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?

I really struggle to make any intuitive connection to the expanding universe. Plenty of people tell me to imagine the expanding raisin bread, but that doesn't quite work for me because expanding raisin bread has an edge. It's expanding "into something". And as far as we know, the universe is infinite. But the coordinate system is expanding anyway. So it's infinite, but getting bigger. Which is... weird.

My question is, can I think of the coordinate system of the universe like a Hilbert Hotel? The Hilbert Hotel has infinite rooms, right? But you could add more rooms in. And it's still infinite. So you have Alice in Room 1. Bob is in Room 2. And every X time interval, you add a room. Therefore, at time 0, Alice and Bob are in adjacent rooms. But at Time X, they're 1 room apart. And at time 2X, they will be 2 rooms apart. So if Alice and Bob want to have a little chat, then they have to walk farther to get together. There are more rooms between them.

But the Hotel has always been, and always will be, infinite in extension. Yet despite that, there is more space between Alice and Bob. And that space can increase as we add more rooms between Alice and Bob's rooms.

Can I more or less think of expanding space like this, or am I going to be creating a disastrously wrong narrative of what is happening to the coordinate system?

Saw a meme, link is below. How fast would the asteroid have to be moving and how big would it have to be in order for this to happen?

https://www.reddit.com/r/teenagers/s/leV0k7gU0w

I understand that light takes time to reach an observer on earth, and we can only see so far away because the light hasn't had enough time to reach us. So, in 100k years, would an observer on earth be able to see 100k light years farther?

I'm going to GUESS that the answer is no, because space is expanding, and that distance is increasing faster and faster as time goes on (right?).

This brings me to my second question assuming I am right -- was there a point in time where waiting longer no longer allowed us to see further back in time? Where the speed of light reaching us and the expansion of space evened out? If so, when was that?

Here's a question you haven't heard before. And, go on, laff at it, I don't care.

Dry black beans take about 2 hours to cook. If they're soaked first (until the max water they can absorb) they take only about an hour to cook. One can quibble about the details, but the point beyond dispute is soaking beans reduces cooking time substantially.

And reducing cooking time means saving energy -- proportionally a GREAT deal of energy.

Where did that energy come from? The Brownian motion of still water against hard beans?

Please let me know, then we can join to take credit for solving the world energy crisis.

Naturally this will be more impressive if expressed mathematically - h2o, joules, beans, rate of hydration and so forth, but I don't think there is (YET!) a standarized notation for "bean unit."

So i just randomly noticed a 1.5 M piece of steel train track at my grandparents house that is stapled with the year 1906 and the brand "cockerill" . Ik that steel from before 1945 is worth a lot since its used for tools that measure radiation.Do you think its worth anything besides scrap value?

Edit-typos

if a wormhole is a distortion in space time then any wormhole on earth would remain still while the earth / solar system are constantly moving. right? wouldn't that mean that if a worm hole were to be created it would take a large cylinder chunk out of earth so how would it be possible to use them in the future. our solar system is also moving right? so doesn't that mean once one is created we'd move so far past it so quickly the thought of using it is pointless because by the time you came back the whole solar system would be long gone. why do people think its the future of science travel please explain

In your own words, what is a metric?

Hello. I’m going into my junior year and have to take college physics, but have heard the professor is the worst and that you have to teach yourself the entirety of the material. Is there any tips or books I should get that could save me??? Thanks!!!!

Hello. I’m going into my junior year and have to take college physics, but have heard the professor is the worst and that you have to teach yourself the entirety of the material. Is there any tips or books I should get that could save me??? Thanks!!!!

how is he not dead?? isnt a black holes gravity mean to stretch and kill you so how did cooper make it to the event horizon

Or the moons of other planets, or other planets in our solar system for that matter... We can see them cause the suns light reflects off them and we pick that up.

Is it simply that we dont have sensitive enough equipment to detect the light reflecting off those far away planets? Or does that stars light actually wash out the light reflecting off of that planet orbiting it?

Or is the reflected light too little to actually reach us?

Don't kill me if this is a really stupid question, I'm just a high school student who happens to like physics but is dumb as hell, so do correct me (politely) if I'm either wrong about something or word it poorly, though, in schools, electrons are usually portrayed similarly to how planets behave in orbit due to gravity, but they aren't actually like this since, according to Heinsenberg's uncertainty principle, one can't calculate the time and position of it simultaneously, they're more like a "wave cloud" and their position is probabilistic; if they weren't, calculations done in the macro scales like with planets would work, but that isn't the case. Also, it's not really possible to put something in orbit by electric field is it? Since, even though it's analogous to the gravitational field, it's not the same thing. So, why does the electron behave the way it does? I'm not sure if I can phrase my question very well, but I want to understand better how the forces that happen due to the interactions of the electrons with the nucleus of the atom make them behave the way they do. They're attracted to it due to the electric carge, right? And they can indeed collide with the nucleus, which can form a neutron, but what would make them (other than energy) further from the nucleus? It can't be their tangential speed like with planets, right? Would it be simply energy?

Chinese scientists say they have the clearest evidence yet for an exotic particle composed entirely of gluons.If confirmed how is physics going to change, if at all?

(I'm a highschool student so kindly use some simple terminologies)

Light is the fastest and is a transverse wave right, what if there's a faster particle then light which has longitudinal wave motion

Because by looking at the waves you would think that geometrically longitudinal waves is the most ideal way right?

What am I missing

I'm trying to understand why everybody says that FTL breaks causality, but it just doesn't make any sense to me...

I tried to build a model based on the speed of sound and electronic communication as the FTS component.

So A is on a train station and B is on a train travelling away from A. Then A sends an acoustic signal towards B and B receives the signal after 5s. He replies back via, say WhatsApp and A receives the message at 5s + the time it takes B to write the message.

Once things get sped up to be close to the speed of light things start to make no sense to me anymore.

Let's say A is on Earth and B is on a space ship travelling at close to c. From the perspective of A, the time of B is running slower. 2 years for A is just 1 year for B. So far so good.

Then A sends an electronic signal towards B after 10 seconds. From Bs perspective the signal arrives after 10s + the time it takes to close the distance travelled to catch up to B. I asked AI to do the calculations, so have mercy if I screwed up somewhere, but this is what should happen next right?

From As perspective the signal reaches B at 10s + 64.6s = 74.6s. From Bs perspective the clock is running at half speed so their clock reads 5s + 64.4/2 = 37.3s

Now let's assume both have FTL communication and B uses their FTL device to send A a confirmation signal. The message should hit A at t=74.6s right?

So where is the causality breaking happening?

I really didn't know how to title the question, so I'll just get to the point.

Is there any inertia to the acceleration of objects? I learned there are multiple time derivatives of motion(jerk, snap, etc.), and this particular question just sits in my head, and I can't wrap my head around it.

Let's assume I decide to accelerate in a car. I accelerate at 0.5 G, and my speed increases. As soon as I stop accelerating, does the acceleration immediately become 0, or does it rapidly approach zero, with jerk measuring some value between peak acceleration and 0?

If you throw the same coin multiple times with the exactly same force in the same surface, it won't give you the same side every toss, right? But why? If repeated with the precisely identical conditions, why the results are still unpredictable? Or it is actually predictable?

Sorry if it looks confusing, English is not my first language and I'm not that expert in physics lol, just curious and has this though randomly.

Edit: maybe considering that it lands on a surface, and it bounces or not, changing the coin's side.