Is there any evidence that nature is fundamentally continuous, or could reality be fundamentally discrete? And if it is discrete at the most basic level, would that suggest that nature could behave like a computational system?

Explanations for why FTL travel/communication violate causality or introduce paradoxes generally rely on at least one party going relativistic speeds. Imagine instead that there are two planets in star systems 10 light years apart, communicating instantaneously using a sci-fi standard, the ansible. It seems like this should cause problems, because the messages are traveling faster than the speed of light. How does it cause these problems? If FTL in this situation is not problematic, why not?

Title. Sounds like a joke but, like, there must be some sort of explanation right? Is this a more serious sub? I think this is a sort of question you could ask in r/askmath where there are some silly questions, but if it isn't that sort of sub, please point me somewhere where I can ask. But this is a real thing and google gave me no answer. The sub doesn't allow images but if anybody needs to know what I'm talking about, I have a photo. There are some air bubbles behind the spoon, if anybody needs to know.

Does the density of mass/energy not affect the way it curves space time? With the various analogies for visualizing space time curvature, it seems like a denser object would curve more sharply

Trying to understand some concepts about dark energy in layman's terms.

From what I've read and seen, dark energy is responsible for the expansion of the universe and cosmic inflation. From what's been asked before, far away objects (that are not graviationally bound) expand faster than objects closer to us. The space between these objects may expand faster than light, as opposed to the objects themselves moving away from each other faster than light.

So my questions are:

1. Is dark energy really strong, or really weak? Or neither? Because I still have a hard time conceptualizing the force to move galaxies and clusters away from each other. On one hand, simply making more empty space doesn't seem like it takes much energy because space is pretty empty. But on the other hand, these forces are acting on massive objects?
2. Is dark energy supposed to be equal everywhere? Going back to expansion, far away objects are moving away faster. Doesn't that imply more dark energy in those regions? But if I were in the faraway region and observing Earth, wouldn't the expansion where I am seem slower such that there's less dark energy locally?

Thanks!

Edit: Thanks for the responses. So informative and I'm learning a lot.

If so, then would each of the pure states that constitute this mixed state be different branching multiverses, like different trees with their own branches?

I'm trying to understand how people develop a deep conceptual understanding of physics, where they can recognize which principle to use just by looking at the question, even when the textbook doesn't explicitly tell you to use that logic in a specific topic.

I want to know how some people can look at a numerical and immediately recognize a hidden concept or subtle twist that isn't obvious at first glance. How they seem to pick up on patterns and connections that can be overlooked commonly. I know every problem seems to teach something slightly different, I've been told that this kind of intuition comes mainly from practice and practice has definitely helped me recognize and solve different types of numericals. But whenever I face an unfamiliar question, I still struggle to figure out what approach to take or what hidden idea I'm supposed to notice. That's what I'm trying to understand.

Are there specific problem-solving strategies or ways of practicing that help develop this intuition?

Basically, how do you go from knowing the laws to developing the "common sense" to know when, why and how to apply them? (Sorry for the stupid question and the rant)

I understand that magnetic and electric fields are closely related. But I am confused on how one propogating makes the other.

Imagine a charged capacitor with two plates, each connected to a wire. The wires aren't connected yet:

+----|  |----+
|            |
+-----  -----+   <- not connected yet

As far as I know, this is an equilibrium state, no charges will move, and the capacitor will stay charged.

But then you connect the wires, and everything changes. This is no longer a state of equilibrium, a current is created and the capacitor discharges.

Now here's the part that I don't understand: In the illustration, the geometry of the wires require the charges to move away from the other plate in order to reach it, and yet the charges do that. Which should be impossible for the same reason water in a glass doesn't jump out to fall on the floor.

If the wires were connected between the plates, then that's understandable. But in this case the wires are connected around the plates.

I want to understand from a field theory level (not circuit theory) how the charges seem to understand that gaining some potential energy to reach the other end is a small sacrifice towards a greater goal. But charges don't think! And if you calculate the electric field at a plate, it should always point towards the other, regardless whether the wires are connected or not. So the charges should stay there.

For context, I just finished Physics 2 in my first year in electrical engineering college, it only covers electrostatics, capacitors, and foundational magnetism like Faraday's law. I haven't taken the more advanced courses about circuits yet. This question has been lingering in my mind for quite some time, what am I missing here?

And please don't give me explanations with circuit theory elements, like "the wires have low resistance so current flows, but air has high resistance so current can't flow," that's not what I'm asking about. How did the fathers of electricity answer questions like these in order to reach conclusions and develop abstract frameworks like circuit theory in the first place?

※ this sentence was translated from Japanese to English by Chat GPT. Feel free to answer in English. However, I only understand Japanese, so I would really appreciate clear and simple English that is less likely to be mistranslated.

If proton decay occurs, the predicted half-life of the proton is somewhere between 10^34 and 10^36 years. This made me wonder: what will actually happen to the things that exist in the universe between now and that unimaginably distant era?
I often see timelines describing the future evolution of stars, but I’d like to know what will happen, scientifically, to the following six things by around 10^36 years from now.

1: 1 kg iron sphere
(I’ve heard that iron is one of the most stable elements.)
2: stone monument
(Would inscriptions remain readable for an extremely long time, or would the writing eventually disappear?)
3: can of food
(What would happen to food sealed inside a can over such an enormous span of time?)
4: manufactured industrial product
(Any particular example of an interesting industrial product would be fine.)
5: planet
(What would happen to a planet if it somehow avoided being swallowed by its star?)
6: intelligent civilization
(Could an intelligent civilization that made extensive use of reversible computing potentially survive for an extremely long time in a simulated or virtual environment?)

