## Miscellaneous Science Questions

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matthew turnage
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### Re: RELATIVITY QUESTIONS! (and other common queries)

i don't have much of a point anymore but yeah your right about parallel lines duh

BlackSails
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### Re: RELATIVITY QUESTIONS! (and other common queries)

If you have a killing vector along one of the coordinate axes, does that mean that the christoffel symbol with that direction in the superscript is uniformly 0?

Ie, [imath]\varsigma=(1,0,0,0) -> \Gamma^{1}_\alpha\beta=0[/imath]?

PM 2Ring
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### Re: RELATIVITY QUESTIONS! (and other common queries)

matthew turnage wrote:antimony what are u going on about three lines? and three points. imagine lines coming from all directions on a three dimensional plane. imagine taking a small ball of clay and sticking pins in it from all directions do it right and they all meet at one point.

What do you mean by "a three dimensional plane"? The word "plane" generally refers to a two dimensional structure.

PS. People will take you more seriously on this forum if you use the word "you" instead of the letter "u". Proper capitalization wouldn't hurt, either...

matthew turnage
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### Re: RELATIVITY QUESTIONS! (and other common queries)

ok

Eebster the Great
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Sir_Elderberry wrote:As I understand it, two basic methods underlie stellar distance-judging. For nearby things (in our galaxy? I'm not much of an astronomer) the usual method is parallax. Essentially, you draw a triangle with Earth, the Sun, and the object as the vertices. Then you wait six months, and draw another won. At each point, you measure the Object-Earth-Sun angle. So you know two angles and one side (because we know the distance from Earth to the sun) and you can use trigonometry to find the distance.

For farther away things (i.e., other galaxies) we use a particular kind of star--called Cepheids, I believe--that always burn at the same brightness, and so are called "standard candles". Since we know that how fast a galaxy recedes from us is proportional to how far away it is due to cosmic inflation, we can measure the red shift caused by the movement of the star and determine how fast it is going, therefore, how far away it is.

Wikipedia actually has a pretty good page about this at http://en.wikipedia.org/wiki/Cosmic_distance_ladder. There are apparently a number of methods for measuring distances at different scales, each of which depends on methods for shorter scales. On the shortest scales, we can directly measure the distance between the Sun and various planets by measuring their orbits with radar and applying Kepler's laws. This gives us a precise measurement of the AU.

Based on this, we can use parallax to accurately measure the distance of objects as much as a few hundred parsecs away (based on instruments with a precision of about 1 miliarcsecond).

Beyond this, standard candles like Cepheid variables can be used. If all objects of a particular class (like Cepheid variables or Type 1a Supernovas) have the same absolute brightness or an easily calculated one, then their distance can be determined by comparing this to their apparent brightness. This is not entirely reliable, though, since it relies on the standard candles really being standard. It turns out that there is more than one type of Cepheid variable, for example, which led to incorrect measurements for a long time. Some other standard candles include RR Lyrae variables, X-ray bursts, spiral galaxies (via the Tully-Fisher relation), and elliptical galaxies (via the Faber-Jackson relation). Novae and supernovae that are not type 1a can also be used if they are close enough but have very large errors.

Additionally, if a galaxy is known to be part of a galaxy cluster, its distance can be estimated pretty well. And finally, even stars that are not standard candles can often be fit to the main sequence.

There are about five or six other common methods I didn't want to go into but that are listed in the article, and even more less significant methods that are not. And I think the largest scales of all typically use the redshift that results from the expansion of the universe to determine the time it took the light to reach us from the object, and thus the object's distance.

