Dope Tech Episode 2

<<@MinutePhysics says : Download Opera for free: https://opr.as/Opera-browser-minutephysics>> <<@moustafaali12 says : This is an excellent and classic physics scenario! Let's break it down, because it touches on both relativistic physics and human limitations. The Short, Direct Answer A spaceship accelerating at a constant 8 Gs (as felt by its crew) will never reach light speed. According to Einstein's theory of relativity, it can get arbitrarily close to the speed of light, but it can never reach or exceed it, no matter how long it accelerates. What we can calculate is how long it would take (from the crew's perspective) to reach a very high percentage of light speed. --- Key Concepts & Calculations 1. Constant Proper Acceleration: You've defined the condition perfectly. The ship accelerates so the crew feels a constant force of 8 Gs. This is called "proper acceleration." In the ship's frame of reference, they are pushing against their seats at 8 times Earth's gravity. 2. Relativistic Effects: As the ship's speed approaches light speed, time dilation and mass increase become extreme. From the perspective of a stationary observer (Earth), the ship's velocity increases more and more slowly, forever approaching c. 3. Ship Time vs. Earth Time: Due to time dilation, the crew will experience the journey very differently than observers back on Earth. Their clocks run slower. --- How Long to Reach 99% of Light Speed? Let's calculate the time it takes from the crew's perspective (ship time, τ) to reach a given fraction of light speed. The relativistic formula for velocity under constant proper acceleration (a) is: v(τ) = a * τ / sqrt(1 + (aτ/c)²) A more useful formula for the ship time (τ) needed to reach a given fraction (β = v/c) of light speed is: τ = (c / a) * atanh(β) where atanh is the inverse hyperbolic tangent. · Acceleration (a): 8 Gs = 8 * 9.8 m/s² ≈ 78.4 m/s² · Speed of light (c): ~299,792,458 m/s ≈ 3.00e8 m/s · c / a ≈ 3.00e8 / 78.4 ≈ 3.83 million seconds (about 44.3 days) Now let's calculate for different target speeds: Target Velocity (v) β (v/c) Ship Time (τ) Ship Time (Years) 90% of c 0.9 44.3d * atanh(0.9) 0.96 years 99% of c 0.99 44.3d * atanh(0.99) 2.2 years 99.9% of c 0.999 44.3d * atanh(0.999) 3.4 years 99.99% of c 0.9999 44.3d * atanh(0.9999) 4.6 years From the crew's point of view: In just over 2 years of constant 8 G acceleration, they would be traveling at 99% the speed of light. Each extra "9" (getting closer and closer to c) takes about an additional 1-1.5 years of their time. --- The View from Earth (Stationary Observer) From Earth, due to time dilation, the trip would appear to take much longer, and the ship's acceleration would appear to slow down as it approached c. The Earth-time (t) to reach a given velocity is: t = (c / a) * sinh(atanh(β)) = (c / a) * (β / sqrt(1-β²)) For the crew to reach 99% of light speed (β=0.99): t ≈ 44.3 days * (0.99 / sqrt(1-0.99²)) ≈ 44.3 days * 7.09 ≈ 314 days of Earth time just to get to that speed. To reach 99.99% of c, it would take over 35 years of Earth time, while the crew has only experienced about 4.6 years. --- Practical Human Limitations You identified the main one: 8 Gs is not survivable long-term. · 1 G is comfortable (Earth gravity). · 3-4 Gs is the limit for sustained acceleration over hours/days for well-trained, reclined astronauts. · 8 Gs is in the realm of extreme, short-duration fighter pilot maneuvers (minutes at most), with severe strain and risk of blackouts (G-LOC). A more realistic scenario uses 1 G of constant acceleration. · It provides the comfortable feeling of Earth gravity. · The math is elegant: c / 1g ≈ 1 year. So: · Ship time to reach 99% of c: ~ 2.5 years · Ship time to cross the galaxy (100,000 light-years from Earth's perspective): only about 12 years of ship time, thanks to time dilation and length contraction! Summary & Conclusion 1. Impossible Goal: Reaching exact light speed is fundamentally impossible for any object with mass. 2. Rapid Approach: With a brutal but physically possible (for short periods) 8 G acceleration, a ship could reach 99% of light speed in about 2.2 years of crew time. 3. Human Factor: Sustaining 8 Gs for years is biologically impossible. A 1 G acceleration is the sustainable maximum, which still allows for reaching 99% of c in a few years of ship time. 4. Relativity is Key: The real wonder is that constant acceleration like this, even at a modest 1 G, makes interstellar travel theoretically possible for the crew within a human lifetime, due to time dilation—though centuries or millennia would pass back on Earth. The ultimate limit isn't the laws of physics in this case, but the human body's ability to withstand the acceleration and the engineering challenge of providing fuel for years of constant thrust.