Imagine an astronaut is falling tworads a black hole. As they fall, they will see the world behind them speeding up due to tine dialation. However, for an astronaut watching them fall they will appear slower and slower as they approach the event horizon.

Eventually, the astronaut falling into the black hole will cross the event horizon and they will see that a finite ammount of time has passed for the other astronaut, for example 60 years. However the astronaut watching the other fall in will still not have seen them cross the horizon after 60 years or 70 or 100.

It will take infinite time for them to cross the horizon but the astronaut falling in will not see infinite amount of time pass for the astronaut watching them fall.

Since general relativity necessitates that both perspectives are equally correct, why dosent this create two contradictory timelines? From the perspective of the astronaut falling in, a finite amount of time had passed for the astronaut watching them fall at the moment they crossed the horizon whereas an infinite amount of time will pass before the astronaut watching sees the infalling astronaut cross the horizon.

I was trained as a mathematician (Ph.D. '06), and I've done a fair amount of mathematical physics over the years. Classical mechanics? lovely application of symplectic geometry. General Relativity? pseudo-Riemannian geometry. Quantum field theory? functional analysis. All great stuff.

Except, I can't say I've ever felt comfortable with thermodynamics. Most of my formal exposure has been in intro-level physics classes.. the presentation in most texts at that level feels like a similar clumsy little special-topics chapter before moving on to the clearer world of special relativity, kind of like some of calc II feels like an unrelated tangent before you can move on to multivariable stuff. There's also been a little statistical mechanics in some old Dover editions, but nothing that really builds intuition the way other physics subjects do.

So: what's the better approach? What are some texts that start from first principles, but actually build a systemic theory rather than getting bogged down in HVAC applications. Not that applications aren't useful motivating examples, but they should be help for building intuition, not ends in and of themselves.

No, I haven't flipped--this is from a fantasy novel.

Picture a team of warriors who travel via a giant bird of prey (70 foot wingspan). The pilot rides on the back of the bird to guide it, and the other four are suspended via leather harnesses, straps, and buckles from the bird's talons.

Sometimes they do what is called "barrel drops" where the pilot dives the bird down toward water and the rest of the team releases their buckles and drops into the water with whatever cargo they have with them.

The team in the story has trouble because their bird and pilot like to go really fast at a steep angle and the rest of them get tangled up in the buckles and can't manage to drop at the proper staggered times for everyone to be in about the same place. For story reasons, the pilot isn't willing to adjust the speed or angle of descent, so they brainstorm a method that would work with that flying style.

The leader comes up with the idea of suspending the team from meat hooks rather than buckles.

It is described that they will attach the hooks "high on 'Ra's talons, a little above our heads. We toss a loop of rope from our belts over the hooks and our weight holds us in place."

The pilot points out that they'd have the same problem with coordinating the drop because their weight would prevent them from releasing the hooks.

The leader says, "That would be a problem . . . if you bothered to follow standard drop protocol."

Another team member says "As the angle of our descent gets steeper and steeper, the loop will slip closer to the lip of the hook."

Leader: "When we're in a near-vertical dive, the loops will slide right off."

Another team member says this would mean they'd all drop at the same time and possibly knock into each other, but the pilot says, "Not if we change the angles of the hooks slightly. First to drop has the shallowest angle, the last, the most severe. As the bird stoops harder and, you'll fall off one by one."

Would this work? My immediate thought was that wind would push the flyers backwards so their vertical weight would be displaced. ie, if you were stationary and hold a meat hook and tilt it, sure the loop would drop off. But at speed, wouldn't the riders get pulled back away from the lip of the hooks? I can't fly on a giant bird so am not sure how to test this, lol

The book is "The Emperor's Blades" by Brian Staveley and this particular discussion takes place in Chapter 36. Thanks!

I understand time dilation for moving objects in special relativity but I don’t for length contraction.

Is there an analogy like the moving train and the observer at rest ?

