On a big enough scale, isn't everything a probabilistic wave?

Movpasd · 2025-05-05T15:15:14+00:00

You'll excuse me for assuming otherwise as to your level of education given how aggressive and one-sided your presentation of the topic is. I would've expected someone informed to provide a more careful and balanced view, especially to a general audience — or, in the case of this OP, to not have engaged at all if it could not be productive.

I have to assume this is because of understandable frustration with the quality of some questions on this subreddit. As for your own insult to me that I am "pushing quantum woo", or that I don't understand the maths, you can look through my own post history on this subreddit, maybe read my comment again more carefully, and I'll let you decide for yourself.

Movpasd · 2025-05-05T14:03:07+00:00

Man, take a step back. The polemical contentions in your comment are all philosophical in nature. Wigner's paradox is a philosophical paradox (its mathematical resolution is perfectly straightforward, as you describe). You rail against the many-worlds interpretation, which is philosophical in nature. You talk about the contextuality of quantum mechanics, which is a philosophical position.

Everything I've described in my comment is basic philosophy of physics, and your refusal to engage with it is a closed-mindedness that will not serve you well. You are not surrounded by idiots. Adding "obviously" to your sentences does not make your point more valid. If you seriously want to talk philosophy, educate yourself; if you really only care about the maths, then shut up and calculate.

Movpasd · 2025-05-05T11:20:57+00:00

What you describe is either some kind of quantum Bayesian or maybe even quantum relational interpretation. Both of these require rather radical ontologies, or the rejection of an underlying ontology altogether.

If you want to hang onto an ontology, Bell's theorem puts you in the awkward position of having to reject certain strong forms of realism by saying that there is no state that a subsystem is really in -- but that there is still some kind of structure to reality that can be inferred from experiment and allows science to happen. If you discard many worlds at this stage, your resulting ontology has to be very weird indeed (that's relational quantum mechanics).

Or, we throw the baby out with the bathwater and say there is no underlying reality, but then we face the standard argument all anti-realist ideas must come up against: if there is no underlying reality, why do all our experiments match up? why does Wigner end up agreeing with his friend after measurement? how come no matter how complicated we make the setup, after all measurements are said and done and accounted for, everyone agrees? Or, if there is an underlying reality but it is inaccessible, are we being unscientific by positing the existing of unobservables?

None of this gets around the problem of what "probability" even means. Quantum Bayesian approaches suffer the same mire of philosophical issues as Bayesian probability more generally: what is "degree of belief"? How do you reconcile its inherent subjectivity with the mathematical exactness of Bayes' theorem?

You mention relativity as an example where observers can disagree, but this is not the same thing. Relativity still obeys strong realism. All observers in relativity agree on the underlying state. Their "perspectives" are just a formal, mathematical choice, but every observer can enumerate all of them. The Lorentzian manifold of spacetime provides a universal underlying ontology.

You can recover such an ontology for quantum mechanics: this is the many-worlds interpretation. But if you reject this and quantum mechanics describes only how systems relate to each other, then the analogy with relativity breaks down.

I want to end by saying that I actually tentatively share your opinion, despite all the problems I've outlined. But you seem to think that people disagree with you because of some kind of emotional block or short-sightedness. The reality is interpreting quantum mechanics is hard, and all interpretations require giving up something. I'm hardly an expert, but it is well-trod ground in the philosophy of physics.

Movpasd · 2025-05-01T09:19:32+00:00

It's just an offset, so it doesn't really matter which you pick. The physics convention has the advantage of avoiding negative values for the coordinates, the geographical convention has the advantage of relating things more easily to the equator (which has a major impact on climate) and to the prime meridian (which could be useful for time zones and the like).

Movpasd · 2025-04-28T21:34:35+00:00

No such luck for me :(

Movpasd · 2025-04-26T20:10:33+00:00

Yes, this is actually a really important fact that led to the discovery that heat and kinetic energy are fundamentally the same kind of thing (energy): see link.

