Topic: Which hits first, the hammer or the feather?

[Markcb750]

Some physicists would say it's not random at all, it's merely an undefined parameter in the equation, making the equation imperfect, not the actual physics.

  True 


Some of which I point out above.   


The original obfuscator  has had issues defining the starting conditions in this simplified nbody problem...

Fun to think about; although I refuse to vote until every parameter of the experiment is established to at least nine decimal place accuracy.

[mlinder]

Some physicists would say it's not random at all, it's merely an undefined parameter in the equation, making the equation imperfect, not the actual physics.

  True 


Some of which I point out above.   


The original obfuscator  has had issues defining the starting conditions in this simplified nbody problem...

Fun to think about; although I refuse to vote until every parameter of the experiment is established to at least nine decimal place accuracy.

I think the point is to make people think about defining parameters of any given theoretical experiment.

I mean, given the simple terms of this experiment with all else being equal (all-else being a universally static environment, complete vacuum, and since the universe is static otherwise, the 'disappearance' of one object while the other is being droped {which precludes the question of the ACTUAL mass of said objects}) that obviously, the hammer and moon (or other moon-sized body of mass, give or take) would meet before the feather and moon do.

I don't think that's what these exercises are about, which is why I like them. In a PM so sochiro, I stated that once these parameters were defined, the game is no longer fun, because cold math answers said questions without doubt. The joy in these is logically defining what parameters are relevant to obtaining the correct answer.

[burmashave]

Does it become fun again if I admit that the randomness I spoke of was due to crappy design and non-existent maintenance of the speed of gravity demonstration at the Boston Museum of Science? (Don't look for any science there.) It wasn't really a thought experiment, but the demo was actually more fun for my nephews who bet on which container (the heavy or the light one) would land first.

Besides, we know that the hammer would fall faster because it is heavier due to the fact that hammers are weighed in troy ounces.

[mlinder]

Now that that's settled, I'd like to ask a question that bugs the #$%* out of me.

First, we know that nothing can travel faster than light, barring rules that, at this point, aren't really rules, concerning quantum physics. Even then, we are talking less about the speed at which things travel, than how they can travel. Meaning, that using our extremely truncated quantum rules, that relatively speaking, light is still traveling at 299,792,458 meters per second, no matter what the percieved departure and arrival time is from where you may be observing it. From someones viewpoint, it's still traveling 299,792,458 meters per second.

That's pretty goddamned fast. We could say also that anything could arrive at the same instant it leaves using quantum mechanical theorems to deal with the frailty of time in our perception.

But that doesn't hold a candle to the qualities of the so called weak-force attraction of mass, better known as 'gravity'. Far as I can tell from my (limited) studies, gravity is #$%*ing instantaneous. No matter where the #$%* you are looking at it from. There's no relativity in terms of speed, only in force. Not anywhere. Does that #$%* with anyone elses head, at all?

[mlinder]

Does it become fun again if I admit that the randomness I spoke of was due to crappy design and non-existent maintenance of the speed of gravity demonstration at the Boston Museum of Science? (Don't look for any science there.) It wasn't really a thought experiment, but the demo was actually more fun for my nephews who bet on which container (the heavy or the light one) would land first.

Besides, we know that the hammer would fall faster because it is heavier due to the fact that hammers are weighed in troy ounces.

metric fu(ktons are way heavier, in any fraction, than anything else, obviously they will fall faster than anythin gmeasured in troy ounces.

[Duke McDukiedook]

Modern science can barely grasp what gravity is and how it affects particles and our perception of this thing we call time.
We can only understand it on a cosmological scale.

Hopefully the GUT will explain it better, if such a thing exists.

[DammitDan]

Light follows time.  The light you are seeing is actually being "transmitted" and which "section" of light you are viewing is totally dependent upon the time at which you view it.

But time follows gravity.  Gravity actually has the ability to warp both the space AND the time around it.

Makes you wonder if this is one of the reasons why light cannot escape a powerful gravitational field (a.k.a. black hole), besides the fact that light carries momentum and therefore has mass.

Gravity is pretty gnarly

[DammitDan]

But that doesn't hold a candle to the qualities of the so called weak-force attraction of mass, better known as 'gravity'. Far as I can tell from my (limited) studies, gravity is #$%*ing instantaneous. No matter where the #$%* you are looking at it from. There's no relativity in terms of speed, only in force. Not anywhere. Does that #$%* with anyone elses head, at all?

One question I have is, is every object in the universe being affected by every other object in the universe at once in some infinitesimally small (or large) way?

I mean, the way I imagine it, I am being affected by every massive body in the universe, but the effects cannot be felt or measured because they are so small.  The Earth's gravity well may have the largest pull, but at the same time I am also being pulled by every planet and moon and star in the universe, as well as every other object on Earth with mass (which all carry minor gravitational fields of their own).

This could explain your "instantaneous gravity" comment.  Because we are always being affected in one way or the other, there is no time relativity involved.

[Duke McDukiedook]

Which brings great truth to the phrase "We are all one". It literally is true, as far as science understands.

