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There are estimated to be 70 billion trillion stars in the observable universe. That's 7*10^22Quote:
apparently atoms in the sun is just 10^57
Multiply that by your number here, and we're at 7*10^79
Not even close to 10^120, which is many orders of magintude bigger. It's fucking ludicrous how big 10^120 is.
I figure that for every atom in the observable universe, there are a thousand billion billion billion different chess positions.
yea but i dont want that to be true because fuck chess
You only say that because you're shit at it.
indeed
Well, I'm glad that's sorted.
the only thing that was cleared up is that the universe is a pussy
I'm currently counting to 10^120
I got to 45 before I realised that 10^120 is more than a googol, and it's rather futile counting to such a number.
There's more than a googol different chess positions. That is sick. I didn't think there was a googol of anything.
just pick any ol thing and it's googol^googol
like positions of atoms in the galaxy
Can we go back to the part where Renton has watched 8 hour-long physics lectures and hasn't asked any questions.
http://www.reactiongifs.com/r/2013/05/urkel.gif
Kind of blew through them. My style of content comprehension is generally to watch as a background thing and then rewatch while paying actual attention. As far as actual comprehension and understanding, I'm up to about the fifth lecture of 801 Classical Mechanics.
Anyway more gravity questions. I'm not sure you really answered in the thread why the "curved spacetime" theory of gravity explains why an object at rest will still be accelerated toward the dominant mass by gravity. If "falling" bodies are moving in straight lines through curved spacetime at with their existing momentum, why does something with no momentum fall to the ground?
Somewhat unrelated question. As I understand it, if you're moving through space at constant speed (acceleration = 0) from your reference frame you appear not to be moving and do not feel as if you are moving. This is why we aren't pushed into our seats when on a moving train except when it accelerates from rest. And from a stationary reference point in space, the Sun (and hence its satellites) is moving 370 km/s. But since the earth orbits the Sun at about 30 km/s, that would mean my actual speed is 370 km/s +/- 30 depending on where the earth is in it's revolution. Does this mean that we are in a constant sine-wave like state of acceleration and deceleration that we would be able to feel if our sense of inertia were finely tuned?
:/Quote:
Originally Posted by Renton
Tough one. I've thought about this one a bit and I just don't know. I'm going to do some research and get back to you.
I can do some hand waving and say that nothing is truly at rest in any non-accelerating reference frame, so any 2 bodies will have (or develop) very slight relative motions which are amplified over time.
Once the bodies are moving relative to each other, then things fit the picture.
It's a weak, and probably incorrect, assessment.
Some heavy math and physics by a group of people trying to measure exactly that.Quote:
Originally Posted by Renton
Short answer: Yes. A bit.
The Earth is in free-fall orbit around the sun and moon, so we don't feel their gravitational forces on the Earth's surface.
If you're in a free falling elevator (god forbid), you would not feel Earth's gravity. You would appear weightless in an elevator (for however brief a time).
Things are heavier at sunrise/susnet than at midnight and noon. This is due to tidal forces of the sun.
Which brings up the tidal forces.
The moon's tidal forces are much more prevalent than the sun's, due to the proximity of the moon.
***
Things are heavier near the poles than near the equator. Since the Earth is spinning, objects within the spinning (non-Newtonian) reference frame will feel centrifugal force. This force is expressed in opposition to gravity.
***
The Earth's mass in not evenly distributed, so the gravitational force varies across the surface.
Things are heavier on mountains, because there's a mountain of extra mass underneath them, pulling them down.
Has anyone ever accurately represented the distortion of 3D space by gravity geometrically? It would be sweet to see what a 3d wireframe grid would look like with a very massive body distorting it. I seem to only see the "2D projection" of gravity where the earth is weighing down a flexible surface which seems to me like a little too convenient of an analogue to use. Looks cool, not sure it explains well what's going on here though.
It's easy for us to visualize a 2-d sheet being distorted into the 3rd spacial dimension we perceive. It's not so easy to visualize that sheet being distorted within its 2-d plane. We could use color to show the magnitude of distortion, or a vector field to show both magnitude and direction of distortion.