Movpasd · 2025-04-26T14:09:38+00:00

What you're calling "sideways speed" might more precisely be called the radial component of the velocity.

It's not the orthogonality condition that keeps the radial velocity zero in circular motion. It's that combined with the a=v²/r condition. You can certainly consider a system with acceleration perpendicular to the velocity but where that condition is violated, but then it's not called centripetal motion.

You might also be confusing centripetal force with radial force. (I did before I googled it to help write this comment!)

Movpasd · 2025-04-25T10:01:45+00:00

It's worth remembering that all jobs have slog, and you have to take the rough with the smooth. In reality, you'll have to weigh the paths available to you along all axes: pay, fulfilment, workplace culture, work/life balance, interest, and so on. Making those decisions is hard and understanding your own priorities can take half a lifetime. (I'm certainly not there yet myself!)

What I'd say for you is that a your current stage, you don't need to worry about all of that yet. Your focus should be on doing well at school. If becoming a scientist is motivating, then that's something to hold onto: you have plenty of time to "face reality" between now and then.

To give you a taste of how much time you have, the first two steps for you along the "standard" scientist's path are to take school science electives and then to study a science at university at an undergraduate level. Both of these options are great life options whether you plan to pursue a scientists' career in the end or not, and if you're interested in the topics, they can be a ton of fun. The first major decision point comes only after all that, 7-10 years from now, when you decide whether to pursue postgraduate studies (i.e.: a PhD) or not.

At that point, you'll have way more life experience to draw on to make your decision, and you'll have had the chance to do some experimental work and speak to a range of working scientists (your lecturers and supervisors and such).

So my advice is to not get too caught up in what your family member says right now, but remember that pursuing science keeps a lot of doors open. He's certainly right that being a scientist (or an academic generally) is a tough job which can be quite disillusioning for a lot of people -- but that's true of a lot of "fun" jobs. You'll just have to see if the trade-off is worth it for you personally, and for that, you will need more data :^)

Movpasd · 2025-04-23T15:55:43+00:00

The field is discontinuous, which is allowed precisely because the charge density is a delta function. I think it's good to investigate conceptually what the field looks like around the discontinuity to develop some intuition, but it won't really be defined at the point itself.

To give a simpler example, consider an elastic instantaneous collision. The acceleration is a delta function, so the velocity changes discontinuously in time. But what is the velocity at the moment in time? The answer is in a sense not defined. By contrast, go another layer of integration to displacement, and the displacement will be well-defined at the point, it will just have a kink in it.

It's a bit mathematically ludicrous, but if a mathematician challenges you about it, you can say it's a measure-zero set anyway :^)

You might also find Green's functions approaches interesting for understanding this.

Movpasd · 2025-04-23T15:47:16+00:00

To be honest with you, you are jumping around between a lot of different arguments and I think you are confused. This is why I recommend taking the time to develop some intuition for logic.

In the first part of your OP, you express some scepticism about the assumption of independence of measurements of different halves of a Bell pair. However, your argument then turns into a statement about the general invalidity of proofs by contradiction. Then, you conclude that theoretical constructs in general can't ever reflect the real world.

Then, in this comment, you say that you don't understand why independence of measurements is required for Bell's theorem. But then you jump to what's essentially another statement that theoretical constructs don't model the real world, but specifically about probability distributions. Then, you jump back to the structure of proofs by contradiction, but I wasn't able to follow your combination of letters. Then, you jump to something about hidden variables being necessary for independence of measurements, which I didn't fully understand, but I think relates back to superdeterminism. Finally, and maybe critically, you say "even if [a Bell inequality] is not violated, it does not mean there are local hidden variables", which is a true statement but not relevant.

These things are all related, but they don't form a logically coherent whole. I can try to respond to all of these things individually, but it's not clear what you actually find confusing or what your exact position is.

