If you saw Interstellar, you know one of the most interesting storylines was about timeshifting near a massive black hole. The astronauts were near a super-massive gravitational field, on a planet next to a giant black hole, and as a result, time slowed considerably for them. But here's my dumb question: Doesn't that mean that the force of gravity would have had to be HUGE on the planet itself, thereby crushing the astronauts? And if not -- if the planet was orbiting the black hole at a distance that reduced the effects of the supernova's field at the planet's surface, why would they have been subject to such significant time distortion? Is that due to the required speed at which the planet would have had to be rotating around the planet? If so, then the time dilation, while equivalent, isn't due to gravitational effects, but to special relativistic effects of differential speed. How does gravity from a giant object like a super massive black hole dilate time but not manifest itself greater than about 1G where the observers experiencing the time dilation are located?
No - the planets were orbiting, so there is no net gravitational force. (The planets are effectively in free-fall.) There is, however, a tidal force, and thus it would tend to try to rip the planet apart. Close enough to the black hole itself it would even try to rip the astronauts apart. For the same reason that ISS astronauts don't feel the 1G that the Earth provides.
Thanks, Bill, I kinda figured it had something to do with being in free fall. But I've been out of the game for so long, I'm way too rusty. I guess it's just as if you jumped of a skyscraper. You'd feel weightless (ignoring the feel of wind friction) for about as long as you'd take to splat on the ground. But ... you're still in the sway of time as governed by our 1G field. Still true, I assume, is the fact that the effects of gravity diminish as the square of the distance from the center of the singularity, and therefore so does the effects of time dilation.
The other factor to keep in mind is that gravitational time dilation is not related to the local gravitational strength but to the difference in gravitational potential. Gravitational time dilation near for a black hole is related to sqrt(1-r0/r) where r0 is the event horizon radius. So for example, at an r of 2r0, the time dilation factor is 0.707 and at 4ro it is 0.866 just a 22% difference. however the gravitational strength from 2r0 to 4r0 differs by a factor of 4. It is in fact possible to have a lower weaker gravity and a greater time dilation. An example would be Earth and Uranus. Because of Uranus' low density, its surface gravity is less than that of the Earth's, however, because of its much greater mass, the surface of Uranus is in a deeper gravity well than the Earth's (The Escape velocity from Uranus is greater than it is from Earth.) As a result, a clock sitting on the surface of Uranus would run slower than one on the Earth, even though it would weigh slightly less than it would on Earth.[/tex] But you are right in that the orbital speed would factor in also. Taking this into account, the time dilation for a circular orbit works out to sqrt(1-3r0/2r) Now it also works out that objects can only orbit a BH at distances greater than 1.5ro and as you get closer and closer to this limit gravitational time dilation gets stronger and stronger. at 1.51 r0 it is 0.08138, at 1.501 r0 it is 0.0258, at 1.5001 it is 0.0082, etc. I haven't seen the movie, so I don't know what time dilation factor they are dealing with or how massive a black hole they are using, so I don't know what exact numbers would go here.
A little more information. For the Schwarzschild coordinates the last possible stable orbit is at r=6M with the Schwarzschild radius at r=2M. It's possible to establish a knife edge orbit between r=2M and r=6M by firing rockets to stabilize an orbit between r=6M and r=2M. The coordinates you wrote down (3r_o/2r)^1/2 can be written like this dTau/dt = (1-3r_o/2r)^1/2 = (1-3*2M/2r)^1/2 = (1-3M/r_shell)^1/2. This includes the deta tick ratio due to the clocks position in the gravitational well and the relative velocity between the clocks [dTau/dt_bkkpr]. So somebody wanting to know what the different tick rate between the ships clock and the remote observers clock you can use this formula. Setting the remote observers tick rate at 1. M_solar mass = 1477meter. Derived from the effective potential of the equation of motion The derivation Put the derivative of the effective potential term (from the equation of motion) into quadratic form (to find critical values) r*^2 - L*^2r + 3L*^2 = 0 Where r* = r/M, and L* = L/mM Then divide through by L*^2 and manipulate to get r*^2/L*^2 = r* - 3 [saving this for a later substitution] Setting dr = 0 in the Schwarzchild metric and substituting dphi = (L*/r*^2)dTau the metric becomes dTau^2 = (1 - 2/r*)dt^2 - (L*^2/r*^2)dTau^2 To find the ratio dTau^2/dt^2 divide through by the bookkeeper time dt^2 and simplify to (dTau/dt)^2 = (1 - 2/r*) / (1 + L*^2/r*^2) Now substitute 1/(r*-3) for L*^2/r*^2 and simplify to dTau/dt = (1 - 3M/r)^1/2
Still another factor to bear in mind is that Hollywood movies seem to have no sense of obligation to keep things scientifically accurate. They'll have happen whatever suits their storyline and the drama. Remember how Gravity was panned for ignoring the great distances that must have been involved in its story lines. Things that would have been thousands of miles apart appeared to be five minutes away. That's just one example. There are thousands of others.
[QUOTE="Still another factor to bear in mind is that Hollywood movies seem to have no sense of obligation to keep things scientifically accurate. [/QUOTE] To the credit of the writers/producers of Interstellar, they engaged Kip Thorne to weave actual science into their script. That's kinda cool.
Shoot! Gilligan's Island had that! Unexpected storms, (meteorology), the courage of the fearless crew (psychology) uncharted desert isles (geography and navigation) coconuts falling from trees and hitting , mostly The Skipper on the head (physics and botany), innovative use of bamboo and thatched grass, bamboo bicycle-power electricity and radio battery re-generation, a professor who actually said scientific things nearly every time he spoke... shall I continue?
