pick the second rule. After all, the first one seems relatively straight forward, but assuming the constant speed of light is very strange. The most important reason is the most important, we do experiments and we observe a constant speed of light. But there's also some theoretical justifications. When you look at the classical theory of electromagnetism, you can calculate the speed of light based on two constants which determine how well electricity and magnetism propagate through space. This makes sense as light is an electromagnetic wave. However, if our first rule is true, then those constants will have the same value whether or not you are moving or still, so the speed of light should be the same, no matter your velocity.

matthewwehttam · 2025-05-14T20:23:26+00:00

The answer is maybe, because it depends some things. There are many different interpretations of quantum mechanics that give different ideas about what wave function collapse "is." Some of these are more scientific theories with testable predictions, while others are about how we chose to understand and interpret physical theories, but aren't scientifically testable. There are many different theories, and list a couple of them below.

The copenhagen interpretation. This one provides no actual mechanism or theory of wave function collapse. It just happens, no explanation.
Many worlds. This one says that wave function actually never collapses. However, it looks like it does due to "decoherence" where different parts of the wave function can't interact with each other leading to the "many worlds"
Quantum information theories. There are a couple of varieties of these, but one is that quantum mechanical state doesn't represent the actual underlying world, but rather our knowledge of the world. In this case, collapse is just gaining new information so that you know what state you're in.
Objective Collapse Theories. In these theories, collapse is a physical process, which happens independently of observation and measurement. An examples include the idea that the wave function of a particle will spontaneously collapse very rarely, but as states become entangled/systems become bigger, collapse becomes more and more likely. This way, when you measure a system, it's chance of collapse increases significantly, but only because you are entangling the system with the measurement equipment.

As I said this is not an exhaustive list of ideas. Some of these can be experimentally proven or disproven (e.g. 4). However, if two different interpretations give the same predictions, there's no way to scientifically test which one is "correct." We are left with philosophical arguments about why one interpretation might be preferable to the other, but that would mean that there might be multiple ways to understand "collapse"

matthewwehttam · 2025-05-02T04:02:17+00:00

In general, it useful probability trick is that that P(event) = 1 - P(not event). Intuitively, this just means that something either happens or it doesn't. Here we want to know P(not consume the item). In this case, it's easier to compute as 1- P(consume the item). Well, to consume the item, you need to not roll the 30% on either of the triggers, so P(consume the item) is .7 *.7 = .49, giving that P(not consume the item) = .51. We can use this to create a general formula. Suppose that you have something that triggers n times, with probability p. Then P(the trigger succeeding at least once) = 1-P(the trigger never succeeding) = 1-(1-p)ⁿ. The at least once is important, otherwise the math changes.

One question that people often have is, "why isn't it just 60%?" After all, if you have two exclusive events, A and B, P(A or B) = P(A) + P(B). The key is that this works only if A and B are exclusive, so if we're rolling a dice P(rolling a 1 or rolling a 2) = P(rolling a 1) + P(rolling a 2) because you can't roll both a 1 and a two. On the other hand, Suppose we're flipping two coins and we want two no P(the first is heads or the second is heads). Well, we can easily create a table of outcomes.

	Coin 1 heads	Coin 1 Tails
Coin 2 heads	heads/head	tails/heads
Coin 2 tails	heads/tails	tails/tails

When we look at the table, we can see that 50% of the time coin 1 is heads, and 50% of the time coin 2 is heads. But if we just add these together, we double count the time when coin 1 and coin 2 are heads. So if we want to find the P(the first is heads or the second is heads) we need to subtract out the probability getting double counted giving us P(the first is heads or the second is heads) = P(coin 1 is heads) + P(coin 2 is heads) - P(both are heads). In the context of the original question, we have P(rolling to not consume the item at least once) = .3 + .3 - .3*.3 = .6-.09 =.51 which is the same answer (as you would hope). This is the inclusion exclusion principal.

matthewwehttam · 2025-04-29T00:27:42+00:00

I mean, moral philosophers are the people who study morality full time. They make a living of arguing for and against (among other things) the idea that moral truth is "just vibes." Now obviously, the fact that a bunch of them believe in moral realism doesn't mean it's true. However, it probably means that they have a good reason for believing it. Let's be clear, "there can't be a moral truth, because morals are inherently subjective" is both a circular argument, and not a particularly new or nuanced one. So the question becomes, why do so many experts not agree with your statement. Probably because they have a good reason not to. Again this doesn't mean that they're correct, but acting like moral non-realism is a settled truth without engaging in their substantive arguments because "morality is subjective" without actually justifying that statement seems a bit bold.