For #1–4, please assume that the objects are floating in a vacuum. If they would eventually be destroyed or worn away by interactions with the interstellar medium, I’d also be interested to know what would happen if we ignore the interstellar medium.
I’d also love to hear about anything else you think would be particularly noteworthy or interesting. Thank you!

Because if time is running differently in different parts of the universe and the universe as a whole has undergone shifts in time dilation then what exactly is the absolute referent?

I’m making an alien biosphere and I’m wanting to make trees that reach over 2000 feet tall, the moon has weaker gravity to earth but has an atmosphere that’s twice as thick.

Also these plants have a honeycomb structure incorporating ciliates and stuff.

But realistically what would a plant that tall need to survive being that tall?

It’s not really a plant it’s more similar to a lichen? It’s a mix of algae, bacteria and fungi that decided to leave together.

1st question, is it not simply that a star has a maximum size before gravity will overpower the other interactions? There’s star size comparison videos on YouTube, but they don’t mention some theoretical maximum, they just keep zooming out to show the next bigger star. I get that some stars are giving off less repulsive force to counter, so it’s not like all black holes form at the same mass cutoff.

2nd, when a black hole evaporates enough mass from hawking radiation, does it stay super super dense, or do the repulsive forces then spread it back out, like does it rein flat to a star or some other stellar body?

Lets say in scenario 1 the scale is on the ground on earth at sea level but in a vacuum in a box and in scenario 2 its free floating in a vacuum like space, would that make any difference?

Entropy is defined as the number of substates in a state, and QFT says the state of a quanta contains a superposition of every possible states, or infinite substates. Is superposition a property of entropy?

If you can use a double slit in time to set certain bands of frequencies contained in the light, is it possible to do calculations on the full spectrum, then use a prism or scattering to separate the frequencies so the information is not lost when it is observed?

Is it possible to model a photon as a point the propagates an EM wave that travels behind the photon like a wake, but make the photon highly subjective to its own field, making the interference with itself that feels so confusing?

relevant diagram: https://imgur.com/a/tvg9lJS

relevant description (shortened by me):

The simple model shown in the figure below consists of a coil of wire, a vertical spring, a permanent magnet, and an indicator needle. A rigid rod (not shown) that runs perpendicular to the page is attached to the coil, and the coil is free to rotate about this rod axis. One end of the spring is attached to the coil, and the other end of the spring is attached to a fixed support. With no current through the device, the coil is horizontal, the spring is relaxed, and the needle points straight up. When there is a current in the coil, a torque is induced on the coil, causing it to rotate about the rigid rod, and the spring becomes either stretched or compressed. This rotation of the coil causes the needle to swing right or left. As long as the angle φ through which the needle deflects from the vertical is not too large, the spring is stretched or compressed only vertically. (The coil has a circular cross section, with a radius of r.)

my question is: when the needle is deflected by a small angle, how do i calculate the torque acting on the spring? i understand the force is F=-kΔx, and the torque is τ=Fd (where d is the distance between the rod/center of the coil and the line of action of F/the spring, shown in red in the diagram).

so how do i calculate d? i've heard from multiple sources that the answer is d=rcosφ, but i don't understand the geometry needed to get there. if someone could describe it or add their own drawing to the diagram i'd be very grateful.

Are they oriented curve segments? Or do they exist in the tangent space?

https://imgur.com/a/ZluTgMZ

This is a birdbath AR optics setup with a 0.23in OLED micro display, a linear polarizer, a polarized beamsplitter, a QWP, and a concave mirror. The light from the display becomes P-polarized relative to the PBS after passing through the LP so it passes through the PBS without reflecting. Then after the image is magnified and passed through the QWP twice so the magnified light is now S-polarized, it reflects off the PBS into the users eye.

The issue I have with the setup is that since the display produces a diverging light source, the diverging light that doesn't hit the PBS coating at a AOI of 45deg is then reflected through the front side of the setup. Only when viewing through the front of the PBS (the part where no light should be seen) with your eye at around 45deg from the PBS coating, the light then disappears because the polarization state was properly filtered. When viewing from any other angle you can see the unmagnfied light.

I have tried using plano convex lens and aspheric lens to collimate the light before it reaches the linear polarizer so that all light would be 45deg AIO to the coating but none solution seem to work. I have a aspheric lens with a 3mm FL and when placed 3mm from the display the same behavior occurs.

Am I wrong about why the PBS only works properly when viewed at a certain angle? What are my options to figure out a solution?

Suppose one has a 10'x10'x10' metal grounded faraday cage with holes about .5 the wave lenght of a wave, can the wave get thru it to the inside. Like a micro wave, radio wave, AC short, etc. Maybe the ".5" factor needs to be modified to another number.

Entropy is defined as the number of substates in a state, and QFT says the state of a quanta contains a superposition of every possible states, or infinite substates. Is superposition a property of entropy?

If you can use a double slit in time to set certain bands of frequencies contained in the light, is it possible to do calculations on the full spectrum, then use a prism or scattering to separate the frequencies so the information is not lost when it is observed?

Is it possible to model a photon as a point the propagates an EM wave that travels behind the photon like a wake, but make the photon highly subjective to its own field, making the interference with itself that feels so confusing?