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19 Aug 2017 10:02

You are welcome  :D
 
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21 Aug 2017 09:53

Watsisname wrote:
the photo guy, the better choice is escape velocity.  For any black hole, the escape velocity at the event horizon is equal to the speed of light.  In fact, if you set the escape velocity of an object to be equal to the speed of light, you'll end up with the formula for the size of a black hole:

Escape velocity is [math]

Set that equal to c, then solve for r, and we get [math]

which is exactly the formula for the size of the event horizon, or "Schwarzschild Radius", of a black hole.  Actually, this is a coincidence.  It used Newtonian gravity, where we really should be using general relativity, but it happens to give the right answer in this case.


The problem with using acceleration for this is that acceleration and velocity are incompatible.  They have different units.  So there is no sense in which an acceleration is faster or slower than light (or any other velocity that you choose).  You just can't compare them.

For a black hole, you could with Newton's Laws calculate the acceleration due to gravity at its event horizon, and the answer will vary depending on the mass of the hole.  For a larger black hole, you'll get a smaller acceleration due to gravity at its horizon.  But, this is misleading.  It implies you could hover at the horizon of a sufficiently massive black hole -- or even hover at any distance inside of the black hole if your thrusters are strong enough.  That implication is wrong.  It actually takes infinite acceleration to hover at the horizon, and no matter how large your acceleration is, you cannot hover inside the horizon.  You get swept into the singularity. 

Similarly, we should be careful about interpreting "escape velocity" at the event horizon.  It might imply that a light ray emitted from there would just barely escape to infinity, like a rocket launched at the escape velocity from a planet.  Or it may imply a light ray emitted from just inside the horizon would escape a little bit outside of it, and then fall back in.  These implications are wrong.  A ray of light emitted outward exactly at the horizon will simply be stuck there, as if it is climbing up a downward-moving escalator at the exact same speed that the escalator is moving.  And a light ray emitted outward from just inside will be immediately pulled further inward, just like a fish trying (and failing) to swim up a waterfall. 

Some might also think that you would be suddenly able to see the singularity (or whatever it is) deep inside the black hole, after you've fallen through the event horizon.  But you'll never see it.  Even when the singularity is mere inches in front of you (and assuming you haven't been torn apart by tidal forces yet), it is still invisible.  That's because all light is being pulled into the singularity -- none is leaving from it.

The reason these intuitions fail are because there are based on Newtonian experience, whereas what's really happening involves a general relativistic treatment of the space-time.  In a very real sense, a black hole in general relativity is a stronger attractor than anything in Newtonian gravity.  The behavior of things near or inside black holes is less like the orbits of satellites around planets, and more like fish caught in a current about to go over a waterfall.  Space itself is dragging things in, and inside the horizon it is completely overwhelming, while far away it is quite escapable.


Hopefully this "escalator" or "waterfall of space" analogy helps remove some of the mystery of black holes for you and answers your last questions. But if it is still confusing, feel free to ask more!  

And the last thing I want to say is that the speed of light does not get violated in a black hole.  Everything that falls in is moving at or less than the speed of light through the space.  But the space itself is flowing into the singularity faster than light, like the river going over a waterfall.  This might seem unsettling (and in fact this is a little bit of a simplification for how it really works -- the more correct explanation again requires general relativity and a description of space-time curvature), but the helpful answer is that special relativity places a limit on how fast things can move through space (speed of light), while general relativity allows the space itself to move, dragging things along with it, and the motion of space isn't limited by the speed of light.

The funny thing is that the universe does expand at faster than the speed of light (it's the basis for the Alcubierre drive).
 
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21 Aug 2017 09:57

Watsisname wrote:
the photo guy, the better choice is escape velocity.  For any black hole, the escape velocity at the event horizon is equal to the speed of light.  In fact, if you set the escape velocity of an object to be equal to the speed of light, you'll end up with the formula for the size of a black hole:

Escape velocity is [math]

Set that equal to c, then solve for r, and we get [math]

which is exactly the formula for the size of the event horizon, or "Schwarzschild Radius", of a black hole.  Actually, this is a coincidence.  It used Newtonian gravity, where we really should be using general relativity, but it happens to give the right answer in this case.


The problem with using acceleration for this is that acceleration and velocity are incompatible.  They have different units.  So there is no sense in which an acceleration is faster or slower than light (or any other velocity that you choose).  You just can't compare them.