>> <<@dvadcacpapoy says : because i ated the color of rainbow>> <<@D1gitalOutcast says : But are there black rainbows over Hawaii?>> <<@scp-foundation_05-14_Dr-scp says : Resonance Cascade: \[ m \frac{d^2x}{dt^2} + b \frac{dx}{dt} + kx = F_0 \cos(\omega t) \] Here, \( m \) is mass, \( b \) is the damping coefficient, \( k \) is the spring constant (or restoring force), \( F_0 \cos(\omega t) \) is the external driving force with frequency \( \omega \), and \( x \) is displacement. The natural frequency is \( \omega_0 = \sqrt{k/m} \). When the driving frequency \( \omega \) matches \( \omega_0 \), resonance occurs, and the amplitude grows. The steady-state solution’s amplitude is: \[ A = \frac{F_0 / m}{\sqrt{(\omega_0^2 - \omega^2)^2 + (b\omega/m)^2}} \] If damping \( b \) is small and \( \omega \approx \omega_0 \), \( A \) becomes very large, amplifying energy as \( E = \frac{1}{2} k A^2 \). In a Resonance Cascade, imagine this system isn’t isolated—energy from this oscillation feeds into another system. Now, couple this to a second oscillator (e.g., a nearby field or structure), modeled similarly: \[ m_2 \frac{d^2y}{dt^2} + b_2 \frac{dy}{dt} + k_2 y = \alpha x \] Here, \( y \) is the displacement of the second system, and \( \alpha x \) is a coupling term where the first system’s motion drives the second. If the first system resonates, \( x \) grows, increasing the driving force on the second. If \( \omega \) also matches the second system’s natural frequency \( \omega_2 = \sqrt{k_2/m_2} \), it too resonates, amplifying further. This cascade could chain across multiple systems, each feeding energy into the next, modeled as a set of coupled differential equations: \[ \frac{d^2x_n}{dt^2} + \gamma_n \frac{dx_n}{dt} + \omega_n^2 x_n = \beta x_{n-1} \] where \( n \) indexes each system, \( \gamma_n = b_n/m_n \), \( \omega_n^2 = k_n/m_n \), and \( \beta \) is the coupling strength. If damping \( \gamma_n \) is insufficient, energy exponentiates across the chain—a physical cascade. For a high-energy twist, consider a relativistic particle beam. The energy of particles follows \( E = \gamma m c^2 \), where \( \gamma = (1 - v^2/c^2)^{-1/2} \) is the Lorentz factor. If resonance synchronizes particle oscillations (e.g., via cyclotron motion in magnetic fields, \( \omega_c = qB/m \)), their collective energy could surge, destabilizing containment. Finally, tie this to spacetime. The energy-momentum tensor \( T_{\mu\nu} \) from this concentrated energy (e.g., \( T_{00} \approx \rho c^2 \), where \( \rho \) is energy density) enters Einstein’s field equations: \[ G_{\mu\nu} = \frac{8\pi G}{c^4} T_{\mu\nu} \] A spike in \( T_{\mu\nu} \) warps the metric \( g_{\mu\nu} \), potentially producing gravitational waves or stress. The cascade’s runaway energy thus has a physical footprint in spacetime curvature. In equations, a Resonance Cascade is a chain of resonant amplifications (\( A_n \propto F_{n-1} \)) across coupled systems, driving \( E \to \infty \) unless checked, with \( T_{\mu\nu} \) reflecting the chaos in spacetime. It’s a mathematical runaway rooted in oscillator physics>> <<@ProzacAkira says : double rainbow oh my god : 0>> <<@OmniScienceMind says : 🎉>> <<@sanular says : Check out birefringence. It is commonly used property to visually determining mineral characteristics in petrographic microscopy (not related to petroleum).>> <<@PotusImpact says : 👍 Liked! Wow, white rainbows are truly magical 🌫🌈✨. Feels like nature giving a special surprise to those patient enough to notice 😍. Sometimes I also like exploring “big impacts from small things,” like I do in my mini corner on Potus Impact 🏛💡 — it’s always fun to see the effects of decisions from an unusual perspective.>> <<@vidarton says : Double rainbow across the sky 🎶🎵>> <<@HypocriticalPigeon says : Yes, but is there Black Rainbows? /ref>> <<@SimplePanda93 says : Man, “slit” sounds like such a dirty word…>> <<@vvijatov says : Take it seriously! https://www.youtube.com/watch?v=5OiqCMoWbys>> <<@SergiMedina says : It's climate change. We're all gonna die.