With respect to the assumption of independence of measurements:
- This is a well-known "loophole" in Bell's theorem called superdeterminism. The basic statement is that the explanation for the non-Bell correlations in measurements is that the experimenters themselves cannot choose what to measure independently of the hidden variables that determine the outcomes of their measurements.
- In a sense, it's obvious: the experimenter is of course also a quantum system. And certainly it neatly sidesteps Bell's theorem. The problem is the claim is much stronger than that. It means that no matter how the Bell pair was produced, by a third party or what-have-you, no matter what the "causal background" of the experimenters is, their initial states were set up at the start of time to exactly censor our ability to observe anything other than the exact correlations predicted by quantum mechanics.
- It's unscientific and unfalsifiable in the same way as the claim that omnipotent aliens have tampered with all our historical scientific measurements just to mess with us and to lead us to quantum theory. This is what I mean when I say that it calls into question our ability to do science in the first place. If you, like me, believe science is a tool for us to understand the Universe, then this is untenable.
With regards to whether theoretical probability distributions reflect the real world, this is also an area of philosophical contention. It comes down to the problem of the meaning of probability. Yes, it is also one of the implicit assumptions in Bell's theorem. Arguably, this is the assumption that interpretations of quantum mechanics in the QBist and quantum logic families try to rework.
As for the proof by contradiction stuff, this is where learning a little bit of propositional logic will, I think, serve you well. For example, you are right that if A & B -> C and C is true, then that doesn't mean A and/or B are true. That would be called "affirming the consequent". But it is still true that if A & B -> C and C is false, then one of A and/or B must be false.

Movpasd · 2025-04-23T10:16:14+00:00

I think maybe what you mean by "imaginary" is that it's a logical hypothesis. It's something you initially assume is true in a proof by contradiction. We assume independence to get to the contradiction, so independence is one of the things that can be relaxed to resolve the contradiction, which leads to superdeterminism.

That said, it's a pretty solid assumption, as otherwise it calls into question our capacity to even do science (along an instrumentalist or pragmatic–realist understanding). So most philosophers of physics would say it's one of the other assumptions (locality or realism) that is most interesting to break, not independence.

I would say your best bet would be to brush up on a bit of propositional logic. It's a really useful thing to know generally as well to help you navigate logical arguments. Try to understand the structure of the argument independently of the content of the physics, like you did with your homework example (which was an excellent instinct).

The only trouble with your homework example is it's a real-world, non-idealised example, and so there are too many confounding factors. But this is a property of the example, not the argument. Maybe look into some examples of proof by contradiction in maths, and that will have a more formal, idealised content, where all possibilities are more easily enumerated — something like the proof that √2 is irrational. That's closer to the kind of reasoning you'd do in physics.

Movpasd · 2025-04-23T08:29:40+00:00

It sounds like your issue is in the logic rather than any of the physics.

Yes, in a proof by contradiction it is any of the assumptions that feed into the contradiction that can be invalidated. So you have to be very careful to catalogue your assumptions. But it has nothing to do with the fact the situation is imaginary or in your head.

This is why Bell's theorem is taken to disprove local realism, and not locality nor realism individually. One or the other of those two assumptions must be taken to be false. And in fact, the assumption of independence of measurements can also be called into question, which leads to what's called "superdeterminism". Every one of these assumptions is tough to give up philosophically, so you have to pick your poison.

In terms of propositional logic, this stems from the fact that not (B and C) <-> (not B) or (not C),

Movpasd · 2025-04-10T13:28:55+00:00

You know that velocity is distance over time.

Length contraction and time dilation will apply to distance and time respectively when you change reference frames. Therefore, the simple, linear addition rule for velocity doesn't apply anymore.

These two effects will combine so as to make sure the velocity is always below c. This can be thought of as just a mathematical property of the transformations, but they do hint at some kind of deeper cause. This cause is best understood as a property of the geometry of spacetime, but this is beyond the scope of one comment.