I found this. I don't like it much, but I do like it a little.
http://cdnimg.visualizeus.com/thumbs...h.jpg?ts=93246
Then there's this:
http://astro.physics.sc.edu/selfpace...56/Fig56-1.GIF
which at least has a clock at each intersection.
http://en.wikipedia.org/wiki/Equivalence_principle
I've been trying to understand this. Particularly the following bit:
Suppose that the earth is the only massive object in the universe. It doesn't orbit anything and it doesn't rotate. Under these conditions, if i picked up an apple and released it, apply no forces to it, would it remain motionless in mid air?Quote:
Originally Posted by Einstein
If the Earth is the only massive object in the universe, the what are "you" and what is an "apple". They are massless objects, which would not experience a gravitational force.Quote:
Originally Posted by Renton
Otherwise, both you and the apple are massive objects which are accelerating.
The Equivalence principle broadly states that gravitational forces are indistinguishable from other forces in the way they accelerate masses.
Meaning that if I'm in a closed room, and I experience 9.8 m/s^2 of acceleration in 1 direction, then I can't perform any test inside the room that can say whether I'm in a uniform gravitational field or if I'm somehow being accelerated by some other means (a rocket or the hand of god).
***
For the record, this notion of 2 stationary objects alone in an otherwise empty universe is griefing me, but not troubling me. Clearly the objects would attract each other by Newtonian mechanics. I just don't know how Einstein's Relativity explains it in terms of geodesic lines in curved spacetime.
Okay, can you just explain to my why general relativity is necessary? I get why special relativity is. What are some scenarios where the statement "massive bodies attract" isn't sufficient to describe gravity? Could weird things like gravitational lensing not occur with classical mechanics?
edit: to answer your question, i meant the earth "system" is the only massive entity. So the atmosphere and objects on its surface would be a part of that.
I found this quote from a man trying to explain the difference between general and special relativities to his 8-year-old daughter.
It needs to be noted that gravity doesn't cause space-time to curve; gravity is the curve in space-time.Quote:
Special relativity says that how things happen can look different to people in different places or moving at difference speeds--except for things involving the speed of light in a vacuum. Things moving at the speed of light always move at the speed of light compared to you, no matter how fast you're moving.
General relativity says that space and time are actually different aspects of the same thing--space-time--and that space-time is curved. Exactly how curved space-time is at any point in the universe depends on how much gravity there is in the area. In addition to bending space-time, gravity can also bend light, radio waves, and all kinds of other stuff.
Mass-energy curves space-time, and space-time guides the movement of mass-energy.
Gravitational lensing hinges on the curved paths of massless photons. Newtonian gravity can not account for this.
The precession of the orbit of Mercury is explained by GR.
The fact that GPS must account for clocks ticking at a different rate is explained by GR and gravitational redshift.
***
I don't see how the stipulation that the Earth is the only thing in the universe changes anything. The Earth is in free fall around the sun, so only minimal tidal influences bear any effect on the Earth's surface.
The apple's mass attracts the Earth's mass in that equal and opposite way that the Earth's mass attracts the apple's mass. The combined curvature in space-time pulls both bodies proportionally toward the center of mass of the system.
In this way, the sun is in orbit around the Earth as much as the Earth is in orbit around the sun. They each orbit the combined center of mass of the system, toward which each is accelerated at any moment in time.
Is the effect of gravity asymptotic with distance? For example does a single proton floating around exert a tiny effect on space on the other side of the galaxy? It seems to me like gravity can't know what constitutes a contiguous mass-energy, so it must be just the accumulation of the effects of every particle in the vicinity. And if the particles in my body are exerting a tiny amount of gravitation to matter in Andromeda 2.5 million light-years away, is this effect instantaneous? These seem like questions that can't really be answered, but I'm curious where the math/theory points.
Yes. gravity is space-time curvature, and everything effects everything.Quote:
Originally Posted by Renton
That said. The intensity of the interaction between 2 masses diminishes proportional to the square of the distance between them.
F = GMm/r^2
It's the {...}/r^2 part I'm talking about.
Suppose: 2 objects are some distance apart, call it {ong}, and they express an equal and opposite force on each other of {bonga}.
If all else is the same, but the distance between the 2 objects is doubled to 2*{ong}, then the force they NOW express on each other is {bonga}/4.
Over very long distances, the force expressed is so tiny as to be nearly non-existent except when applied over vast distances for a vast time period.
Ultimately, theory states that the space-time curvature caused by any mass has no limit to spacial influence, given infinite time for the gravity to propagate the distance.
I mean. The pull of gravity of every object in the universe extends to every other object in the universe. Gravity moves at the speed of light, so it takes time for changes to be 'felt' by distant observers.
