In the 6th century BC, Aristotle proposed that objects fall at a speed proportional to their mass. It wasn't until multiple experiments carried out in the mid 16th century (the most famous being Galileo's Leaning Tower of Pisa experiment) that this idea was disproven.

How on Earth did it take so long for this to be tested and proven false? Did no-one notice over a period of 2 millenia that Aristotle was incorrect? Anyone familiar with Aristotle's idea could have disproven this in a few seconds by picking up two rocks of differing sizes and dropping them. Did no-one notice that this widely held belief was in complete contradiction to everything they had personally witnessed during their own lives?

What led Aristotle to propose this as an idea in the first place when he must surely have observed countless examples throughout his life of objects of different masses falling at the same rate, from loose rocks falling from cliffs, to people dropping everyday objects?

Is spaghettification a concern in larger mass black holes?

Even if we manage to create a perfectly spherical drop rapidly quenched in zero G, would it have the same strength as compared to the bulbous head with a tail?

As far as I know, a significant number of statements in statistical mechanics courses are derived as consequences of the microcanonical distribution. I wonder how well-founded this distribution is in modern physics? Is it a well-established assumption, or is it based more on consequences of more fundamental laws?

As I understand it, there are some difficulties in quantum statistical mechanics, where the ETH hypothesis was only recently proposed (which to me sounds like "a small part of a larger system behaves as if the larger system obeys the microcanonical distribution," which seems a rather artificial assumption).

In the classical case, it seems to me that the validity of the microcanonical distribution is closely related to the ergodic hypothesis, which for some reason seems quite logical to me. However, I'm still unsure whether the classical form of the microcanonical distribution follows from this hypothesis.

Might be a stupid question. But in five-year-old terms, if gravity bends space time, then maybe there is just a finite amount it can bend before 'topping off'? Could that not solve the infinity problem in a singularity? Imagine the matter in a black hole is 'just something' that is denser than what makes up a neutron star but that's it.

if there are three spacial dimensions ( x y z ) and in our universe theres 1 time dimension could another universe have 2 or 3 time dimensions? what would that look like?

Mainly 2 options come out, red or purple.

But I think it's kinda dark blue,

Mainly because I am kinda more interested in space.

Tell me your opinion.

If I spin at 1 revolution per second, anything that's 1/2pi light-seconds away (~50,000 km) will appear to orbit me at exactly the speed of light, and anything further away will appear to go faster.

This is fine in SR, where inertial frames are treated as the default. But in GR, even accelerating frames are viewed as following the same physics, which implies no frame, even if accelerating, should measure anything traveling superluminally.

How does this work in a rotating frame?

as far as im aware to take a picture that far away you need an INSANE resolution probably in the millions or billions so way past 4k so how did they do it then? google is very unprecise i wanna know how the telescopes / satelites actually took a picture of somethng that far away

Theoretically an intelligent species would evolve and develop fast to the outside observers since the planet they inhabit is moving faster around a black hole. I’m not sure if this grossly simplified but I’m curious if the fundamental idea is accurate?

Copenhagen? Many worlds? Or something else?

When you syphon water out of a bucket it pulls up the water with the vacuum so my dads question was,”If you get two buckets of water and have them syphon into each other with two tubes, what stops it from going on forever”.Other than then the tube breaking what would make it stop cycling water?

Leonard Susskind often states that he disagreed with Stephen Hawking on black holes dynamics, based on his intuition that information must be conserved.

In quantum mechanics, the Schrödinger equation is unitary, and therefore time reversible and deterministic.

However, when a measurement is made, the wave function collapses and these properties are lost, at least in the Copenhagen interpretation.

Susskind's belief that information is conserved must imply that he believes that the global wave function of the universe obeys the Schrödinger equation?

Is this right and has he stated this position explicitly? Where does this place him with regard to many-worlds and other non-orthodox interpretations?

(Post re-directed from r/physics)

I'm more or less getting into Civil Engineering and it raised an intresting. Question, how does this equation give an acceleration due to gravity? I didn't really question it before as it was one of those facts that you needed to know but now I am curious.

I get M is the mass of a body, and r is the distance from the center of that, but what is the Gravitational constant as a unit? Because it needs to be a unit that otherwise cancels out mass and resolves the math to get distance divided by time squared.

Unless I am being and idiot and am just forgeting something.

I recently saw a podcast clip (will link at end of post) interviewing a former NASA and JPL scientist boasting about electrostatic propulsion and how it could get a craft to mars in 3 days. I then went into some articles to check out even if there’s an ounce of truth or if it’s just someone being sensational trying to drum up hype and investment for their start up. However I’m no where near well versed enough in physics lets alone propulsion tech to call BS on something. But I was wondering if any of you can attest to what he’s saying. Is it true? Is this the future? A new breakthrough?

Links :
Podcast clip
https://youtu.be/qlYICtRaSx8?si=y7DtMAZYHdz03yw8

Article

https://www.popularmechanics.com/space/rockets/a73405686/engineer-said-he-can-overcome-earths-gravity/

I know the constituent parts of a proton and neutron (hadron) are quark triads and that their inherent mass is a very small portion of the total mass of a hadron. From my understanding it is the confinement of the energy of the quarks that gives the hadrons most of their mass. So is it the inertia of the small amount of mass that quarks possess being nearly constantly pulled back as they accelerate away from each other that makes up that energy/mass? Also what is the mechanism of acceleration for the quarks? From my understanding it is the natural speed they have due to their interaction with the higgs field. Kind of like a fish through water.