[mlinder]

But that doesn't hold a candle to the qualities of the so called weak-force attraction of mass, better known as 'gravity'. Far as I can tell from my (limited) studies, gravity is #$%*ing instantaneous. No matter where the #$%* you are looking at it from. There's no relativity in terms of speed, only in force. Not anywhere. Does that #$%* with anyone elses head, at all?

One question I have is, is every object in the universe being affected by every other object in the universe at once in some infinitesimally small (or large) way?

I mean, the way I imagine it, I am being affected by every massive body in the universe, but the effects cannot be felt or measured because they are so small.  The Earth's gravity well may have the largest pull, but at the same time I am also being pulled by every planet and moon and star in the universe, as well as every other object on Earth with mass (which all carry minor gravitational fields of their own).

This could explain your "instantaneous gravity" comment.  Because we are always being affected in one way or the other, there is no time relativity involved.

I can't remember what the math is for that, but yeah, everything, theoretically, is being affected by everything else in the universe.
The instantaneous factor though, need to be looked at this way:

With light, we are seing something from however far away the light source is, and how long it takes to get there. The light we see is old news.
Gravity, however, is completely different. As we rotate around the sun, we aren't picking up 'gravitational waves' that left the sun 8 minutes ago, like light, we are dealing with a force that is 'right now'. If we could teleport an object with the mass of a sun into our galaxy. every body of mass would be influenced by that body of mass immediately, even though we'd have to wait to actually see the object depending on how far away it was.

Thats freakin nuts.

[DammitDan]

If we could teleport an object with the mass of a sun into our galaxy. every body of mass would be influenced by that body of mass immediately, even though we'd have to wait to actually see the object depending on how far away it was.

Thats freakin nuts.

Wow.  I've never thought of that before!

[mystic_1]

http://en.wikipedia.org/wiki/Speed_of_gravity

mystic_1

[mlinder]

http://en.wikipedia.org/wiki/Speed_of_gravity

mystic_1

Great link. I should look at wikipedia more often. I love this:

"Aberration in general relativity"

to describe 'anomalies' in our current understanding of gravity. Again, all it really is, is our lack of being able to quantify it's properties.

Gravity is #$%*ing awesome.

[sangyo soichiro]

Makes you wonder if this is one of the reasons why light cannot escape a powerful gravitational field (a.k.a. black hole), besides the fact that light carries momentum and therefore has mass.

Gravity is pretty gnarly

Yes, gravity is pretty gnarly, and light has momentum, but it actually doesn't have mass.  How do we know light is massless... for one thing, it travels at the speed of light.  No massive particle can do that (assuming physics as we know it is not wrong).  (By the way, because light has momentum is why it can produce a pressure on an object, even though it has no mass.  Just a curious thing I figured I'd throw in.)


So one may ask then how does gravity "bend" light, or keep it from escaping a black hole?

Einstein postulated in his general theory of relativity that massive objects warp this thing called 'space-time'.  The photon of light follows the 'easiest' path (nature is lazy), called a geodesic, which happens to follow the warped space-time, and alters the trajectory of the light.


So how is it that light can't escape a black hole?
First a definition (MarkCB750 is probably peeing his pants with joy about not having to think about defining it himself)
A black hole is anything from which light cannot escape.  (Are you happy MarkCB749?)
If light can't escape, and nothing can travel faster than light, then nothing can escape (barring Hawking radiation...).

In order for something to escape the gravitational pull of a massive object (that is, to not be gravitationally bound to the massive object), it has to reach escape velocity.  The astronauts that went to the moon had to reach or exceed Earth's escape velocity (something like 11 km/s).

We can calculate the escape velocity if we equate the kinetic energy to the potential energy:

mv²/2 = GmM/r,

where m = the mass of the object trying to 'escape',
M = mass of the other object (earth, black hole, moon, etc.),
r = distance between the masses,
v = velocity.

If we do the algebra, 'm' cancels from both sides, and we get for the escape velocity:

v_escape = √(2GM/r) 

where √ is the square root.  If you plug in the mass and radius of the earth, in consistent units, you can get the 11 km/s escape velocity.

If we ask what happens if v = c (the speed of light), and keep in mind that c is the fastest anything can go, we can solve the above equation for the distance ('r') and get

r = 2GM/c².

Anything within this distance cannot escape the gravitational pull of the object with mass M.  This value of 'r' is called the "Schwarzschild radius".  In terms of the black hole, it is the "event horizon".

Notice that M was never specified (to the fuming malcontent of MarkCB748).  You can plug in your mass and calculate your Schwarzschild radius!  Every massive object has one (even MarkCB747).  And if you were to somehow be compressed into a volume with a radius smaller than your Schwarzschild radius, you would become a black hole!


The more carefully calculated Schwarzschild radius calculation, taking general relativity into account (we didn't in the above calculation!) oddly gives the same answer as our naive calculation.  That is, our naive calculation gives the answer that is consistent with general relativity.  It's one of those little things that happens from time to time.

