Objects take up space and time. If gravity bends space-time, why don't objects shrink under its effect? Most explanations I've read suggest that gravity affects only empty space. Isn't occupied space also space?

I suppose if you try to measure the shrinkage with a ruler, the ruler itself would shrink too, so maybe we can't detect it. Other than that, I don't know.

Typically, in quantum mechanics classes, we're taught that position eigenstates "aren't real states" because they're not square integrable, so not in the Hilbert space.

In the more general algebraic quantum mechanics though, states aren't specifically identified with vectors in a Hilbert space, but rather positive, normalized linear functionals on the C*-algebra of observables.

The delta "state" fits this definition. You can, for example, take a subsequential weak* limit of well-defined Hilbert space states that are getting skinnier and taller. This is guaranteed to exist by the compactness of the state space in the weak* topology. This resulting state would behave exactly like the delta state.

Of course, it wouldn't be a normal state with respect to the standard representation, but it would still be a valid state.

On a kind of related note, if this is true, does this interpretation kind of follow to type III von Neumann algebras?

I've read that the interpretation of mixed states as probability measures over pure states breaks down in type III von Neumann algebras, since the pure states making up the mixed states are not normal in the mixed state's GNS representation.

However, if the non-normal pure states behave like deltas, I don't really see the issue with still interpreting the mixed state as a probability distribution over the pure states. We essentially do that all the time in classical mechanics.

I know mass is convertible to energy.

So, mass can become energy.

But is mass energy, just in a special form?

Or is it even possible to answer this clearly?

Ok now this might seem like a dumb question but whenever I search it up they give straight bullshit like "since the magnetic field is changing and nature hates that we have a emf that is generated which opposes this change." THAT IS THE EQUATION AND I'M ASKING FOR THE CAUSE. Now I understand that lorentz causes an electron to experience a force if we have a rod moving in a magnetic field, but how is this related to the magnetic flux and even more so how is it related to area. To get to the heart of my question, I don't understand what it is that causes a relationship between magnetic flux and the potential difference across a loop

I am trying to understand the physical and intuitive origin of the $𝑟^2$ factor in the moment of inertia (𝐼=𝑚𝑟2) from first principles, but I keep running into circular or unsatisfactory definitions in standard textbooks.

Usually, the [𝑟2] factor is justified using one of two methods:

1. The Kinetic Energy Derivation: Substituting (𝑣=𝜔𝑟) into (𝐾𝐸=12𝑚𝑣2) yields (12(𝑚𝑟2)𝜔2). While mathematically elegant, this simply groups variables; it doesn't give a dynamic, force-based intuition as to why the resistance scales with the square of the distance.
2. The torque derivation: Using (𝜏=𝑟𝐹) and (𝑎=𝛼𝑟) to get (𝜏=𝑚𝑟2𝛼). I got a reasonable explanation for 𝑟2 explanation from somewhere but it require prior understanding of the torque. I have still stated the explanation below When you try to rotate an object (like spinning a ball on a string), the distance from the pivot point ([𝑟]) works against you twice:
   • First Factor of [r] (Leverage/Torque): To make something rotate, you apply a force. However, what actually causes rotation is torque ((𝜏=𝐹×𝑟)). If a mass is twice as far away ([2𝑟]), the force we apply has less "rotational leverage" over it. You have to push twice as hard just to apply the same rotational action to that distant mass.
   • Second Factor of [r] (Linear Speed): For a wheel to spin at a certain angular speed (RPM), the outer edge has to travel much faster than the inner part. If a mass is twice as far away ([2r]), it must travel along a circle that is twice as large. To keep up with the rotation, it has to move with twice the linear velocity ((𝑣=𝜔𝑟)). Accelerating a mass to twice the linear speed requires twice the effort. Because these two factors happen at the same time, they multiply together to give 𝑟2 dependence

My issue with the second method is that textbooks rarely define torque independently. They either call it a layman "rotational analogue of force" (which is just a metaphor), or they define it as (𝜏⃗ =𝑑𝐿⃗ 𝑑𝑡), which requires defining angular momentum [𝐿⃗ ] first. If [𝐿⃗ ] is then defined as (𝐈𝜔⃗ ) or (𝑚𝑟⃗ ×𝑣⃗ ) by calling it a "rotational analogue of momentum," the entire argument becomes a circular tautology.

Finally, is there a way to understand 𝑟2 dependence without going circular, or by at least defining one of the things properly without using layman terms like rotational analogues and then throwing up formula. I mean a definition of something should be such that it is self explanatory and directly links to mathematical expression or it lays method by which we can derive the expression

So recently I think an explanation for why the SoL is the maximum speed of the universe just clicked for me, correct me if this explanation is completely wrong, but I think this is a good explanation for dummies (such as myself) as to why Spaceships can't reach the Speed of Light.