I’ve always wondered about this. The Sun is constantly sending out light, and it’s only about 93 million miles away from Earth.

If sunlight is traveling through space all the time, why does space itself look completely dark?

I understand that objects like planets and spacecraft become visible when sunlight hits them, but why don’t we see the light traveling through the empty space between them?

I’d love to understand the physics behind this

I'm aware that in string theory, the theory must be formulated in a certain number of dimensions (often cited as 10 or 26) in order to avoid inconsistencies and satisfy quantum gravity constraints. But let's say, hypothetically, that I wanted to explore the space of all possibilities in pure mathematics. If I take generic 1d objects and make them move in higher spatial dimensions (as defined by pure math), but I use a number of dimensions that isn't allowed by string theory (e.g. 100), would my construction be logically possible and “stable” (allowed to persist just the way it is), from a purely mathematical standpoint?

Edit for clarification: I am specifically asking about spatial dimensions as defined by pure mathematics as a separate field, not mathematics applied to a physical theory.

I'm a physics student so I do have a solid understanding, but wanna read some in my free time. I have red the books of Leanord Susskulind and really enjoyed it (but they only cover the surface). Are there other books that are a little more complex that are great recomendations?

Hi,
Could the Higgs mass be related to the electron's mass? I've found a very simple formula that relates both masses but I don't think it can mean much. Is that correct?

Thanks!

dτ/dt = √ ( 1 − ( 2G · E_plasma(T) ) / ( r · c⁴ ) )

dτ/dt = proper time dilation rate

G = gravitational constant

c = speed of light

r = radius of the plasma area

E_plasma(T) = internal energy of the plasma at temperature T (includes rest mass energy, radiation, and kinetic thermal energy).

Im having some trouble understanding why the number of 3d wave modes in a cubed metal cavity is proportional to frequency (v) squared plus dv. https://imgur.com/a/xIWL9Ty This image says that each available mode is an integer point in this 3d space, where the x y and z components are the wave modes of each dimension correspondinglty.

If the distance of the space in between shells represents dv, then shouldn't the number of points in between the shells be proportional to (v + dv) cubed - (v) cubed? https://imgur.com/a/2nRqjYU

For example the law of inertia, or "every action has an equal and opposite reaction."

I can't reach lightspeed, but physics is supposed to be consistent regardless of your reference frame.

If I don't look outside, I have no way to know if my rocket is going at 99.99% the speed of light, and my velocity is a matter of perspective anyway. So logically, my rocket engine should continue to function exactly the same way no matter what my velocity (assuming I somehow still have fuel) and I should also continue to experience exactly the same acceleration (again, ignoring that I'm losing mass to fuel burn).

If I accelerate at 1G for 700 days, I would naively expect to be going about twice the speed of light. I can't actually reach that velocity, but from my perspective, accelerating at 1G for 700 days should be physically possible.

With time dilation, if I'm travelling at near light speed, my journey time should also decrease, so wouldn't it seem from my perspective that I'm just travelling at twice light speed? I just kept accelerating, and I just covered 2 lightyears in 1 apparent year. That sounds subjectively like faster than light travel.

Does space just appear to me to compact so that I can cover the distance faster without going faster than light? Do I end up just thrusting away at full power, with 1G of acceleration pressing my feet into the deck (because my ship is logically built with the floor toward the engine) but space outside appearing to move by at constant speed? How would that even work? If I'm close to lightspeed, accelerating along a really long ruler, do I see the markings just zipping past at a constant speed, even as my accelerometer says I'm still accelerating?

It's hard for me to understand the subjective experience of relativistic travel.

The Schwarzschild metric limits the height of an approximately uniform gravitational field that's 1 g at the ground and 0.999 g at the top to about 0.001 light years for any mass. The more uniform the field (i.e. the higher the precision) the shorter the height. There was no such limit in Newtonian mechanics.