EDIT: Fixed qutoes
Last edited by Eebster the Great on Sun Feb 28, 2010 8:04 pm UTC, edited 1 time in total.

matthew turnage
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### Re: RELATIVITY QUESTIONS! (and other common queries)

i appreciate the post but why does it say that i wrote that? it wasn't me. is wikipedia the best site to go to? it is wikipedia

matthew turnage
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### Re: RELATIVITY QUESTIONS! (and other common queries)

that post was something u wrote okeedokee thanks

matthew turnage
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### Re: RELATIVITY QUESTIONS! (and other common queries)

if a supernova can reach another solar system would the radiation from the other solar system's star do anything to affect the supernova? assuming they were the size and roughly the same age.

feedme
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Matthew, can you condense your posts into one? Instead of posting multiple one sentence posts.

(Unless someone else has deleted their posts leaving only yours)

Birk
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### Re: RELATIVITY QUESTIONS! (and other common queries)

matthew turnage wrote:if a supernova can reach another solar system would the radiation from the other solar system's star do anything to affect the supernova? assuming they were the size and roughly the same age.

No, the supernova would most likely sterilize the solar system.

PM 2Ring
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### Re: RELATIVITY QUESTIONS! (and other common queries)

matthew turnage wrote:i appreciate the post but why does it say that i wrote that? it wasn't me. is wikipedia the best site to go to? it is wikipedia
Yes, that post was written by Sir_Elderberry, but Eebster the Great buggered up the quoting.

Wikipedia is usually a very good starting point for hard science & mathematics questions. Most of the Wikipedia articles on physics & astronomy are excellent.

matthew turnage
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Birk wrote:
matthew turnage wrote:if a supernova can reach another solar system would the radiation from the other solar system's star do anything to affect the supernova? assuming they were the size and roughly the same age.

No, the supernova would most likely sterilize the solar system.

wow how quickly would the radiation travel from starting point to earth?

PM 2Ring
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### Re: RELATIVITY QUESTIONS! (and other common queries)

c

matthew turnage
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### Re: RELATIVITY QUESTIONS! (and other common queries)

PM 2Ring wrote:c

what does that mean?

Sir_Elderberry
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### Re: RELATIVITY QUESTIONS! (and other common queries)

The speed of light. If it doesn't have mass, it travels at c.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

BlackSails wrote:If you have a killing vector along one of the coordinate axes, does that mean that the christoffel symbol with that direction in the superscript is uniformly 0?

Ie, [imath]\varsigma=(1,0,0,0) -> \Gamma^{1}_\alpha\beta=0[/imath]?

No.

For example, in Schwarzschild geometry, there's a Killing vector field in the t coordinate direction, meaning the geometry is static in the t direction. If you scatter a trashcan full of marbles around space at time t = 0, and the marbles each move in the t direction to coodinate time t = 1, then the 4-distances (in this case, all purely spatial) between the marbles doesn't change. There's a symmetry for the geometry along this direction. (Whereas if each marble moves in the r direction, the distances between them would have to change.)

But even though [imath]\varsigma=(1,0,0,0)[/imath],

$\Gamma^{t}_{tr}=\frac{m}{r^2(1-\frac{2m}{r})}$

A symmetry in the t direction doesn't necessarily imply that moving in the t direction will be following a geodesic. In the example of the marbles moving in the t direction, they'd be hovering at constant distance from a mass - some force is required to make them follow this non-geodesic path.

Or, looking at it another way, the t component of the t coordinate vector changes as you move in the r direction.
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QwertyKey
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### Re: RELATIVITY QUESTIONS! (and other common queries)

I know this exact question has been asked before, but my googlefu + lazyness do not mix well to get answers.

I also read last 5 pages of this thread and both black hole threads which do not answer this "I know I have seen it before!" question

The -> means 'goes to' or 'approaches' or the most practical 'increases to'

As v -> c
γ -> ∞
m=m0γ
m -> ∞

My question is
Rs=2Gm/c2
Where...

This is the part where I do not know, I know Rs is the Schwarszchild radius,G is the grav. constant and c is the speed of light, but what is m? What m is that? m0 or relativistic mass? If an object is travelling at speeds inadequate to become a black hole, does it observe more black holes than a less energetic/slower object? Assuming that their velocity is a constant, and they have infinite time to observe an infinite universe of infinite variety of stars/masses/whatever in space.