So let's say a Spaceship, from the perspective of Earth, flies away at an acceleration of X speed per second. At first, from Earth's POV, the ship does seem to gain X speed every second. But because of Time Dilation, the faster an object moves, the faster it experiences time. So eventually, what the Ship experiences as one second is, say, 100 years on Earth. So at that point, even though the Ship accelerates at what it percieves as X/s, on Earth it looks like it took the Ship 100 years to accelerate to that speed. And the faster the ship gets, it takes longer and longer from Earth's POV for the ship to accelerate every subsequent X. And no matter how much time passes, it will never reach the speed of light from an outside perspective.

Now if this explanation works (feel free to call me a dumbass if it doesn't), one thing didn't click for me yet: Why does the Time Dilation happen in the first place? Time Dilation seems to be defined as occuring due to the Speed of Light being the same from all points of view, but we just used Time Dilation to define the SoL in the first place.

The setup:
There's a ferromagnetic plate with a very large area sitting on a frictionless surface. The magnetic field points to the positive z-direction. A charged particle (mass m, charge q, initial velocity v) enters the plate's magnetic field, traveling towards the positive x-direction.

From elementary electromagnetism, a charged particle in a uniform magnetic field will end up travelling in a circular path, due to the force F=q (v x B) from the ferromagnet.

Knowing that:
1. Forces come in pairs (Newton's 3rd law, for every action there's equal and opposite reaction)
2. The charged particle now has a finite angular momentum about the center of the circular path

Will the force caused by the charged particle on the ferromagnet result in the ferromagnet spinning in the opposite direction to the charged particle?

Salve a tutti, mi chiamo Lucia. Premetto che sono inesperta in materia ma so che chi l'ha studiata può aiutarmi in qualche modo. Il mio cane anziano purtroppo è morto nel pomeriggio di ieri 15/10/2026 all'età di 16 anni compiuti dieci giorni fa. Probabilmente si è sporto dal balcone del terzo piano dove vivo e avrà perso l'equilibrio ed è caduto. Io vorrei capire come è avvenuto. Perché il cane era perfettamente adagiato al suolo praticamente sotto il balcone del primo piano, come quando un cane sobrio si distende di sua spontanea volontà su un lato per dormire assumendo la consueta posizione rilassata. Questo io lo trovo assurdo e impossibile. Sospetto che abbia impattato le ringhiere dei balconi sottostanti e abbia arrestato la sua caduta finendo in uno di essi per poi esser stato adagiato volutamente al suolo, oppure scaraventato giù e qualcuno che si è trovato lì per caso lo ha trovato e lo abbia adagiato al lato. Il corpo era ancora caldo quando mia madre lo ha prelevato. Aveva il collo molle. La bocca era spalancata con un po' di lingua che fuoriusciva da un lato. Gli occhi erano ancora aperti. E sulla coscia sinistra aveva una piccola lacerazione. Mi potete aiutare per favore a capire se è morto cadendo e impattando direttamente il suolo o come vi ho descritto nei miei sospetti? Per favore... non mi do pace

it says that energy cannot be destroyed, only transformed/transferred. When you burn something, for example, the energy transforms to heat, right?
Is it hypothetically possible to harness energy to the point where we can use its every 'transformed" form, thus using a fixed amount of energy infinitely?
I hope my question makes sense.

Am I being dense? Pardon the pun

I am reading about how these can be used to cause an avalanche of electrons to flow from a smaller amount. Do you think such a device could be used on a per subpixel basis in a crt to get huge amounts of electrons to strike the phosphor? Like a long tube for each subpixel? or would that number of electrons be way too hot for the glass and cause it to expand too much?

I'm trying to envision how one would fix poor black and white contrast of crts and have more brightness and from what I have read the poor black white contrast might actually be from the photons traveling through the thick faceplate? I originally though it was caused by light bouncing back into the tube, which is why I envisioned subpixel tubes initially, but grok tells me there is metal coating between the phosphor and the beam that reflects light back out of the tube and that prevents light bouncing around inside the tube?

Why is it not possible to measure the speed of light in one direction? Would it not be possible to have a laser angled ever so slightly off being parallel with a wall, and seeing how fast the laser illuminates the wall as it travels along it?

And that this is because there has to be a source of neutrons for atoms to capture. But, I have also read that there are things called neutron sources. Even devices that have been made at universities that produce neutrons. Am I incorrect?

