|
Science and Astronomy Questions
|
|
| steeljaw354 | Date: Tuesday, 11.10.2016, 10:31 | Message # 841 |
 World Builder
Group: Users
Pirate
Messages: 862
Status: Offline
| Watsisname, I understand now.
|
| |
| |
| DoctorOfSpace | Date: Tuesday, 11.10.2016, 20:30 | Message # 842 |
 Galaxy Architect
Group: Global Moderators
Pirate
Messages: 3600
Status: Offline
| I think this is more directed towards Watsisname, but I welcome others input.
While watching a rendering of a warp bubble the antigravity region of the bubble appeared to become disconnected from the rest and move on its own.
This made me wonder what one would perceive of an object moving at superluminal velocities.
How would an object appear to someone if it exceeded the speed of light?
Does the object simply vanish once it exceeds c, does one see it run in the reverse direction, or would something else happen entirely?
This is assuming it had a way to reach c and exceed it and assuming you could actually see the object.
Intel Core i7-5820K 4.2GHz 6-Core Processor
G.Skill Ripjaws V Series 32GB (4 x 8GB) DDR4-2400 Memory
EVGA GTX 980 Ti SC 6GB
|
| |
| |
| Destructor1701 | Date: Tuesday, 11.10.2016, 21:01 | Message # 843 |
|
Pioneer
Group: Users
Ireland
Messages: 533
Status: Offline
| As I understand it, the first photons emitted by the ship that could possibly reach you would be the ones emitted as the ship passed its nearest flyby range to you.
So it would appear to pop into existence at that location.
Then, the next photons to reach your eyes would be from the moment both before and after the ship passed closest approach.
So it would split into two images as soon as it appeared, and both would recede at what appeared to be FTL velocities from one another. The forward version may appear to recede faster, not sure.
As to the gravitational lensing distortion and doppler colour/wavelength distortions, I couldn't begin to guess.
|
| |
| |
| Watsisname | Date: Thursday, 13.10.2016, 07:45 | Message # 844 |
 Galaxy Architect
Group: Global Moderators
United States
Messages: 2613
Status: Offline
| Destructor has it right.  The object would appear to suddenly pop into existence and split in two -- one moving backwards and the other moving forwards.
Which one appears to move faster? Let's work it out.
Consider a particle moving in a straight line at twice the velocity of light. The particle passes by an observer (at rest) with a closest approach of one light second distance.
Let t=0 be the time (in the rest frame) that the particle was at its minimum distance. Then at t=1s, it has moved a distance of 2 light seconds further along. And at t=-1s, it was 2 light seconds back.
When does the observer receive the light from these three moments (t=-1, 0, and 1)?
From the particle at t=0 to the observer it is a distance of 1 light second, so the light arrives at t=1s.
By Pythagorean theorem, the distance from the particle at t=1 to the observer is sqrt(12 + 22) = sqrt(5) ~2.24 light seconds. By symmetry, the distance from the observer to the particle at t=-1s is the same.
The light from the particle at t=-1 reaches the observer at -1+2.24 = 1.24s
The light from the particle at t=1 reaches the observer at 1+2.24 = 3.24s
Therefore the observer sees it take 2.24 seconds for the particle "moving forward" to progress one light second of distance, while it only takes 0.24 seconds for the particle "moving backwards" to progress the same distance. This one seems faster than light.
Pretty weird!
Added: In fact, this very mechanism of the particle seeming to move faster than light on its approach part holds true even for particles moving slower than light. We see the effect with relativistic jets from active galactic nuclei, pointed in our direction. For example, the jet of M87. (See bottom of page.)
|
| |
| |
| PlutonianEmpire | Date: Friday, 14.10.2016, 06:30 | Message # 845 |
 Pioneer
Group: Users
United States
Messages: 475
Status: Offline
| I was working on one of my own custom planets, when I was wondering about the breathability of my atmosphere for that world.
My composition for a surface pressure of 1.62 atm: 0.976 atm N2 (60.2 % ) , 0.459 atm O2 (28.3 % ) , 0.112 atm H2O (6.92 % ) , 0.0745 atm Ar (4.59 % ) , 221 ppm CO2, 3.8 ppm SO2, 1.68 ppm H2S. Obviously my question involves the final two gases. I tried to follow the table in the Breathable Atmosphere thread, but didn't want to kill humans trying to live there. I do know that SO2 and H2S are stinky gases.
So is this planet livable? And what exactly might the air smell like there?
Specs: Dell Inspiron 5547 (Laptop); 8 gigabytes of RAM; Processor: Intel® Core™ i5-4210U CPU @ 1.70GHz (4 CPUs), ~2.4GHz; Operating System: Windows 7 Home Premium 64-bit; Graphics: Intel® HD Graphics 4400 (That's all there is :( )
Edited by PlutonianEmpire - Friday, 14.10.2016, 06:35 |
| |
| |
| Watsisname | Date: Friday, 14.10.2016, 10:31 | Message # 846 |
|
Galaxy Architect
Group: Global Moderators
United States
Messages: 2613
Status: Offline
| It would smell like burnt matches and rotten eggs (the sulfur dioxide and hydrogen sulfide gases, respectively -- both are above the odor threshold). The air be safe to breathe for a while, but it would cause some respiratory problems.