If two objects are travelling at a speed equal or slightly lower than that, do they see each other as black holes?

Of course, all these questions would be broken if that m is m0 but really maybe someone should go change that equation on wiki.

And another question: Why did the Big Bang not become a black hole?(EDIT: I realised this is a quantum gravity question, and is beyond scope of current science, but I would like to hear ideas from the people here.) From what I understand, the Big Bang was a big silent bang.

Space(or volume) was near-zero, why could stuff be so energetic and massive yet not gravitationally attract each other to form a black hole? The stuff would not expand as fast as space itself. Pardon me for my poor physical cosmology, but I thought it was a question I wanted better answers than I could ever get so here I am.

Yet another question, though this is more mathematical: what exactly is (Lorentz) covariance and invariance? Can anyone explain it with simple physics and/or english? The first few lines on wiki deals with mathematics too far from my current level of education.

Another question more on mathematics: what exactly are tensors? What rank tensors are used in physics? Can anyone kindly provide examples of rank 2 or higher tensors?

Finally, what are the Einstein Field Equations?

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### Re: RELATIVITY QUESTIONS! (and other common queries)

Relativistic mass is at best useless and at worst misleading. I'd banish the concept from your mind. Always take m to be the rest mass when you see it somewhere.

Right now the favored view is that the big bang isn't the very beginning. Instead what used to be the big bang is called "reheating," and it happens after a period of inflation. Inflation is a time when the universe expands exponentially quickly due to the vacuum energy of a field (different from the current dark energy, but the same effect). So now the reheating surface is fairly big, but inflation explains why it's all mostly flat and in equilibrium, with a particular spectrum of deviations. Why didn't the pre-inflation surface collapse into a black hole? Because there was more vacuum energy (which pushes apart) than mass around. Schwarzschild stuff assumes the only kind of thing that exists is normal matter. When you have competing forms of matter/energy you have to count them differently.

Lorentz transformations are the boosts and rotations. Lorentz covariance of a vector or tensor means that if you boost or rotate the observer's frame, you change the vector or tensor by the appropriate powers of the same transformation matrix you used for the boost or rotation. Lorentz invariance means that you don't have to change it at all. A scalar is Lorentz invariant. Now, in the language people actually use, these are often interchangeable. I will often say "invariant" when I mean "covariant." Both of the words mean "well behaved under transformations," they are just separate words for vectors/tensors or scalars, but the only thing I really need a new word for is the well-behavedness.

Tensors are... A good example is the stress tensor. Momentum is a vector - the 4 components are energy, p_x, p_y, p_z. For stress tensor, you have in 00 the energy density, in 0i and i0 the flow of energy in the x, y and z directions, the momentum density of p_x, p_y and p_z (these match up!), and for just space you have the shear stresses and normal pressures. That's what kind of stuff tensors store information about - more than one direction matters at a time. Like, how does the component of momentum in direction a change when I move in direction b.

Higher rank tensors that are popular are Reimann curvature or Weyl curvature, which have rank 4.

Einstein field equation is
$G_{\mu\nu}=8\pi T_{\mu\nu}$
This relates a curvature tensor to the stress tensor I just mentioned. It tells you when there is a particular stress-energy around what the resulting curvature must look like, or vice versa.
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QwertyKey
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### Re: RELATIVITY QUESTIONS! (and other common queries)

By the way, you did not answer the question regarding the black hole. I knew I read about it somewhere, and the answer lies:

http://math.ucr.edu/home/baez/physics/R ... _fast.html
"The answer is that a black hole does not form. ... blah blah blah... It is actually quite difficult to determine the correct conditions for a black hole to form."

Well, the obvious next question is how difficult is it? Do the EFE tell you what are the correct conditions for a black hole to form?

http://math.ucr.edu/home/baez/physics/R ... verse.html
Also, it already had the question about Big Bang being a black hole... I should be less forgetful, haha.