>> <<@rcrichard8969 says : fogbow isn't gay>> <<@Seeriosa says : >AI plug Yeah ok I'm unsubscribing>> <<@MV96_ says : Iris forgot her colored coat 😂 Or mistakenly took the one for the night to go around Selene 😂 (Yep, the Greeks called both the rainbow and the halo of the moon “iris”)>> <<@SimplySpacetime says : Time feels so obvious until physics tries to explain it — and suddenly, nothing makes sense anymore. ⏳” “If time doesn’t exist, maybe we’re just watching the universe update itself frame by frame. 🌌>> <<@Brockbuiltmore says : why do some rainbows turn white? because they are freakin racist. thats why.>> <<@arnonymous7211 says : Double Rainbow?>> <<@Italianjedi7 says : So fascinating.>> <<@HighTechRedneck29 says : How fast would you have to spin a steak for the friction from the air to cook it>> <<@You2oob says : Cool>> <<@Fourestgump says : My guess was that the white rainbow came from a pot of white gold>> <<@turbotasticsciscratcher says : the PUN in 0:19...>> <<@graduator14 says : Incredible!>> <<@mollof7893 says : I allready watch this on Opera>> <<@marksusskind1260 says : Light is notoriously difficult (impossible) to pin down. Instead of breaking down into a typical pattern of colors, the colors return to being mixed (rather than becoming a spectrum of laser-ly lights, I s'pose).>> <<@goneutt says : I expected it to be about moonbows.>> <<@HannahLemurson says : I'm starting to think my voice training text might not 100% complete and accurate. _"When sunlight strikes raindrops in the air, they act as a prism and form a rainbow._ _A rainbow is a division of white light into many beautiful colors._ _These take the shape of a long round arch with it's path high above,_ _and its ends apparently beyond the horizon._ _There is, according to legend, a boiling pot of gold at one end._ _People look, but nobody ever finds it."_>> <<@timeless8 says : Do not watch this video on a good sound system that has bass. Something really weird is going on and makes the monologue sound awful. Watch this on your phone or some other device that only can produce treble.>> <<@moogamooga2100 says : This is fascinating. I’d never even heard of a fogbow until now.>> <<@CaritasGothKaraoke says : Pacific Northwest here. We do see concentric rainbows. Quite often. I’ve seen up to 4.>> <<@ChadFaragher says : Color is fundamentally a perceptual experience. Light has wavelengths. We add the color. White, black, magenta - all in your head!>> <<@KuruGDI says : Can we just stick to that white rainbows will only occur around Halloween? That sound much better than the physically accurate description.>> <<@alexzan13 says : do I get a senior discount if I ask for a double rainbow reference?>> <<@ooqui says : It's a bit sad that even the most perfect rainbows are relatively colorless for tetrachromats. A rainbow doesn't show me even 1% of all the hues that I can optimally see. It still has color, but not nearly as much as it could have. A tetrachromatic rainbow would have to be spherical by the way, with 2-dimensional hues, which is physically improbable.>> <<@CheeseAlarm says : I saw one of these in Finland once. It was very cold, maybe -20C. Possibly tiny ice crystals.>> <<@PaaAL says : Nah... it's just a regular rainbow, except it's in Poland... :-D>> <<@dykam says : Wild. Besmart released a video two days ago about Mars' blue sunsets vs Earth sunsets, and this is so similar yet so different.>> <<@Chad_Thundercock says : So the widest slits have had rhe most light run through them? Miles and miles of light.>> <<@WesleySmith-i4q says : Upon seeing a rainbow, I will now always think about interference. Thanks...>> <<@skenzyme81 says : Awesome, now we just need to do this to the Month of June.>> <<@vidividal says : Isnt it the same way we see clouds white? I thought Mie scattering was playing a part in this… am I wrong?>> <<@soejrd24978 says : Why are you talking at 150% speed, this is unwatchable..>> <<@tristandarsaf2008 says : Ungays the rainbow>> <<@klazzera says : because they are privileged?>> <<@HW-ow9zp says : How do you have a 4 minute video with paid promotion in it hahaha. You aren't even pretending to be showing anything valuable>> <<@janiselmeris5705 says : Opera cannot get the videos to play back without manual hacking (search "The Videos Don't Play Topic" in Opera forums) because of proprietary codecs (although Chromium and Vivaldi can, for example), I wander how they can afford advertisement.>> <<@mrjoe332 says : Companies on the First of July>>