nhaliday + relativity   33

Eternity in six hours: intergalactic spreading of intelligent life and sharpening the Fermi paradox
We do this by demonstrating that traveling between galaxies – indeed even launching a colonisation project for the entire reachable universe – is a relatively simple task for a star-spanning civilization, requiring modest amounts of energy and resources. We start by demonstrating that humanity itself could likely accomplish such a colonisation project in the foreseeable future, should we want to, and then demonstrate that there are millions of galaxies that could have reached us by now, using similar methods. This results in a considerable sharpening of the Fermi paradox.
pdf  study  article  essay  anthropic  fermi  space  expansionism  bostrom  ratty  philosophy  xenobio  ideas  threat-modeling  intricacy  time  civilization  🔬  futurism  questions  paradox  risk  physics  engineering  interdisciplinary  frontier  technology  volo-avolo  dirty-hands  ai  automation  robotics  duplication  iteration-recursion  von-neumann  data  scale  magnitude  skunkworks  the-world-is-just-atoms  hard-tech  ems  bio  bits  speedometer  nature  model-organism  mechanics  phys-energy  relativity  electromag  analysis  spock  nitty-gritty  spreading  hanson  street-fighting  speed  gedanken  nibble 
march 2018 by nhaliday
Is the speed of light really constant?
So what if the speed of light isn’t the same when moving toward or away from us? Are there any observable consequences? Not to the limits of observation so far. We know, for example, that any one-way speed of light is independent of the motion of the light source to 2 parts in a billion. We know it has no effect on the color of the light emitted to a few parts in 1020. Aspects such as polarization and interference are also indistinguishable from standard relativity. But that’s not surprising, because you don’t need to assume isotropy for relativity to work. In the 1970s, John Winnie and others showed that all the results of relativity could be modeled with anisotropic light so long as the two-way speed was a constant. The “extra” assumption that the speed of light is a uniform constant doesn’t change the physics, but it does make the mathematics much simpler. Since Einstein’s relativity is the simpler of two equivalent models, it’s the model we use. You could argue that it’s the right one citing Occam’s razor, or you could take Newton’s position that anything untestable isn’t worth arguing over.

SPECIAL RELATIVITY WITHOUT ONE-WAY VELOCITY ASSUMPTIONS:
https://sci-hub.bz/https://www.jstor.org/stable/186029
https://sci-hub.bz/https://www.jstor.org/stable/186671
nibble  scitariat  org:bleg  physics  relativity  electromag  speed  invariance  absolute-relative  curiosity  philosophy  direction  gedanken  axioms  definition  models  experiment  space  science  measurement  volo-avolo  synchrony  uniqueness  multi  pdf  piracy  study  article 
november 2017 by nhaliday
[1509.02504] Electric charge in hyperbolic motion: The early history and other geometrical aspects
We revisit the early work of Minkowski and Sommerfeld concerning hyperbolic motion, and we describe some geometrical aspects of the electrodynamic interaction. We discuss the advantages of a time symmetric formulation in which the material points are replaced by infinitesimal length elements.

SPACE AND TIME: An annotated, illustrated edition of Hermann Minkowski's revolutionary essay: http://web.mit.edu/redingtn/www/netadv/SP20130311.html
nibble  preprint  papers  org:mat  physics  electromag  relativity  exposition  history  mostly-modern  pre-ww2  science  the-trenches  discovery  intricacy  classic  explanation  einstein  giants  plots  manifolds  article  multi  liner-notes  org:junk  org:edu  absolute-relative 
november 2017 by nhaliday
Hyperbolic angle - Wikipedia
A unit circle {\displaystyle x^{2}+y^{2}=1} x^2 + y^2 = 1 has a circular sector with an area half of the circular angle in radians. Analogously, a unit hyperbola {\displaystyle x^{2}-y^{2}=1} {\displaystyle x^{2}-y^{2}=1} has a hyperbolic sector with an area half of the hyperbolic angle.
nibble  math  trivia  wiki  reference  physics  relativity  concept  atoms  geometry  ground-up  characterization  measure  definition  plots  calculation  nitty-gritty  direction  metrics  manifolds 
november 2017 by nhaliday
general relativity - What if the universe is rotating as a whole? - Physics Stack Exchange
To find out whether the universe is rotating, in principle the most straightforward test is to watch the motion of a gyroscope relative to the distant galaxies. If it rotates at an angular velocity -ω relative to them, then the universe is rotating at angular velocity ω. In practice, we do not have mechanical gyroscopes with small enough random and systematic errors to put a very low limit on ω. However, we can use the entire solar system as a kind of gyroscope. Solar-system observations put a model-independent upper limit of 10^-7 radians/year on the rotation,[Clemence 1957] which is an order of magnitude too lax to rule out the Gödel metric.
nibble  q-n-a  overflow  physics  relativity  gedanken  direction  absolute-relative  big-picture  space  experiment  measurement  volo-avolo 
november 2017 by nhaliday
What is the connection between special and general relativity? - Physics Stack Exchange
Special relativity is the "special case" of general relativity where spacetime is flat. The speed of light is essential to both.
nibble  q-n-a  overflow  physics  relativity  explanation  synthesis  hi-order-bits  ground-up  gravity  summary  aphorism  differential  geometry 
november 2017 by nhaliday
What is the difference between general and special relativity? - Quora
General Relativity is, quite simply, needed to explain gravity.