For a black hole, you could with Newton's Laws calculate the acceleration due to gravity at its event horizon, and the answer will vary depending on the mass of the hole.  For a larger black hole, you'll get a smaller acceleration due to gravity at its horizon.  But, this is misleading.  It implies you could hover at the horizon of a sufficiently massive black hole -- or even hover at any distance inside of the black hole if your thrusters are strong enough.  That implication is wrong.  It actually takes infinite acceleration to hover at the horizon, and no matter how large your acceleration is, you cannot hover inside the horizon.  You get swept into the singularity. 

Similarly, we should be careful about interpreting "escape velocity" at the event horizon.  It might imply that a light ray emitted from there would just barely escape to infinity, like a rocket launched at the escape velocity from a planet.  Or it may imply a light ray emitted from just inside the horizon would escape a little bit outside of it, and then fall back in.  These implications are wrong.  A ray of light emitted outward exactly at the horizon will simply be stuck there, as if it is climbing up a downward-moving escalator at the exact same speed that the escalator is moving.  And a light ray emitted outward from just inside will be immediately pulled further inward, just like a fish trying (and failing) to swim up a waterfall. 

Some might also think that you would be suddenly able to see the singularity (or whatever it is) deep inside the black hole, after you've fallen through the event horizon.  But you'll never see it.  Even when the singularity is mere inches in front of you (and assuming you haven't been torn apart by tidal forces yet), it is still invisible.  That's because all light is being pulled into the singularity -- none is leaving from it.

The reason these intuitions fail are because there are based on Newtonian experience, whereas what's really happening involves a general relativistic treatment of the space-time.  In a very real sense, a black hole in general relativity is a stronger attractor than anything in Newtonian gravity.  The behavior of things near or inside black holes is less like the orbits of satellites around planets, and more like fish caught in a current about to go over a waterfall.  Space itself is dragging things in, and inside the horizon it is completely overwhelming, while far away it is quite escapable.


Hopefully this "escalator" or "waterfall of space" analogy helps remove some of the mystery of black holes for you and answers your last questions. But if it is still confusing, feel free to ask more!  

And the last thing I want to say is that the speed of light does not get violated in a black hole.  Everything that falls in is moving at or less than the speed of light through the space.  But the space itself is flowing into the singularity faster than light, like the river going over a waterfall.  This might seem unsettling (and in fact this is a little bit of a simplification for how it really works -- the more correct explanation again requires general relativity and a description of space-time curvature), but the helpful answer is that special relativity places a limit on how fast things can move through space (speed of light), while general relativity allows the space itself to move, dragging things along with it, and the motion of space isn't limited by the speed of light.

I like this analogy between the space inside black holes and the space of our universe.  It makes me think that the reason that space is allowed to expand at faster than light speeds is because it is expanding in a medium that is outside our own universe and its laws.
 
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Marko S.
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25 Aug 2017 03:28

So, I was wondering on how gravitational waves are working. It just simply confuses me. I was researching about them and I am not really impressed in what I know.

How do they work? What is so special about that theory? Is it proven, or does it need proof? Do they work like ordinary sea waves? I doubt so, but I want other's opinion on this. And also, is it just same as any other gravity theory? Just bending space and some matter falls in?

Thanks for answers! :)
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25 Aug 2017 23:29

A-L-E-X wrote:
Source of the post The funny thing is that the universe does expand at faster than the speed of light (it's the basis for the Alcubierre drive).

The expansion actually doesn't have a speed in that kind of sense. This is a very common confusion and might be worth spending a few moments on.

Suppose you look at a galaxy which is 100 Mpc away, and you find that it is receding at 7,000 km/s.  Then you choose another galaxy that is 200 Mpc away (twice as far).  You will find that it is receding at 14,000 km/s (twice as fast).  Indeed, for a wide range of distances, you'll find recession velocities that increase according to their distance from you (Hubble's Law).  

So, what would you call the universe's expansion speed in this example?  Is it faster than light?  How do you know?

It turns out we cannot define an expansion speed at all, but rather a speed per distance.  That is, the speed depends on distance!  The measure of expansion cosmologists use is called Hubble's Constant, and has units of km/s/Mpc.  

What this means is that no matter how small the Hubble's Constant is (provided it is not zero) there will always be a distance for which things are receding from us faster than the speed of light.  So the notion that the expansion is "faster than light" is totally meaningless. 

Things moving away from us due to expansion is a very different type of motion than things literally moving through the space.  It's not the things that are moving through space, but the space itself expanding between them, so the speed of light is not being violated (the rule is that things cannot move through the space faster than light).