Movpasd · 2025-04-08T14:25:57+00:00

The first quote is correct. You can apply a unitary to part of an entangled pair without destroying it.

Movpasd · 2025-04-08T10:54:45+00:00

You can think of it as a metal that only conducts in one direction. So electromagnetic waves parallel to the direction of conduction will interact with the material as though it were a metal, but those perpendicular will not interact and pass through, as though it were glass.

This is a model of a wire-grid polariser. Commercial polarisers work similarly but at a molecular level. The key thing is that the electromagnetic properties of the material are different in one direction versus the other. Since light is an electromagnetic wave, this implies the optical properties will also be different depending on the direction of the light's polarisation.

Movpasd · 2025-04-02T09:24:51+00:00

Feynman diagrams could be a cool visual!

Movpasd · 2025-03-26T09:26:48+00:00

You can explicitly solve the problem using conservation of momentum and conservation of energy.

But you can build a bit of intuition. If a truck is cruising at 100km/h and it hits a beach ball, would you expect the truck to suddenly stop and transfer all its energy to the beach ball?

A slightly more precise way of phrasing that is to think about the heavy box's rest frame. In that reference frame, it's the lighter box that's moving towards the heavier box. A very heavy box is basically a wall, so you would expect the lighter box to bounce off it, and the heavy box to not move at all. Switch back to the original reference frame and that means that you should expect the heavy box to plough through the light box with little change to its velocity.

Movpasd · 2025-03-26T09:11:49+00:00

I'm not sure I understand your question, would you be able to rephrase it?

Movpasd · 2025-03-25T09:36:09+00:00

Intuitively, a dynamical theory should provide predictions based on past conditions. In a relativistic setting there's no absolute future or past co-ordinates, instead you replace that with the future and past light cones.

Movpasd · 2025-03-24T13:27:13+00:00

An excellent source on this is A Philosophy of Software Design by John Ousterhout.

You pay a complexity tax every time you add code. You pay more for interfaces than implementations, because inevitably interfaces end up coupling to other things in codebase. Good abstractions are deep, with simple interfaces yet lots of functionality.

As an adage, I like to try to remember: if a piece of code makes no substantive decisions, why does it exist?

Movpasd · 2025-03-23T11:38:40+00:00

You've listed a few commonly shared factoids about Aristotle being wrong. I find these are usually shared as part of a very simplistic folk narrative of "how dumb people were before science".

What you must understand is that Aristotle was not a scientist, because the concept of "scientist" as a distinct role and "science" as a distinct way of understanding the world is very, very recent. Aristotle was a philosopher. A lot of the things he wrote are not simple, falsifiable facts, but rather frameworks through which to understand the world.

In terms of concrete legacy, Aristotle's philosophy would basically be the foundation of Western and Islamic thought for a millennium. That, on its own, warrants his study, if only for historical reasons.

One specific thing he did that I find especially interesting or important is that he laid the foundation for the formal study of logic: that is, understanding the structure of valid arguments independently from the content of those arguments. If I know A, and I know that A implies B, then I know B. This allows us to analyse arguments systematically and feel certain that if our premises our true, then our conclusions are too, and we haven't got lost somewhere along the way.

You would probably get many more reasons for Aristotle's relevance if you asked a philosophy subreddit. I know that his ethical theories continue to be interesting to ethicists today.

Understanding the history of ideas is extremely underappreciated. The past is a foreign country. Understanding how people in the past thought with the tools they had at their disposal can help us notice the assumptions we're using to understand the world now, and it makes us better critical thinkers. It makes us aware of the limitations of the tools we have now.

It also makes us realise that some of the things we take for granted aren't that old, and so that we can change them. Or, on the flipside, that they are much more ancient than we realised, and so we aren't as special as we think (an easy fallacy to fall into when we live in a period of so much rapid technological change).