Special Relativity is the special case of GR, when the metric is flat — which means no gravity.

You need General Relativity when the metric gets all curvy, and when things start to experience gravitation.
nibble  q-n-a  qra  explanation  physics  relativity  synthesis  hi-order-bits  ground-up  gravity  summary  aphorism  differential  geometry 
november 2017 by nhaliday
GPS and Relativity
The nominal GPS configuration consists of a network of 24 satellites in high orbits around the Earth, but up to 30 or so satellites may be on station at any given time. Each satellite in the GPS constellation orbits at an altitude of about 20,000 km from the ground, and has an orbital speed of about 14,000 km/hour (the orbital period is roughly 12 hours - contrary to popular belief, GPS satellites are not in geosynchronous or geostationary orbits). The satellite orbits are distributed so that at least 4 satellites are always visible from any point on the Earth at any given instant (with up to 12 visible at one time). Each satellite carries with it an atomic clock that "ticks" with a nominal accuracy of 1 nanosecond (1 billionth of a second). A GPS receiver in an airplane determines its current position and course by comparing the time signals it receives from the currently visible GPS satellites (usually 6 to 12) and trilaterating on the known positions of each satellite[1]. The precision achieved is remarkable: even a simple hand-held GPS receiver can determine your absolute position on the surface of the Earth to within 5 to 10 meters in only a few seconds. A GPS receiver in a car can give accurate readings of position, speed, and course in real-time!

More sophisticated techniques, like Differential GPS (DGPS) and Real-Time Kinematic (RTK) methods, deliver centimeter-level positions with a few minutes of measurement. Such methods allow use of GPS and related satellite navigation system data to be used for high-precision surveying, autonomous driving, and other applications requiring greater real-time position accuracy than can be achieved with standard GPS receivers.

To achieve this level of precision, the clock ticks from the GPS satellites must be known to an accuracy of 20-30 nanoseconds. However, because the satellites are constantly moving relative to observers on the Earth, effects predicted by the Special and General theories of Relativity must be taken into account to achieve the desired 20-30 nanosecond accuracy.

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion [2].

Further, the satellites are in orbits high above the Earth, where the curvature of spacetime due to the Earth's mass is less than it is at the Earth's surface. A prediction of General Relativity is that clocks closer to a massive object will seem to tick more slowly than those located further away (see the Black Holes lecture). As such, when viewed from the surface of the Earth, the clocks on the satellites appear to be ticking faster than identical clocks on the ground. A calculation using General Relativity predicts that the clocks in each GPS satellite should get ahead of ground-based clocks by 45 microseconds per day.