Alcubierre's drive is based on a similar idea. While it is impossible to move something through space faster than light, it might be possible to distort the space-time such that some patch of it can be transported through the universe faster than light.  But to do this, the space-time must be distorted in a very strange way which is most likely impossible -- even if it satisfies the equations of general relativity.
 
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25 Aug 2017 23:53

Marko S., a good place to start with understanding gravitational waves is with understanding light waves.  Gravitational waves are a vibration in space-time in a similar way that light is a vibration of the electromagnetic field.  And where the behavior of light waves is predicted from Maxwell's equations, gravitational waves were predicted from Einstein's general relativity.  It's not too important here to understand what a field is, or what space-time is, but rather to know what can act to cause these vibrations, how those vibrations move, and what they do when they interact with something.

Light is produced when electric charges oscillate (what in physics we call a changing electric dipole moment).  For example, an electron dropping down to a lower energy level in an atom.  This causes a vibration in the electric field, which in turn creates a vibration in the magnetic field, and so on back and forth, propagating at the speed of light as an electromagnetic wave.

Image

Gravitational waves are similar, but there are a few key differences too.  To create one, a mass must not simply oscillate, but oscillate in a particular way (a changing "quadrupole moment").  Examples include two masses orbiting each other, or a bump on a rotating sphere.  Then this causes the space around the mass to be alternately stretched and squeezed, and that distortion propagates out, also at the speed of light.  

The speed of light in this case actually has little to do with light itself, and more to do with the maximum speed at which information can be transferred through the universe.  It happens to be the speed of light, and it is also the speed of gravitational waves.

This stretching and squeezing of space in a gravitational wave will affect any objects it passes through.  First they're stretched in one direction and squeezed in the other, and then that switches, like so:

Image

This effect is very small for typical gravitational waves, especially if they have traveled a great distance.  Just like ripples on a pond or light waves, their amplitude drops as they spread out.  You need very heavy masses moving around each other very fast to produce significant waves.  However, LIGO was finally able to detect them in 2015.  The waves were generated by the spiraling together and merging of two black holes, which are some of the most powerful gravitational wave emitters in the universe.  
 
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26 Aug 2017 02:12

Thanks! So, gravitational waves are only caused if some objects are orbiting each other? I watched some clip of 2 Black Holes orbiting each other and causing gravitational waves.

And, can light travel to the infinity or?? Is there fading to the light if it is traveling through vacuum? Can light weaken when it oscillates through space?

And what gravity is needed for light to orbit the planet or something else? Like, if want light to orbit Earth at 30.000 km away, how much gravity is required for that? 
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26 Aug 2017 02:53

Marko S. wrote:
Source of the post And, can light travel to the infinity or??

I would say no, because if it did I would imagine you would see stars from an infinite distance. but that doesn't happen, stars start to fade after a huge distance. so yes, light does weaken as it travels through the vacuum of space, or even any other place.
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26 Aug 2017 03:02

the photo guy wrote:
Marko S. wrote:
Source of the post And, can light travel to the infinity or??

I would say no, because if it didn't I would imagine you would see stars from an infinite distance. but that doesn't happen, stars start to fade after a huge distance. so yes, light does weaken as it travels through the vacuum of space, or even any other place.

But, we can't see distant light because it merges with some closer light and stronger ones. But, what if we remove other galaxies and stars and add just one and then observe? And, space isn't empty as it has some elements. So, that could also be the factor.
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26 Aug 2017 03:44

Marko S. wrote:
Source of the post Thanks! So, gravitational waves are only caused if some objects are orbiting each other?

They can also be made by an asymmetric implosion/explosion, such as in some supernovae.  In short, you need some mass to change its shape in a way that does not keep cylindrical symmetry.  So accelerating a heavy object in a straight line won't create gravitational waves, but swinging it around in an arc will.  A rotating sphere won't, but a rotating planet with mountains will.

Marko S. wrote:
Source of the post And, can light travel to the infinity or?? Is there fading to the light if it is traveling through vacuum? Can light weaken when it oscillates through space?

Light can travel infinitely far in vacuum without losing energy, though that energy may spread out as it travels.  
For example, you've got the inverse square law for light intensity from a source that emits in all directions -- the brightness will drop by a factor of four if you move twice as far away from it.  But a laser won't obey the inverse square law because it is confined within a beam which spreads out very slowly. 
 