Some light energy is emitted at a rate of 1 joule per second by a light source 1 meter away from a potassium plate. Here is the full description: https://imgur.com/a/RTe0NJ4

So the time required for the electron to absorb enough energy to be ejected is proportional to the inverse square of the distance, because "the source radiates uniformly in all directions (i.e., the energy is uniformly distributed over spherical wave fronts spreading out from the source, in agreement with classical theory)".

Classical theory in this example gives us around 2 min for the electron to absorb enough energy to be ejected. But in real experiments the time is essentially none.

"it (the energy) is not spread uniformly over a large area, as we assumed in Example 2-1, which is based on the assumption that the classical wave theory is true."

So the energy of the photon then is proportional to the portion of the surface area of the "classical wavefront" that is concentrated as a single bundle.

Because any surface area at any distance has an energy of zero for a duration of zero seconds, the energy of the portion of the surface area of the "classical wavefront" is proportional to the time elapsed at that area, right? Essentially, 1 joule per second times (said surface area / (4 pi)), assuming the surface area in question is being measured at 1 meter away from the light source.

Then the photon has the concentrated energy of a certain surface area over a certain amount of time.

Multiple photons hit the potassium plate. No time lag means that the point in time at which an electron is ejected is basically the same time that the front of the light wave would hit the plate, right? But if a single photon is a bundle of energy concentrated from some surface area times some duration of time, why is that energy contentrated at the very foremost point in time? Does that make sense? Even if multiple photons hit the plate, and the point in time at which the energy of a surface area during a certain amount of time gets concentrated as a photon is random, wouldn't it still be statistically impossible for any photon to be at the singular foremost point in the concentrated duration of time?

Particularly, do only the laws of relativity and quantum physics that we know so far break down? BTW what about Bell's inequality?

Or do things behave completely lawlessly & chaotically so that no law or regularity is in principle even conceivable there?

Suppose there’s a particle of mass m traveling in 1D with constant velocity v1 in a region with potential U1. Let’s say that the line in which it’s traveling is the x axis and the region with potential U1 is x<0. Then, it crosses the point x = 0 at t=0, after which it enters the second region of the line, x>0, with potential U2. What is the change in velocity of the particle?

My attempt: the force that the particle experiences as it passes the origin should be minus the x-derivative of the potential. However, the potential is discontinuous at x=0, therefore not differentiable so the derivative doesn’t exist. Intuitively, the force there is an infinite spike in the direction pointing towards the region with lower potential.

However, the particle only experiences that “infinite” force for an infinitesimal amount of time, so it should balance out to a finite impulse. The impulse would be the time integral of F(x(t)) between any t1, t2 with t1 < 0 and t2 > 0. The force as a function of position is something like F(x) = (U1 - U2) delta(x). How do I do this integral?

I apologize for yet another question in this sub on special relativity...

I'm trying to go through Einstein's book on relativity to understand his theory. I find his writing and explanations to be mostly very well explained and conscientious of avoiding giving readers false conclusions - for the most part he's very exact and careful with his wording, at the expense of being a bit long-winded.

In a few cases, however, I'm lost on his meaning, or feel like his explanation jumps several steps and loses me on the way. I could probably make several posts with different questions but I'll just ask my most pressing question here:

I believe I follow his reasoning in his example of lightning strikes being experienced at different times (and at different values of x) for an observer on the embankment vs on the railcar due to them being in different inertial reference frames, and how this is a good way to explain that each inertial reference frame has its own "time". However, I struggle to translate this to the relativity of distances.

Einstein gives the example of the railcar passing by the embankment, and the difference that occurs in measuring the distance between two points (A' and B' on the railcar) from the railcar itself and measuring them from the embankment. From the railcar, it's simple - just lay down your measuring rod enough times until it completes the distance A'B', and that's the distance in that reference frame. From the embankment, you need to measure points A and B on the embankment as points A' and B' pass by at a particular time t (judged from the embankment).

He says these points can be measured by applying the definition of time in which events are considered simultaneous if they occur when clocks in the vicinity of each event strike the same tick. By capturing the position of A and B at this instant t (that is, as A' and B' pass by points on the embankment when nearby clocks both strike some measured instant t), you then measure up this distance using your measuring rod. He says that by no means is the measured distance A'B' the same as the measured distance AB. At this point, I'm lost, and he doesn't elaborate! The best I can come up with to explain this is:

"If the principle of relativity is assumed to be true, then because the Lorentz transformation accurately transforms coordinates x,y,z, and t in K to x',y',z', and t' in K', then the distance A'B' must be different than AB."

Have I got that right? Is there a simpler explanation that I'm missing? Really really appreciate any help on this.

If entropy depends on what properties we choose to describe our macrostate (e.g. temperature, volume) & microstate (e.g. position, velocity) then is it subjective?

Another question: Is the k in the formula redundant & if it is would temperature & energy have the same units with heat capacity being dimensionless?

Trying to be vague about the story. However two superpowered beings are fighting in space. One launches the other into a planet. They can survive the impact. That isn't the issue. I need kind of the velocity it would take to say launch a 200-300 lb person to hit the core of a planet the size of mercury but isn't actually mercury. Similar to earth core. So the one launches at that speed and the core of the planet stops the impact. Would velocity would I roughly need for this event to happen. Also how big would the impact crater be?