By the way, I know the EFE form in that form, but really what does it equate? Newton's Second Law equates something abstract, a 'force', to mass times acceleration.(Ignoring SR, taking the form at that time)
What is so important about its solutions?

http://archive.ncsa.illinois.edu/Cyberi ... tions.html

"The left side of the equation contains all the information about how space is curved, and the right side contains all the information about the location and motion of the matter."
Can anyone say how?

http://archive.ncsa.illinois.edu/Cyberi ... mine1.html
http://archive.ncsa.illinois.edu/Cyberi ... mine2.html
http://archive.ncsa.illinois.edu/Cyberi ... mine3.html

Why are the equations so long? By the way, yes, I'm pretty clueless about GR.

PS. I know I'm trying to run before I can crawl. I was hoping to gain more insight regarding the physical laws of gravity, not a whole bunch of mathematical rigour. Thanks in advance.

doogly
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### Re: RELATIVITY QUESTIONS! (and other common queries)

You got two options for understanding general relativity.
1 Vague Handwaving
[imath]G_{\mu\nu}[/imath] tells you about curvature, and [imath]T_{\mu\nu}[/imath] tells you about the matter's energy, momentum, stress, all that good stuff. Words like energy, momentum and stress all get used sort of interchangeably for the content of [imath]T[/imath] because it only splits up into nice, simple, flat space concepts in flat space. This seems sort of tautological but people forget it all the time, and try to talk about the [imath]T_{00}[/imath] component as if it were an energy density in any spacetime, and it's just not accurate. You have to deal with tensors all together; going component by component is just no good.
So really what EFE says is, when there's 'stuff' here (one component, say [imath]\mu[/imath]) moving there (say, [imath]\nu[/imath]) then the space curves in the same way.

2 Precise Physics
If you want to actually know what is going on you have to gird your loins and do the homework. There is no such thing as "physical insight... not mathematical rigour." I know it is appealing to think that the role of math is to be fussy and get in the way of 'the real physical meaning' or something like this, but it's quite false.
Last edited by gmalivuk on Tue Mar 02, 2010 5:54 pm UTC, edited 3 times in total.
Reason: changed from  to imath, since I think it looks nicer this way
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Goemon
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### Re: RELATIVITY QUESTIONS! (and other common queries)

QwertyKey wrote:Another question more on mathematics: what exactly are tensors? What rank tensors are used in physics? Can anyone kindly provide examples of rank 2 or higher tensors?

If you really, really want to know what a tensor is, you can try reading this:

Spoiler:
When forces are exerted on a block of material, the stresses felt by a molecule somewhere in the interior are described by a tensor.

Suppose we have a block of solid gold. We attach a grey handle to each of the N, S, E, and W faces of the gold block. Forces are applied to the handles as shown in the upper left diagram in the illustration: the red force is stretching the block east and west; the blue force is compressing the block north and south; the green force is a shear force which is attempting to slide the right half of the block upward and the left half downward, sort of twisting it into a diamond shape.

If you were a molecule located in the center of the block (blue circle), what forces would your neighboring molecules exert on you?

First consider what forces the molecule directly EAST of you (whose name is Edward) might be applying to you. As a thought experiment, suppose the block is cracked vertically, as shown in the top left diagram. You are the sole remaining molecule whose job is to keep the left and right halves of the block in position.

The red force is pulling Edward eastward, so Edward is in turn exerting an eastward pull on you. Likewise, the green force is pulling Edward to the North, attempting to slide the right half of the block northward. So Edward is also exerting a component of force on you that's in the northern direction. The blue force, however, is acting on both the left and right halves of the block equally, so it does not pull or push Edward relative to you.

The lower left diagram shows the net force that Edward is exerting on you: a red force to the east, plus a green force to the north, and no contribution from the blue force equals a net force to the northeast, as shown by the yellow force vector.