Exactly. You have excellent word-choice here.Quote:
Originally Posted by Renton
(Even though space-time curvature can't "know" anything. It can be quite hard, even for physicists, to avoid anthropomorphic terms when describing things.)
Changes in space-time curvature propagate at the speed of light, according to the Einstein Field Equations.Quote:
Originally Posted by Renton
Low probability of monkeys answering questions here:
http://www.space.com/28496-gravitati...ector-ama.html
AMA on reddit this Friday with researchers from LIGO.
Vsauce says lots of things I already said about the speed of light, but in a video.
http://youtu.be/ACUuFg9Y9dY
On the Observable Universe:
If we know, give or take, when the big bang happened, and if we know, give or take, how quickly space has been expanding since the big bang, then how come we can't make an educated estimation of the size of the universe outside of what we can actually observe? Or am I wrong about the knowns?
I don't know where we left the size of the universe conversation. I do know that my initial response in this thread was quite bone-headed.
I suggested the universe is a sphere which is 13.7 billion light years in radius. This is evidence of a mind with just enough information to be dangerous. Sorry.
The major problem with my analysis is that it assumes that space and time are independent and non-relativistic. Both of which are assumptions which are not remotely justified in this case.
The real story is that it's not straight-forward to answer.
Here's a start.
More to come.
I've seen that video before, but I didn't really understand the last part. I always thought the big bang came from a single point, and that single point was everywhere, because it was the only space that existed. Apparently the time of the big bang was just an infinitely voluminous universe that was infinitely dense? Why do you need two infinities?
I don't think he says it was infinitely voluminous, just that the concept of the volume of the universe, as a substance that occupies a region, could be wholly wrong.
He's saying the only thing is the universe. By saying that the universe may be expanding into itself, he's implying that it is the inside and the outside of itself, essentially. He's calling into question the notion that the universe has an outside. He's speculating that such a conceptualization may be erroneous.
I think.
To take it back to your original question: it all depends on what you mean by "educated estimate."
The more information we get, the more refined our estimates.
We're dealing with something that is remarkably difficult to prove. Our theories are good only up to a point, after which they become nearly impossible (if not theoretically impossible) to test. Exhibit CERN and the Chinese endeavor to build an even bigger particle smasher. This is the only means we know of to test anything that happens at such high energy densities in a controlled environment. It is only through testing our theory at higher and higher energies that we can show which parts of the theory extrapolate correctly (are better than others).
It's hard to come up with tests for even measuring gravity waves, which nearly all physicists expect to be detected eventually. Our understanding of the cause of gravity (as opposed to the effect of gravitation) is truly rudimentary. We are right on the heels of proving the Higgs field theory, which describes gravity in the tiniest scales.
We have no grasp on dark matter or dark energy, whose explanations seem highly relevant to this line of speculation.
(hand waving galore)
Okay, correct my current lack of understanding of black holes.
My layman's knowledge of SR is that if a human was accelerated to nearly c, he would experience time dilation. His clock would tick normally, while time rushed by for stationary observers. If your mass could be accelerated to c, your time dilation would be infinite, and you would see the entire universe shrivel up and die around you in a nanosecond.
Carrying that same concept over to GR, something has me confused about black holes. According to a physics forum thread I read, the effects of gravitational time dilation are identical to velocity time dilation at the escape velocity of the mass that is creating the gravitational field. This means, as far as I can tell, that everything within the event horizon of a black hole experiences infinite time dilation, i.e. a person in the process of crossing the event horizon would see the entire universe go dark in a fraction of a second. And observers from an arbitrary distance would see him start to get flattened into the EH asymptotically but he would never get swallowed up.
My problem with this account is that everything I've read suggests that a person/mass/whatever would survive crossing the EH unscathed, and wouldn't even experience extreme tidal forces until well within the EH assuming a large, non-spinning black hole. It seems far more plausible that mass is incapable of existing in a c-escape-velocity gravitational field, and that black holes are just big balls of tiramisu that just perpetually flatten objects onto their EH's. If one could cross the EH unscathed, wouldn't the black hole just spit him out in an instant because it would evaporate enough mass of Hawking radiation well before he was in any danger? Of course trillions of years might have elapsed.
I'll give it a shot.Quote:
Originally Posted by Renton
You have this so close, just the opposite effect.Quote:
Originally Posted by Renton
The faster you travel relative to another ... umm ... anything, the more you observe time dilation (and space contraction in the direction of your relative motion).