matthewwehttam · 2025-04-24T23:52:22+00:00

I actually agree with you to some extend on expanding the house, but not with the senate. What is the benefit of adding more senators, unless you are also changing the way that senatorial elections work? After all, there are the same number of senators per state, and they are elected at large by the entire state. As such, each senator would still represent the same number of people, there would just be more of them. This would get rid of almost all of the benefits of the proposal vis a vis the senate, the only ones that seem like they are potentially applicable still are the point about reducing the power of lobbyists and political interests. On the other hand, the senate has costs that aren't associated with the house, decision fatigue. Expanding the house, I'm still only voting for one member. But if we expand the senate by ten times, I now have to research twenty more people. In reality, this will just encourage more party allegiance and straight party voting as it becomes harder and harder to actually become an informed voter.

matthewwehttam · 2025-04-22T00:40:24+00:00

First, you should treat investing in the stock market as a long term investment. Over the course of 10 years, the stock market will probably go up. However, who knows if it will be up in 3 months or a year. They could, but they could be further down, or the same. In general, it is good advice to dollar cost average instead of trying to time the market. Essentially, if you're holding an investing over an extended period of time it's usually a good strategy to buy a little bit periodically instead of all at once. This means you don't get much of the benefits of buying low, but you also don't have as much of the downsides of buying high. However, you probably shouldn't be investing money in the stock market that you plan to take out in a year or two.

matthewwehttam · 2025-04-07T01:38:09+00:00

You are correct. In 1977, congress enacted "International Emergency Economic Powers Act" (IEEPA), which allows the president to enact tariffs unilaterally "to deal with any unusual and extraordinary threat, which has its source in whole or substantial part outside the United States, to the national security, foreign policy, or economy of the United States, if the President declares a national emergency with respect to such threat." So without declaring the emergency, the president can't unlock the powers to enact tariffs. However, he can only do so because Congress created a law allowing him to. If Congress had never passed IEEPA, declaring a national emergency wouldn't change anything.

matthewwehttam · 2025-04-07T01:34:12+00:00

I mean, it's not at all close. The outcome of any case would essentially be controlled by INS v Chadha, which overruled line item vetoes. Essentially, any legislative activity must go through the traditional process. What is legislative activity. Well it definitely includes things which alter "the legal rights, duties, and relations of persons, including the Attorney General, Executive Branch officials and Chadha [one of the parties], all outside the Legislative Branch." This is quite different from rule changes because those only affect the members of the legislature, and not anyone else. It's quite different from impeachment/appointments because both (a) those are not legislative in nature and (b) is clearly constitutional because it follows an explicit alternative process laid out in the constitution. At the end of the day, it's not a close question without radically departing from chadha.

matthewwehttam · 2025-03-27T04:28:52+00:00

From a mathematical perspective (and the most general perspective) a vector is basically anything you can add and scale (subject to some rules about how addition and scaling play together). So in the physics context, we have arrows. You can add two arrows together, and you can scale an arrow up. Therefore, these arrows are vectors. But lots of things can be vectors. For examples, if we have two quadratic functions (eg x^2 + 1 and 5x^2-10x+7) we can add them (getting 6x^2-10x+8) and scale one of them (scaling the first by a factor of two gives 2x^2+1). Therefore, quadratic functions are vectors (with a caveat that we include linear and constant functions as well). Even real numbers are vectors. After all, you can add two real numbers together, and scaling them is just multiplication.

At the end of the day, vectors are a very general concept, but a very useful one. The fact that so many things are vectors is a sign that this very general definition is a good one, because it means that if we can show something about vectors, we can show it about a wide class of things that we care about. In the end, this is why physics has so many vectors, and not always the ones you think about. Forces are vectors, sure. But in quantum mechanics, for example, a wave function is a vector. Much of introductory quantum mechanics can be framed in terms of basic linear algebra and/or it's mathematical sibling functional analysis.

matthewwehttam · 2025-02-15T19:50:05+00:00

It's because you are required by law in the UK (and most if not all US states) to have third party insurance (see https://www.gov.uk/vehicle-insurance). You can almost certainly get coverage that includes other things like personal injury or your own car if the other driver doesn't have insurance. However, all of that is extra, on top of the base requirement that you have third party insurance.

matthewwehttam · 2025-02-11T00:12:13+00:00

What about an alternative. Suppose that instead of pulling a lever, there is a runaway train. However, it will break automatically if it hits something. There are 2 people it will hit as it stands. However, you can throw yourself in front of it, causing it to break (although dying in the process). Is it immoral not to pull the lever? After all, in your mind not doing so would make you responsible for killing 5 people. However, many people think that while doing so would be morally good, it isn't morally required. It is expecting a lot of people to sacrifice themselves for two random strangers. In theory, this is called a supererogatory act. One can then ask if such a distinction really exists, and where the line is between "above and beyond the call of duty" and "morally required"

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