The combination of these two relativitic effects means that the clocks on-board each satellite should tick faster than identical clocks on the ground by about 38 microseconds per day (45-7=38)! This sounds small, but the high-precision required of the GPS system requires nanosecond accuracy, and 38 microseconds is 38,000 nanoseconds. If these effects were not properly taken into account, a navigational fix based on the GPS constellation would be false after only 2 minutes, and errors in global positions would continue to accumulate at a rate of about 10 kilometers each day! The whole system would be utterly worthless for navigation in a very short time.
nibble  org:junk  org:edu  explanation  trivia  cocktail  physics  gravity  relativity  applications  time  synchrony  speed  space  navigation  technology 
november 2017 by nhaliday
If there are 3 space dimensions and one time dimension, is it theoretically possible to have multiple time demensions and if so how would it work? : askscience
Yes, we can consider spacetimes with any number of temporal or spatial dimensions. The theory is set up essentially the same. Spacetime is modeled as a smooth n-dimensional manifold with a pseudo-Riemannian metric, and the metric satisfies the Einstein field equations (Einstein tensor = stress tensor).
A pseudo-Riemannian tensor is characterized by its signature, i.e., the number of negative quadratic forms in its metric and the number of positive quadratic forms. The coordinates with negative forms correspond to temporal dimensions. (This is a convention that is fixed from the start.) In general relativity, spacetime is 4-dimensional, and the signature is (1,3), so there is 1 temporal dimension and 3 spatial dimensions.
Okay, so that's a lot of math, but it all basically means that, yes, it makes sense to ask questions like "what does a universe with 2 time dimensions and 3 spatial dimensions look like?" It turns out that spacetimes with more than 1 temporal dimension are very pathological. For one, initial value problems do not generally have unique solutions. There is also generally no canonical way to pick out 1 of the infinitely many solutions to the equations of physics. This means that predictability is impossible (e.g., how do you know which solution is the correct one?). Essentially, there is no meaningful physics in a spacetime with more than 1 temporal dimension.
q-n-a  reddit  social  discussion  trivia  math  physics  relativity  curiosity  state  dimensionality  differential  geometry  gedanken  volo-avolo 
june 2017 by nhaliday
Orthogonal — Greg Egan
In Yalda’s universe, light has no universal speed and its creation generates energy.

On Yalda’s world, plants make food by emitting their own light into the dark night sky.
greg-egan  fiction  gedanken  physics  electromag  differential  geometry  thermo  space  cool  curiosity  reading  exposition  init  stat-mech  waves  relativity  positivity  unit  wild-ideas  speed  gravity  big-picture  🔬  xenobio  ideas  scifi-fantasy  signum 
february 2017 by nhaliday
Einstein's Most Famous Thought Experiment
When Einstein abandoned an emission theory of light, he had also to abandon the hope that electrodynamics could be made to conform to the principle of relativity by the normal sorts of modifications to electrodynamic theory that occupied the theorists of the second half of the 19th century. Instead Einstein knew he must resort to extraordinary measures. He was willing to seek realization of his goal in a re-examination of our basic notions of space and time. Einstein concluded his report on his youthful thought experiment:

"One sees that in this paradox the germ of the special relativity theory is already contained. Today everyone knows, of course, that all attempts to clarify this paradox satisfactorily were condemned to failure as long as the axiom of the absolute character of time, or of simultaneity, was rooted unrecognized in the unconscious. To recognize clearly this axiom and its arbitrary character already implies the essentials of the solution of the problem."
einstein  giants  physics  history  stories  gedanken  exposition  org:edu  electromag  relativity  nibble  innovation  novelty  the-trenches  synchrony  discovery  🔬  org:junk  science  absolute-relative  visuo  explanation  ground-up  clarity  state  causation  intuition  ideas  mostly-modern  pre-ww2  marginal 
february 2017 by nhaliday
Albert Einstein - Five Books
"Like many geniuses, he was not particularly successful in his university training."
don't think that's really true
history  einstein  giants  physics  books  top-n  review  profile  list  recommendations  eh  relativity  letters  org:popup 
february 2017 by nhaliday
Are You Living in a Computer Simulation?
Bostrom's anthropic arguments

https://www.jetpress.org/volume7/simulation.htm
In sum, if your descendants might make simulations of lives like yours, then you might be living in a simulation. And while you probably cannot learn much detail about the specific reasons for and nature of the simulation you live in, you can draw general conclusions by making analogies to the types and reasons of simulations today. If you might be living in a simulation then all else equal it seems that you should care less about others, live more for today, make your world look likely to become eventually rich, expect to and try to participate in pivotal events, be entertaining and praiseworthy, and keep the famous people around you happy and interested in you.

Theological Implications of the Simulation Argument: https://www.tandfonline.com/doi/pdf/10.1080/15665399.2010.10820012
Nick Bostrom’s Simulation Argument (SA) has many intriguing theological implications. We work out some of them here. We show how the SA can be used to develop novel versions of the Cosmological and Design Arguments. We then develop some of the affinities between Bostrom’s naturalistic theogony and more traditional theological topics. We look at the resurrection of the body and at theodicy. We conclude with some reflections on the relations between the SA and Neoplatonism (friendly) and between the SA and theism (less friendly).

https://www.gwern.net/Simulation-inferences
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september 2016 by nhaliday

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