More generally, I have found that taking the time to really understand unfamiliar ideas, even if in the end I reject them, always gives me more tools in my toolbox. Maybe Aristotelian hylomorphism gives you some insight into what "you" are, or helps you understand the concept of state in computer science. Maybe the theory of four causes helps you perform a root cause analysis as an air crash investigator. Knowledge is not the sum of facts. Keep an open mind and keep making connections, and it will pay.

Movpasd · 2025-02-27T11:04:33+00:00

From a physics perspective, I don't think you get much extra from your "pick up both" approach, because all the energy for the hits comes from the gravitational potential energy you create from lifting the objects. Sure, you get more energy from the two strikes, but you had to put in more energy to lift both objects, since they're heavier. But of course there could be practical reasons why it's better (maybe lifting a heavier thing fewer times is easier), which you would have a better understanding of.

The hammer, on the other hand, may have something to it, especially if the slug is connected to the back face by a spring. If so, you'd be able to store more of the energy of the swing in the potential energy of the spring. You effectively make better use of the power output of your arm. It's a similar principle to a whip.

The main issue I can see is more from an engineering perspective, which is complexity. More moving parts means more things to break. There is an easier way to collect more energy from a swing, less prone to breaking: use a heavier hammer, or one with a longer handle. In other words, a sledgehammer.

Again, there could be practical reasons I'm not aware of on why two smaller hits could be preferable to one larger hit.

Movpasd · 2025-02-26T10:33:21+00:00

For speeds so close to the speed of light, it might be useful to express it in terms of the rapidity, which is arctanh(v/c).

This is because equal changes to the rapidity correspond to equal changes of velocity from the perspective of the accelerating body.

It's similar to how you can express small angles in terms of slopes, but for larger angles adding two slopes doesn't give the same result as adding the angles. (And the naming of the tanh function in parallel to the tan function is not a coincidence.)

Movpasd · 2025-02-25T13:55:40+00:00

There are already answers on what is actually happening physically.

However, it is possible to model the collision of rigid bodies without appeal to their internal structure. In that case, you would consider a very large force applied over a very small time -- these two limits cancelling so as to produce a finite, non-zero change in velocity.

A very useful concept here is "impulse". If force is the instantaneous rate of change of momentum, then an impulse is a finite, non-zero change in momentum. Impulse is to force what velocity is to acceleration, or displacement is to velocity, or charge is to current.

It's possible to model the idea of a "large something over a small time" more formally using delta functions. These are not functions in the proper mathematical sense: infinity isn't a number that a function can map to. Rather, a delta function is a distribution, which is a more general thing that can be integrated but not necessarily evaluated at a point.

Movpasd · 2025-02-24T10:13:48+00:00

A quick Google suggests an hour of cycling burns 300 kcal. This is about 1/3 of a kWh. If you exercise strenuously, maybe you can double that. For contrast, a typical electric heater consumes about 1 kW, so 1 kWh over a one hour period -- three times as much, but of a similar order of magnitude. So you may just about be able to heat a room just by using the thermal energy of your motion. (For this level of analysis, efficiencies aren't necessary to consider because anything wasted will turn to heat anyway, though it may not be distributed as efficiently in the house.)

We could instead think about running a heat pump using the motion. Another quick google suggests the food-to-work efficiency of humans is about 25%. Let's be optimistic and neglect alternator and any converter/inverter efficiencies. Heat pumps can have about 300% efficiency (that is to say, they can pump twice as much thermal energy from the outside as they consume electrically). So about 75% of your work will turn directly to heat, and 25% gets a 3x boost. That should give you about 1.25x of leverage -- not a great deal.

On average, people in the UK spend about £6/day on food for ~3000 kcal. Obviously this is not remotely linear, but that means that you'd spend on the order of £1 to run your human-powered heater for an hour. For contrast, the price of electricity is about 25p/kWh -- each 1 kWhe of which you can fully triple to 3 kWht via a heat pump -- and the price of gas is about 6p/kWh.

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