Now consider the molecule directly north of you, whose name is Nancy. To get an idea of what forces Nancy is exerting on you, imagine that the block is cracked horizontally, as shown in the diagram in the upper right. The blue force is clearly pushing Nancy into you. The red and green forces have no affect on your relationship with Nancy (*). The lower right diagram shows the net force that Nancy applies on you: the blue arrow pointing southward.

How about a molecule that's not located directly east or west of you, but somewhere in between? It turns out that so long as we know what force Edward and Nancy exert on you, it's a simple matter to calculate the force that ANY neighbor exerts on you, because the relationship of the force and direction is linear. In other words, if a molecule named Roger is located next to you in a direction that's not quite due east, but three degrees north of east, then the force Roger exerts on you is almost the same force as Edward does, but with a little bit of Nancy's force added to it. Mathematicaly, it's simply cos(3) times the force Edward exerts on you plus sin(3) times Nancy's force. Just take the yellow vector (exerted by Edward), adjust its length by cos(3) = 0.998; take the blue vector (exerted by Nancy), adjust its length by sin(3) = 0.052; and add them together. That gives you the force exerted by a molecule three degrees away from due east.

Apparently, the force applied on you by molecules in your vicinity is not described by a simple vector, because the applied force depends on the direction of the molecule. Molecules located in different directions apply different forces on you. We can't use a single ordinary vector to completely describe the forces acting on you - we need a more complicated mathematical object called a tensor; in this case, a second rank tensor. Because the forces follow rigid rules of linearity, we can get a complete picture of all the forces acting on you by writing down (in this two dimensional case) a set of four numbers. All we need to know is the magnitude of each component of Edward's force vector (red and green), and the two components of Nancy's force vector (blue and zero). These four numbers, together with the linearity rules, describe completely the forces acting on you by any and all molecules in your vicinity: these are the components and rules of the stress tensor. For a three dimensional analysis, we need 9 numbers because there are three primary directions, and the force applied in each direction is a vector with three possible components.

Tensors can be of any rank. One special case is a scalar such as the temperature at a point, which is considered to be a tensor of rank zero because you only need one number to describe it completely. A vector, such as the wind velocity at a point, is a tensor of rank one: it can be broken down into separate components for each direction, but the individual components are each a single number. A second rank tensor is the next most complicated object. It can be broken down into separate components in each direction, but each component is itself a VECTOR which has multiple components of its own. The eastern component of a second rank tensor is a vector, which itself has components in each direction. The eastern component of a third rank tensor is itself a second rank tensor, and so on until your brain explodes.

Spacetime curvature is described using a fourth rank tensor at each four dimensional point of spacetime. A general fourth rank tensor in four dimensions would be described by 256 independent components! Fortunately, however, there are symmetry constraints to geometry that reduce the number of components to only (!) twenty.

(*)

It's not very intuitive from this diagram, but in real life, the green force would distort the block into a diamond shape, and the force distributions would balance somewhat: the green force on Edward would be smaller, and there would actually be a green force pushing Nancy eastward. Although in general the eastern component of a tensor is completely independent of the northern component of a tensor, the stresses in a block of material have symmetries that ensure the shear components of the forces must always be equal in magnitude.
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uknowurright9
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Just an interesting idea here:

If space is constantly expanding, (which it is), and not just the edges but also the space between objects in the universe, is it possible that the calculations we have for the distance between celestial bodies such as galaxies and such could be erroneous based on the fact that these objects are possibly (and probably) "moving" faster than the speed of light relative to our position? It would seem that if these bodies are "moving" faster than light relative to us that the light we are seeing is from before the space between us and the observed object had expanded. I put quotes around the word "moving" because the bodies themselves are not being moved by a force but rather are farther away or closer due to the expansion of space itself.

doogly
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### Re: RELATIVITY QUESTIONS! (and other common queries)

What do you mean by "the calculations we have" ? Any extragalactic calculations you see already take into account the expansion of space.
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Eebster the Great
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### Re: RELATIVITY QUESTIONS! (and other common queries)

uknowurright9 wrote:Just an interesting idea here:

If space is constantly expanding, (which it is), and not just the edges but also the space between objects in the universe, is it possible that the calculations we have for the distance between celestial bodies such as galaxies and such could be erroneous based on the fact that these objects are possibly (and probably) "moving" faster than the speed of light relative to our position? It would seem that if these bodies are "moving" faster than light relative to us that the light we are seeing is from before the space between us and the observed object had expanded. I put quotes around the word "moving" because the bodies themselves are not being moved by a force but rather are farther away or closer due to the expansion of space itself.

The metric expansion of space is unimaginably slow, on the order of 70 km/s/Mpc (that is, 70 kilometers per second per megaparsec) = 2.3 x 10-18Hz (2.3 attohertz). This means that even objects 300 light years away are moving (due to the metric expansion of space) at only 7 m/s, which is less than 16 mph. Only objects extremely far away move at appreciable speeds. A distant galaxy 5 Gpc away is moving at about 350,000 km/s, which is about 10% faster than the speed of light. The light it emits now will never reach the Earth.

uknowurright9
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Eebster the Great wrote:
uknowurright9 wrote:Just an interesting idea here:

If space is constantly expanding, (which it is), and not just the edges but also the space between objects in the universe, is it possible that the calculations we have for the distance between celestial bodies such as galaxies and such could be erroneous based on the fact that these objects are possibly (and probably) "moving" faster than the speed of light relative to our position? It would seem that if these bodies are "moving" faster than light relative to us that the light we are seeing is from before the space between us and the observed object had expanded. I put quotes around the word "moving" because the bodies themselves are not being moved by a force but rather are farther away or closer due to the expansion of space itself.

The metric expansion of space is unimaginably slow, on the order of 70 km/s/Mpc (that is, 70 kilometers per second per megaparsec) = 2.3 x 10-18Hz (2.3 attohertz). This means that even objects 300 light years away are moving (due to the metric expansion of space) at only 7 m/s, which is less than 16 mph. Only objects extremely far away move at appreciable speeds. A distant galaxy 5 Gpc away is moving at about 350,000 km/s, which is about 10% faster than the speed of light. The light it emits now will never reach the Earth.

That's interesting, I was under the impression the universe is expanding faster than that for some reason. My next question was actually going to be whether there are distances from which light will never reach earth but you already answered that.

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### Re: RELATIVITY QUESTIONS! (and other common queries)

300 light years is nothing in astronomical scales. Our galaxy is 100,000 ly across, and the local group of galaxies is about 100 million ly across. Yes the expansion only happens at large distances, but large distances is where everything actually is.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

There are objects far enough away that their light will never reach Earth. However, this event horizon is farther out than the distance at which they're receding faster than light. I know this seems strange, but it's because expansion is accelerating. There's more information in the article about the Hubble volume.
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uknowurright9
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### Re: RELATIVITY QUESTIONS! (and other common queries)

gmalivuk wrote:There are objects far enough away that their light will never reach Earth. However, this event horizon is farther out than the distance at which they're receding faster than light. I know this seems strange, but it's because expansion is accelerating. There's more information in the article about the Hubble volume.

Cdevon2
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Correct me if I'm wrong, but gravity is a constant fundamental force. If it's constant, then how do you get the speed of gravity?
The only 3 laws I need:
Moore's Law
Godwin's Law

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### Re: RELATIVITY QUESTIONS! (and other common queries)

Cdevon2 wrote:Correct me if I'm wrong, but gravity is a constant fundamental force. If it's constant, then how do you get the speed of gravity?