I haven't seen the movie, but I have heard from a few people that it is very thought provoking. These individuals knew next to nothing about relativity, and were fascinated by its depiction in the movie. I hope they actually got the science right. It seems to be sparking some interest in people who otherwise would have never thought about such things.
Gravitational effects on time could be ignored for science/engineering purposes be until the advent of GPS technology using orbiting satellites. This statement might be overlooking some critical laboratory experiments. The clock frequencies in the GPS satellites are adjusted for gravitational effects due to being thousands of miles(circa 23000?) from the Earth. Those systems would be incorrect by many miles in a few days. I would not bet money on my estimates of the error, but I know it would be significant enough to render GPS systems unusable. BTW: For a while (or maybe still), the US government deliberately introduced some error in their GPS systems.
Real-World Relativity: The GPS Navigation System The GPS satellites have to take their speed and their altitude into account. Their speed makes the satellites clocks 7 microseconds per day slower than Earth based and their altitude makes them 45 microseconds faster for a net of 38 microseconds per day. President Clinton stopped the "intentional degradation" of the GPS system back in 2000.
TBodillia's time dilation calculation is correct, but anything (like the Earth and all of its satellites) orbiting 93 million miles from the sun also suffers a measurable gravitational time dilation from that effect. The Shapiro delay between the orbits of Venus, Mercury and Earth was likewise an early confirmation of the time dilation effects of General Relativity. For a deep space probe like the ones that have left our solar system, the telemetry must compensate for time dilations of that magnitude as well. The "intentional degradation" also known as "selective availability" for GPS is still in effect near large military bases and other random targets of interest to terrorists or other military powers. It is there to assure that precision bombing is something reserved to our own military, from whose funding both GPS and the internet were initially developed.
Fair enough. It's like the King's palaces and military installations in Saudi Arabia appear on no publicly available maps. The Saudis figure they are just playing into the hands of their potential adversaries by publishing the exact locations. Very sensible really. Why would anyone need the exact location of such places, where they are not welcome to visit, unless they were up to no good?
Man Spends Holiday in U.S. After Arrest as Spy Back in 1997, Qualcomm was taking land surveys in Russia in preparation for installation of cell phone towers. The problem was/is "Under Russian law, survey measurements accurate to within 30 yards are considered a state secret." Even before Clinton removed the "intentional degradation", everybody had already figured out work arounds. It was just a little extra bit of programming. I can hit Google maps, satellite view, and pull up great maps of King Abdulaziz Historical Centre, Riyadh.
Time is only the perspective of what the speed of things happening around ones self. It has no phisical effect on matter in the universe . The universe has a central point, that is where matter started outward in all directions at once, no matter of the reason for the propulsion. People speak of a big bang but now one really knows the process.post: 3243943, member: 279778"]If you saw Interstellar, you know one of the most interesting storylines was about timeshifting near a massive black hole. The astronauts were near a super-massive gravitational field, on a planet next to a giant black hole, and as a result, time slowed considerably for them. But here's my dumb question: Doesn't that mean that the force of gravity would have had to be HUGE on the planet itself, thereby crushing the astronauts? And if not -- if the planet was orbiting the black hole at a distance that reduced the effects of the supernova's field at the planet's surface, why would they have been subject to such significant time distortion? Is that due to the required speed at which the planet would have had to be rotating around the planet? If so, then the time dilation, while equivalent, isn't due to gravitational effects, but to special relativistic effects of differential speed. How does gravity from a giant object like a super massive black hole dilate time but not manifest itself greater than about 1G where the observers experiencing the time dilation are located?[/QUOTE] Time is a Time is only thr
Time is not effected by gravity, time is a mental scale used by the observer to compulate flux of matter around it.sir. Robert L. Bobo J. R., post: 3269420, member: 281218"]Time is only the perspective of what the speed of things happening around ones self. It has no phisical effect on matter in the universe . The universe has a central point, that is where matter started outward in all directions at once, no matter of the reason for the propulsion. People speak of a big bang but now one really knows the process.post: 3243943, member: 279778"]If you saw Interstellar, you know one of the most interesting storylines was about timeshifting near a massive black hole. The astronauts were near a super-massive gravitational field, on a planet next to a giant black hole, and as a result, time slowed considerably for them. But here's my dumb question: Doesn't that mean that the force of gravity would have had to be HUGE on the planet itself, thereby crushing the astronauts? And if not -- if the planet was orbiting the black hole at a distance that reduced the effects of the supernova's field at the planet's surface, why would they have been subject to such significant time distortion? Is that due to the required speed at which the planet would have had to be rotating around the planet? If so, then the time dilation, while equivalent, isn't due to gravitational effects, but to special relativistic effects of differential speed. How does gravity from a giant object like a super massive black hole dilate time but not manifest itself greater than about 1G where the observers experiencing the time dilation are located?[/QUOTE] Time is a Time is only thr[/QUOTE] Gravity
Time is affected by gravity, but time dilation is not observed within ones own FoR, only in relation to another FoR. An observer in low gravity, will observe a clock to be going slower in a stronger field. This effect has been confirmed beyond doubt. No, the Universe has no central point and no edges. The BB was an evolution of space and time itself.....It did not happen in a particular region of space....it evolved space. [and time] It in effect, happened everywhere at the same time. We may not know the how and the why of the BB, but overwhelming evidence supports the concept that the Universe evolved from a hot dense state.