[DammitDan]

I'm still trying to remember how to make a square root into ^2 

mv²/2 = GmM/r,

where m = the mass of the object trying to 'escape',
M = mass of the other object (earth, black hole, moon, etc.),
r = distance between the masses,
v = velocity.

Is the G in the equation gravity?  And is gravity always a constant (9.8m/s^2)?  Hey, I remembered something! 

*edit* Doh, sorry I made a stupid.  9.8m/s^2 is the acceleration DUE to gravity.  So what is gravity?

[mystic_1]

If light can't escape, and nothing can travel faster than light, then nothing can escape (barring Hawking radiation...).

It's my understanding that Hawking radiation eminates not from the singularity itself, but from pairs of virtual particles that are being created right at the event horizon.  One particle of the pair escapes, the other falls into the black hole.  Thus, the radiated particles aren't actually escaping the black hole.

mystic_1

[sangyo soichiro]

I'm still trying to remember how to make a square root into ^2 

mv²/2 = GmM/r,

where m = the mass of the object trying to 'escape',
M = mass of the other object (earth, black hole, moon, etc.),
r = distance between the masses,
v = velocity.

Is the G in the equation gravity?  And is gravity always a constant (9.8m/s^2)?  Hey, I remembered something! 

*edit* Doh, sorry I made a stupid.  9.8m/s^2 is the acceleration DUE to gravity.  So what is gravity?

G is the gravitational constant.  Its value in SI units is

G = 6.672 x 10^-11 m³ kg^-1 s^-2.

The 9.8 m/s² is approximately the acceleration of gravity near the earths surface.  It varies a little, for various reasons, depending on where you are at on Earth's surface.  It changes from planet to planet.  On the moon, g is about 1.6 m/s².


Edit:  BTW, I use the 'sup' button provided above the little smile faces to get x², etc.  To get √, I use the option key and v (on a Mac).

[mlinder]

êëïûá╛╞┼─└╔╬╠╪αΓ☺²♂♪↕¶!→éàÅæû⌐¼┤╖╜┐╦▌Φ⌡░∟

My keyboard has 1700 keys. Almost as cool as gravity.

[burmashave]

1,700 keys? Do you touch type?

My question is this: If I'm riding my CB750K at the speed of light, and I flip on the high beam, does anything happen?

[mlinder]

1,700 keys? Do you touch type?

My question is this: If I'm riding my CB750K at the speed of light, and I flip on the high beam, does anything happen?

Depends on the viewers relation to the bike.... (barring the problem of you becoming infinitely large at such a speed..)

[mlinder]

I should add, that at relativistic speeds, since you mass is ∞, no light would be able to escape, anyway, so the headlight is a moot point.

[burmashave]

Ha! It was a trick thought question. The high beam on my bike does not work.

[mlinder]

Ha! It was a trick thought question. The high beam on my bike does not work.

Lawl.

[mystic_1]

Ha! It was a trick thought question. The high beam on my bike does not work.

Touché.  Well played


mystic_1

[sangyo soichiro]

If light can't escape, and nothing can travel faster than light, then nothing can escape (barring Hawking radiation...).

It's my understanding that Hawking radiation eminates not from the singularity itself, but from pairs of virtual particles that are being created right at the event horizon.  One particle of the pair escapes, the other falls into the black hole.  Thus, the radiated particles aren't actually escaping the black hole.

mystic_1

I'm no Hawking radiation expert, but you pretty much hit it on the head.

The Heisenberg uncertainty principle (hereafter, I'll abbreviate it as HUP) deals with the inherent uncertainty in certain observations.  For example, we cannot know, with infinite precision, the momentum of a particle and its position at the same time.  We can measure one quantity, but only at the expense of the other.  The very act of observing the quantity changes its value.

In mathematical form, the HUP is

∆p∆x ≥ h/4π

where h = a really really small number, called "Planck's constant,"
p = momentum,
x = position,
∆ = "change in" or the uncertainty
π = pi ≈ 3.14159...

If you do a little mathematical trickery (which means to multiply it by a clever form of 1) we can get the HUP in the form

∆E∆t ≥ h/4π

where E = energy,
t = time,
and the rest mean the same as before.


This second form of the HUP is what allows Hawking radiation.  What it means is that we can break the rules of physics, but only if we do it in a time ∆t less than h/4π∆E.  That is, we can 'create energy' but only if it disappears again within the time limit set by the HUP.  That's how we can get those 'virtual particles,' and that's why they're called 'virtual'.

Virtual particles 'pop into existence' and then recombine and disappear all within that small time interval set by the HUP, and we are none the wiser from it.  But if they pop into existence near the event horizon of a black hole, like Mystic said, they can become separated and are not allowed to recombine.  If we see the particle that makes it out, then it would seem that energy was created.  But this can't be, because energy can neither be created nor destroyed.     So what must happen is that the particle that goes into the black hole annihilates with a particle of the black hole, thus removing one of the black hole's particles.  Little by little, particle by particle, as these virtual particles happen to pop into existence in the wrong place and time, they eat away at the black hole, and that's what is meant when they say that black holes evaporate.

Whew!