It is hard to say if it would be permanently habitable. The problem is you have 1.62atm of pressure, so this is actually equivalent to 6.2ppm of SO2 at Earth's pressure. This is above the OSHA permissible exposure limit for an 8 hour work period (5ppm), but well below the "immediately dangerous to life and health" level of 100ppm.
The H2S concentration is equivalent to 2.72ppm at Earth's pressure. This isn't dangerous, but it would be unpleasant, both by the odor and its effect on your health (it irritates the eyes, causes headaches, loss of sleep, and overall just isn't very fun.)
Of the two, I think the SO2 would be the less pleasant at those concentrations.
|
| |
| |
| Huesudo | Date: Friday, 14.10.2016, 13:27 | Message # 847 |
|
Observer
Group: Users
Spain
Messages: 11
Status: Offline
| Quote Watsisname (  ) Of the two, I think the SO2 would be the less pleasant at those concentrations.
I don't know. I love the smell of burnt matches 
|
| |
| |
| Watsisname | Date: Friday, 14.10.2016, 15:43 | Message # 848 |
|
Galaxy Architect
Group: Global Moderators
United States
Messages: 2613
Status: Offline
| At several ppm concentration, continuously? I guarantee you don't  SO2 gas becomes sulfuric acid on contact with water. That includes in your eyes and mucous membranes.
|
| |
| |
| PlutonianEmpire | Date: Friday, 14.10.2016, 19:55 | Message # 849 |
|
Pioneer
Group: Users
United States
Messages: 475
Status: Offline
| Watsisname, so to get the partial pressure, I just multiply the percentages and ppm by the new atm pressure?
Specs: Dell Inspiron 5547 (Laptop); 8 gigabytes of RAM; Processor: Intel® Core™ i5-4210U CPU @ 1.70GHz (4 CPUs), ~2.4GHz; Operating System: Windows 7 Home Premium 64-bit; Graphics: Intel® HD Graphics 4400 (That's all there is :( )
|
| |
| |
| Watsisname | Date: Friday, 14.10.2016, 20:53 | Message # 850 |
|
Galaxy Architect
Group: Global Moderators
United States
Messages: 2613
Status: Offline
| Precisely. Partial pressure is the part of the total pressure caused by that particular gas. Usually it's the partial pressure that matters for things like toxicity or breathability.
|
| |
| |
| PlutonianEmpire | Date: Friday, 14.10.2016, 22:45 | Message # 851 |
|
Pioneer
Group: Users
United States
Messages: 475
Status: Offline
| Thank you!
Specs: Dell Inspiron 5547 (Laptop); 8 gigabytes of RAM; Processor: Intel® Core™ i5-4210U CPU @ 1.70GHz (4 CPUs), ~2.4GHz; Operating System: Windows 7 Home Premium 64-bit; Graphics: Intel® HD Graphics 4400 (That's all there is :( )
|
| |
| |
| Huesudo | Date: Saturday, 15.10.2016, 11:50 | Message # 852 |
|
Observer
Group: Users
Spain
Messages: 11
Status: Offline
| Quote Watsisname ( ) At several ppm concentration, continuously? I guarantee you don't wink SO2 gas becomes sulfuric acid on contact with water. That includes in your eyes and mucous membranes.
Hm... that doesn't sound so good 
|
| |
| |
| Watsisname | Date: Saturday, 15.10.2016, 12:35 | Message # 853 |
|
Galaxy Architect
Group: Global Moderators
United States
Messages: 2613
Status: Offline
| PlutoniamEmpire: Sure thing.
I was thinking back to the visual appearance of a faster-than-light particle, and decided to work out the appearance of its flyby a bit more rigorously. I wanted to gain some further insight to the problem, and there are a few interesting cases to explore. There's some math involved, so feel free to skip to the end if you just want to know the result.
To start, the time at which the observer receives photons from the particle, emitted from where the particle was at a position x, is
where 'b' is the 'impact parameter', or how much the particle missed the observer by, and β is the particle's speed as a fraction of the speed of light (β=v/c).
If we let b=1 (like one light second) and β=2 (twice the speed of light), then we get the following curve:
To interpret this, think of time (for the observer, in seconds) running vertically up the graph, and the apparent position of the particle is the horizontal axis (in light seconds). Notice the particle is never seen for times less than ~0.866 seconds. The particle first appears there at that time, at a position of -0.577 light seconds. In other words the particle appears just before its closest approach point. As time progresses forwards, the particle splits and is seen both in front of and behind that point. The steeper the curve, the more time passes for a given change in its apparent position. So a shallower slope represents a faster apparent speed. In this case, to the left (backwards) is faster.
Now it might be easier to visualize what's happening if I plotted its apparent position over time, but that turns out being messier. It must result in two functions (we see two particles), and isolating x requires solving a quadratic. Just to show it:
We could use that, but it's more of a hassle. Better to stick with time as a function of apparent position.