I have seen this question asked before but for people learning from scratch. I have my bachelors in Physics and graduated 6 years ago. I find myself missing it and, more devastatingly, forgetting most of it. I am struggling with memory/brain fog issues. I feel so incapable. I miss the feeling of academia where I felt challenged and, occasionally, intelligent. I am also hoping using my brain this way may help.

I was wondering if anyone has any resources for refreshing physics. I miss solving problems and do very well with the lecture/homework structure of college.

I looked through this sub and found a link to David Tong lecture notes/problem sets. I would do better with a video format, but I do not think the MIT lectures are paired with practice problems (unless I am mistaken). I could combine the two (DT and MIT), but I figured I would ask if there is a resource like that thats readily available? I am expecting no and also welcome any other resources even if they do not 100% fit the bill. Thanks a ton for any help!!

Can a bound particle have a momentum eigenstate? And since they can't be normalized, we use a fourier transform to get normalized wave packets? Sorry if my quesitons aren't very clear.

I feel like a massive idiot asking this but if it's true that gravity and light in a vacuum travel at the same speed, how can light ever be affected or consumed by gravity unless gravity moves faster than light in the first place? Like the only way for a blackhole to consume light would be to have a gravitational pull that acts faster the light it's 'chasing' if you know what I mean. Otherwise the light would just escape the gravitational pull? Which would mean it's faster than gravity?

Do you have any recommendations on articles, books, whatever about the current theories on this subject? To clarify: I have a degree in biology, I'm in my way to be teacher and I've realised how little I know about this topic, I'm trying to have a reasonable understanding about it and I just discovered the inflactionary theory as "a part" of Big Bang theory. I'm currently at the "all I know is that I know nothing" stage and I would like to move at least a bit closer to "know something". I know that it is a higly complex topic, requiring a lot of knowledge in maths and phisics but I would like to try it. Just for the pleasure of knowing but also thinking about my future students.

I hope my question is appropriate for this sub and thanks!

Hello All!

Non-physicist here with another (probably bad) idea/question about the nature of the universe. I have a tech background and tend to see everything in terms of information... so I'm aware that my bias is showing...be gentle.

It occurs to me that every interaction of every fundamental particle, is generating at least one unit of information (bit? qubit?), probably several. All that jazz happening in quantum field theory and Feynman diagrams. The more particles and interactions the denser the information (yes?).

We observe the distance to all cosmic objects like galaxies is increasing. Galaxies would be informationally very dense. We observe that the older the galaxy the faster it is becoming distant to us.

Could this effect somehow be correlated to information density? An older galaxy would have had a chance to generate much more information than a newer galaxy (all those particles boogeying with each other). If there was such a correlation, might it help to explain the old galaxies accelerating away from us faster because they'd generated more information.

Perhaps information density has an effect on the metric of distance?

I feel like Wolfram's ideas are a bit like this... and those don't seem to have been too well received by the physics world AFAIK, so right away I suspect of this whole idea.

Btw no insult intended against Wolfram..he's done a lot of cool things (and who knows...maybe he was on to something).

Could the same 100 meters actually “contain” a different physical distance depending on how much mass shapes the surrounding spacetime? 100 meters in a region shaped by more mass may not be geometrically equivalent to 100 meters in a region shaped by less mass. If mass–energy changes the geometry of spacetime itself, perhaps the very meaning of a given distance depends on how much mass shapes the space in which that distance exists.

heres another:Imagine a cube measuring 10 × 10 × 10 meters, floating in void. Now imagine being able to gradually increase or decrease the gravitational field associated with its mass, without changing its physical dimensions. Would the geometry of spacetime inside the cube change as its gravitational influence changed? Could the cube retain the same nominal dimensions while its internal spatial geometry became different?

(An internal observer would measure different dimensions than an external observer due to the curvature of spacetime caused by the cube’s mass.?)

Hello everyone, I am currently taking AP Physics 2 and I have an exam tomorrow over electric force, field, and potential. I do not understand it at all. I’ve studied like crazy already but it’s not helping (I already failed the multiple choice section). Seeking some help understanding these topics from some people who know more about it than I do! I truly wouldn’t be on here if I wasn’t desperate, but I need a great score on this section to keep my A. THIS IS NOT ME ASKING FOR HELP CHEATING OR FOR WORK TO BE DONE DONE FOR ME — I simply want to improve my understanding of the topics before my test! If you can help, great, and if not no worries. Thank you!!!

I might be dumb , but I think it has something to do with the blade being a conductor and the wooden handle not

I'm assuming each pole with its negligible rotation is perfectly survivable, and a bit of distance from them may be a small jolt. But how far would you have to be from each for this stop to become fatal?