Astronomically, light is dimmed and reddened by scattering off interstellar dust, which blocks much of our view of distant stars in the plane of the galaxy.  Over the even greater distances between galaxies, the cosmic expansion also becomes important, which stretches the photons out and makes them redder (the cosmological redshift).  

Finally, because the age of the universe is finite, and the space is expanding, there are fundamental limits to how far a photon can travel.  There are regions which we cannot see because light has not had time to reach us yet, and there are regions we will never see because the space between us and that light is expanding.
 
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26 Aug 2017 12:25

I find the idea of a gravitational quadrupole creating gravitational radiation very interesting. So, similar to how a spinning magnet creates an electrical current, spinning masses create space-time warping waves that act like light, traveling like ripples in a pond. Perhaps we can create or control anti-gravity like gravity fields with quantum gyroscope lol! How can a magnet with charged poles give electrons to an adjacent wire in terms of a quadrupole? How does that relate electricity to gravity? Strange that the oscillations of mass actually do stretch space-time, creating an elastic like harmonization within our reality.
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26 Aug 2017 15:06

Marko S. wrote:
Source of the post And what gravity is needed for light to orbit the planet or something else? Like, if want light to orbit Earth at 30.000 km away, how much gravity is required for that? 

Sorry I forgot to answer this!  To get light to orbit in a circle, there must be a substantial mass within that circle -- nearly enough to create a black hole!  To find it requires a similar calculation as for how to determine the size of a black hole.  The radius of the black hole's event horizon is 2GM/c2, and it turns out that the radius at which a photon will orbit in a circle (the "photon sphere") is exactly 1.5 times more than that, or 3GM/c2.

So if we want light to orbit the Earth at a distance R, then the mass of the Earth must be c2R/3G.

How much mass must it be for light to orbit at 30,000km?  A lot.  6,772 times the mass of the Sun, to be exact!  And it does not matter if that mass is the size of the Earth, or the size of a pea at the core of the Earth -- the gravitational field and the deflection of the light at that distance will be the same.

What if we want the light to orbit in circles at the height of the ISS (currently 405km above the surface)?  Then the mass contained within the Earth must be 1530 solar masses.

What these large numbers are really telling us is that it takes quite a lot of mass to bend light significantly -- and to bend it into an orbit requires conditions very close to a black hole.  It also tells us that black holes are remarkably small for how heavy they are.  It takes thousands of solar masses just to get a black hole with a comparable size to a planet.  A single solar mass would make a black hole only a few kilometers across.  A black hole with the mass of the Earth would be the size of a small marble.

Gnargenox wrote:
Source of the post Strange that the oscillations of mass actually do stretch space-time, creating an elastic like harmonization within our reality.

For me the strangest thing about gravitation and space-time is still that rotating masses literally drag the space around with them like a whirlpool (the frame dragging effect).  It is real, and has been measured, but I still catch myself thinking "space is WEIRD" when I think about it too much. :)
 
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27 Aug 2017 02:09

Watsisname wrote:
Source of the post Then the mass contained within the Earth must be 1530 solar masses.

I assume it is a write error. When I apply your formula I get 1.52913392 solar masses. (Approximately 1.530)
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27 Aug 2017 02:14

JackDole wrote:
Watsisname wrote:
Source of the post Then the mass contained within the Earth must be 1530 solar masses.

I assume it is a write error. When I apply your formula I get 1.52913392 solar masses. (Approximately 1.530)

Oh, you can create the question I asked?? That's awesome! So, how does it look? It looks the same or? You can set the gravity I think and add light orbiting. It would look similar to Black hole I think. 

EDIT: Sorry, I thought you applied the formula in SE. Anyway, everything is the same. It would be great to see Earth-black hole with light orbiting.
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Watsisname
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27 Aug 2017 10:43

JackDole wrote:
Source of the post I assume it is a write error. When I apply your formula I get 1.52913392 solar masses. (Approximately 1.530)

I think you didn't convert the kilometers to meters (necessary for dimensional consistency, e.g. if speed of light is 3x108 m/s and G is 6.67x10-11 m3kg-1s-2).  So it must be multiplied by a thousand.

Marko S., I think there would be no object other than a black hole that could make light orbit around it by gravity.  A neutron star is closest possible object to a black hole, yet still has not quite strong enough gravity to do this. (Typical mass is 1 to 2 solar masses, within a radius of about 10km, yet the computed size of the photon orbit would be smaller than that radius, so it doesn't exist.)  

So, yeah, this situation would not only "look like" a black hole, but must actually be a black hole.

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