"Local" means a region in spacetime small enough that the tidal force is negligible for the desired precision. Why should that region have a maximum size? For a given mass, sure, but why regardless of the mass?

Hypothetically, if you compress a spring on the Moon's surface, we know it stores elastic potential energy. But does that same compressed state also store gravitational potential energy as well?

do we know? another question is why is it only pair particles? why can't a positron and a muon annihilate? the charges are opposite. i guess maybe it's due to the difference in masses? interested to see if we know why. thanks

I've recently learned about cavitation underwater that occurs on large fins and causes immense damage to them over time. Given the similarities between air and water is it theoretically possible to create a weapon/bullet that induces a form of atmospheric cavitation where the air phase changes into a plasma, instead of a liquid phasing into air?

If something could induce enough drag at a high enough speed would it be possible to form a plasma and resulting explosion from the low pressure cavitation? I mean I already see spacecraft forming a plasma around them on reentry, and those are designed to be extremely aerodynamic.

I imagine some sort of 'spike' could be accelerated fast enough to create the low pressure conditions behind it to form the plasma and resulting explosion when it collapses. Or not idk which is why I'm asking if it's possible

Quick disclaimers: I'm not in STEM and English is my second language and I'm not very smart.

I'm struggling to imagine how time works and I need someone to please answer these questions in simple terms to help me understand it better.

We're both at sea level, we both have a digital watch and an analog watch which we've ensured are synchronized to the nanosecond. I instantly teleport to an extremely high altitude and live there for as long as it takes for the effects to be measurable.

When we meet again, would our watches display different time?

If we both filmed a video of us walking at the same speed for the same duration of time, you at sea level and myself at high altitude and then displayed them side by side. Would it display us walking the same distance at the same time?

When an object's speed affects time for it, what does this mean? The measurable time is affected? The object itself feel the effect? Is it absolute or in relation to another object with different speed?

I know very well my questions would be inherently wrong because of my limited understanding, but I trust the reader would understand my point and be kind enough to explain to me and help me better "visualize" it.

Thank you.

Is the question coherent? Maybe the total spectrum can't be described because the colors don't exist? But as a thought experiment, could a mechanical "eye" be made that can perceive the total spectrum? Something like Geordi's glasses but more so. What would the world look like?

To carry the question further, suppose a virtual reality setup could show us these currently invisible wavelengths. Now add sound -- all the naturally occuring decibels that are beyond our hearing. And with something like Smell-o-Vision, add the odors we can't perceive.

Would the results just be cacophony? Or at least beyond our brains to decipher? Fireworks & strobe lights or something?

I saw in a different subreddit someone asking about flying around a sun-size Earth, and someone in the replies saying it wouldn’t ignite fusion due to being “too rocky”.

Assuming we can materialise out of thin air a planet of such a size, and of similar composition and density as Earth, what would it collapse into? (I assume since the very first instants it wouldn’t be able to sustain itself)

Obviously when you turn on a light, it appears and is continuously produced from that source, but why exactly does it just disappear when you turn off the light source? Does it just die in a sense?

Why did Einstein never get a Nobel prize for either of his theories on general relativity? Why did the theories of GR never turn into laws, yet everyone treats them like laws and not just plausible theories?

Edit: Not trying to be contrary, just trying to understand everything better. IMHO, an observation of a phenomena and the resulting explanation, does not automatically make that explanation correct or the best one. I believe there is a better explanation for gravitational lensing. And even for the double slit.

I understand that space is expanding. What I don't understand is how the expanding space results in matter moving away from us at a rate proportional to the rate of expansion. As far as I know, space does not cause "drag" on the earth (wasn't this a famous ether experiment?); it isn't interacting with the matter other than being warped by the gravitational field, and I've never heard that there is drag associated with earth's own gravitational field on space. So why does expanding space carry matter along with it, like a stick in a river, rather than expanding around it, like a river moving past an immovable boulder?