Let's think about the behavior of that function (the simpler one). For speeds much slower than light (β<<1), x/β will be huge and dominate over the radical. But x/β is a line, so the particle would have virtually constant apparent speed... as we expect for non-relativistic particles. The slope of this line is 1/β, and the inverse of its slope is the apparent speed, which is β. Makes perfect sense. For particles moving much slower than light, their apparent speeds are essentially their true speeds.
But what about as β increases -- the particle getting faster and faster, up to and beyond the speed of light? Can we find apparent speeds for any true speed? Yes we can. Let's use calculus. Differentiating time with respect to position (very backwards from what we normally do in calculus  ), we get
Its apparent speed, then, is the inverse of that:
That's the other reason why I began with t(x) instead of x(t)... differentiating x(t) is a lot less fun than differentiating t(x) and then inverting.
In the case where the particle moves right at or away from you (impact parameter b=0), this becomes super simple:
Minus signs for when the particle is approaching. And here's the graph to visualize it. This is apparent speed vs. true speed, now. Green for approach, yellow for receding.
Now we can figure out some interesting things very quickly. For instance, at what true approach speed is its apparent speed equal to the speed of light? Set v=1, and β ends up being 0.5. Half the speed of light. Its apparent speed after passing you is 1/3 of c.
As the speed goes up toward the speed of light, then its apparent approach speed goes to infinity, and its apparent recession speed rises to 1/2 of c.
Then for increasing speeds which are greater than the speed of light, the apparent approach speed decreases (but is backwards), and the apparent recession speed continues increasing. In the limit that the true speed goes to infinity, its apparent speed goes to the speed of light... in both directions simultaneously.
Neat-o!
[Of course, no particle or information can ever move faster than the speed of light -- that would violate causality for reasons of relativity. But we might instead imagine a long line of flash bulbs, preset to flash with a propagation speed arbitrarily faster than c. No information is traveling faster than c in this case, yet to an observer it looks like a light-emitting particle moving faster than light. In fact, thinking of it that way helps explain why the infinite-speed particle would seem to appear right in front of you and splits off in both directions at the speed of light. It's exactly like looking at an infinitely long chain of flash bulbs which all went off simultaneously. You see the flashes from successively more distant bulbs, with the flashes reaching you at the speed of light.]
|
| |
| |
| FastFourierTransform | Date: Sunday, 16.10.2016, 11:43 | Message # 854 |
 Pioneer
Group: Local Moderators
Spain
Messages: 542
Status: Offline
| WOW, Watsisname, take your fake internet points for making such an effort in calculating all of this and making the plots. Very elegant aesthetics by the way
Quote Watsisname ( ) [Of course, no particle or information can ever move faster than the speed of light -- that would violate causality for reasons of relativity. But we might instead imagine a long line of flash bulbs, preset to flash with a propagation speed arbitrarily faster than c. No information is traveling faster than c in this case, yet to an observer it looks like a light-emitting particle moving faster than light. In fact, thinking of it that way helps explain why the infinite-speed particle would seem to appear right in front of you and splits off in both directions at the speed of light. It's exactly like looking at an infinitely long chain of flash bulbs which all went off simultaneously. You see the flashes from successively more distant bulbs, with the flashes reaching you at the speed of light.]
My question is goig to sound a bit dumb but wouldn't some Cherenkov Radiation appear in this situation?
|
| |
| |
| Watsisname | Date: Sunday, 16.10.2016, 15:46 | Message # 855 |
|
Galaxy Architect
Group: Global Moderators
United States
Messages: 2613
Status: Offline
| Quote FastFourierTransform ( ) Very elegant aesthetics by the way
Thanks. I've taken a liking to optimizing things for the black forum background.
Quote FastFourierTransform ( ) My question is goig to sound a bit dumb but wouldn't some Cherenkov Radiation appear in this situation?
Not dumb at all!
For those unfamiliar, Cherenkov radiation is emitted by charged particles moving through a medium faster than the speed of light in that medium. A classic example is the blue glow in the water around nuclear reactors.
Supposedly, this would also apply to tachyons in the vacuum (the vacuum is a medium and it has the required properties, like an electric constant). However, this is a bit less than theorizing, since have never seen a tachyon, and according to relativity they can't exist. But we can pretend and assume our understanding of sub-light physics works the same for faster-than-light.
Right away we come up with some weird implications. For example, instead of slowing tachyons down like it does to normal particles, the Cherenkov radiation would speed the tachyons up! Tachyons of lower energy move faster, and a tachyon with zero energy moves infinitely fast.
Charge-less tachyons would not be free from this accelerating effect, either. While they wouldn't interact with light, they would instead produce a gravitational Cherenkov radiation, since they go through the vacuum faster than the speed of gravitational radiation. Even if they have no rest mass, they still produce a gravitational field due to their momentum (photons do this, too). So all tachyons would emit this radiation, which would accelerate them to infinite speeds.
Pretty crazy stuff!
|
| |
| |
ENG
New site
Pirate 
Ireland 
United States 
Spain 