Not sure what you mean here. The "speed of gravity" is the speed it takes for changes in gravity to propagate. If I move an object a meter towards you, when do you notice the uptick in gravity? (Theory suggests, and evidence is converging around, the speed of light)
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Ok, thanks. Just the phrasing of the statement that confused me ("Gravity travels at the speed of light")
The only 3 laws I need:
Moore's Law
Godwin's Law

Antimony-120
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### Re: RELATIVITY QUESTIONS! (and other common queries)

To put that in perspective, so does the Electromagnetic force (Electricity, which depends on something called drift velocity, and also on the speed of electrons under the influence of the force, travels slower).

Basically what they mean is that the force of gravity is GMm/r^2 and all that, and if you screw with one of the masses (say removing the sun) then the force the other mass feels will change at the same time light from that change arrives. So if I were to remove the sun right now, the earth would be happily orbiting and the sun appearing to be shining for around 8 minutes, at which point suddenly everything would go dark and we'd fly off into interstellar space.
Wolydarg wrote:That was like a roller coaster of mathematical reasoning. Problems! Solutions! More problems!

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Eebster the Great
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Antimony-120 wrote:To put that in perspective, so does the Electromagnetic force (Electricity, which depends on something called drift velocity, and also on the speed of electrons under the influence of the force, travels slower).

Correct me if I'm wrong, but shouldn't the electric signal in a circuit travel at nearly the speed of light and be independent of the drift velocity? Also, it seems trivial that EM waves travel at the speed of light, seeing as light . . . is an EM wave.

Sir_Elderberry
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Yeah, "electricity" travels much faster than the drift velocity of actual electrons.
http://www.geekyhumanist.blogspot.com -- Science and the Concerned Voter
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I reiterate. Coolest. Guy.

Well. You heard him.

Antimony-120
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Sir_Elderberry wrote:Yeah, "electricity" travels much faster than the drift velocity of actual electrons.

Which would be why I said "depends on" not "is equivalent to". Although the speed of the electrons is taken into account when the drift velocity is calculated, so that was somewhat irrelevant

Actually now I've got to go look that up, EMF might move at the speed of light now that I examine it a little more closely in my head. It's never been particularly relevant to anything I've had to do...but now I need to find out!

And yeah it's trivial that EM moves at the speed of light, although note that waves can move much faster than their medium. (That light doesn't really have a medium is why this is irrelevant here, it IS the medium as it were). By comparison, water waves can travel very quickly compared to the water they are in, similarly with sound waves in air. They're air waves, but they travel faster than the air. But since the photon IS the force carrier for EM, then of course EM travels at the speed of the photon. But in my opinion that is missing the more elegant point that ALL forces travel at that speed (well, one of the four travels at less. Stupid weak force), and they are not carried by photons. Massless particles sure (once again, screw the W and Z) and there are really good reasons those always travel at c, but they're not photons.
Wolydarg wrote:That was like a roller coaster of mathematical reasoning. Problems! Solutions! More problems!

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uknowurright9
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Drift velocity is directly related to the speed of electricity but the electromagnetic force moves at the speed of light (in an ideal world with spherical chickens).

Eebster the Great
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Antimony-120 wrote: . . . ALL forces travel at that speed (well, one of the four travels at less. Stupid weak force), and they are not carried by photons.

Electroweak ftw.

PM 2Ring
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### Re: RELATIVITY QUESTIONS! (and other common queries)

The effective speed of EM through a medium is always less than c. The speed of visible light through glass or water is substantially less than c; similarly, the speed of EM waves through electrical conductors is less than c.
http://en.wikipedia.org/wiki/Refractive_index wrote:The refractive index (or index of refraction) of a medium is a measure of how much the velocity of a wave is reduced inside that medium. For example, typical soda-lime glass has a refractive index close to 1.5, which means that in glass, light travels at 1 / 1.5 = 2/3 the speed of light in a vacuum.

BlackSails
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Isnt the speed of light in vacuum also less than c, due to vacuum polarization?

uknowurright9
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### Re: RELATIVITY QUESTIONS! (and other common queries)

BlackSails wrote:Isnt the speed of light in vacuum also less than c, due to vacuum polarization?

I can't seem to see why this would be the case but it is an interesting idea.