So as you approach c, you see all the other clocks in the universe slow down ever more and more, approaching the asymptote of stopping altogether.
All the objects in front of you and behind you would be much closer than before, while the stuff off to your sides would remain as far away as you expected.
If I am in the universe you are observing, I would see my clock tick normally, and yours would tick very slowly. Also, I would observe your passing ship as squished or shortened in your direction of travel.
Both observers see the other slow to a standstill. Both would observe the other's clocks slow down ever more and more.Quote:
Originally Posted by Renton
Both observers would see the other one becoming more and more faint and ghost-like. The 'number of photons emitted' is conserved in both reference frames, but the time it takes to emit them is not conserved.
The outside observer would definitely see the falling observer as ever more and more red-shifted. I think (and I may be wrong) that the person falling in would see the outside observer as ever more blue-shifted. This is because photons traveling "uphill" lose energy, while photons traveling "downhill" gain energy.
Red light is lower in energy than blue light, so we tend to shorthand "blue-shift" to mean increasing frequency and "red-shift" to indicate decreasing frequency.
"the effects of gravitational time dilation are identical to velocity time dilation at the escape velocity of the mass that is creating the gravitational field"
Umm.. huh? I might not be understanding this, but...
Both are dilation, there is no "balancing" happening here. If one were dilation and one were contraction, then there would be a surface where the opposing effects canceled each other out. These two effects are not opposing each other, though.
"This means, as far as I can tell, that everything within the event horizon of a black hole experiences infinite time dilation"
For anything moving slower than the speed of light, there is not enough energy in the universe to accelerate it to the speed of light.
Experiments and observations reveal, so far as we know, that only photons travel at the speed of light.
If anything, the time dilation would be ever approaching the asymptote of complete stoppage, but would never be truly, completely stopped.
Yeah, event horizons are tricky things. They are currently poorly understood, and the models which provide some understanding have fatally flawed assumptions incorporated into them. E.g. a non-spinning black hole is almost definitely science fiction.Quote:
Originally Posted by Renton
The complicated bit is that we have to always talk about what an observer would observe. The observer always experiences their own time and space as "ordinary" and observe "distant" space-times as distorted. (I think)
Unless the arbitrary "distant" is on length scales of the observer or smaller, there would be no notable effects for the observer. When the difference between the gravitational force near the observer's feet becomes noticeably different from the force near his head, then things are getting bad real fast.
IDK.Quote:
Originally Posted by Renton
I don't think it's "instantaneous." That word is meaningless in GR. Temporally distinct objects don't share a "same time" for things to happen simultaneously.
Entropy theory says a lot of interesting things about the surface of a black hole, as far as conservation laws are concerned.
mmmmmmmm. Tiramisu. :drool:
I think you misunderstood what I said. The physics thread guy said that gravitational time dilation of a mass approaching an event horizon is identical to the the time dilation experienced by an object traveling at velocity approaching c. I mean comparing them as analogues, not that the gravitationally dilated mass is also experiencing SR effects.
This doesn't intuitively seem correct to me. The principle of equivalence only relates gravitational acceleration to actual acceleration, right?
Anyway this seems like an easy thing to check mathematically. Isn't there a simple formula for the amount of common time elapsed per second in a gravitational field of X strength? What strength does that need to be in order for time dilation to be infinite?
Re: my instantaneous usage, what I meant was that from the point of view of a being approaching the EH, a nanosecond of time would be equal to trillions of years of common time outside of the gravitational field of the black hole.
Ahh. Yes. I agree with him.Quote:
Originally Posted by Renton
In both cases, there is a limit approaching infinite time dilation. In one case, it's due to the velocity approaching c. In the other case, it's due the extreme curvature in the local space-time caused by the black hole's mass density. (Local means the "nearby" volume around the observer, with no holes in the volume, in this case.)
The time dilation is the same, whichever the cause. In that regard, they are perfectly indistinguishable.
All time dilation is understood through Einstein's Relativity. I'm not sure whether it came in the GR or SR bit.
Ugh. I mean, maybe you're right, but it's a complicated subject that's hard to wrap up in one sentence.Quote:
Originally Posted by Renton
The phrase "actual acceleration" gets my undies in a bind, but I think I know what you mean.
"We assume the complete physical equivalence of a gravitational field and a corresponding acceleration of the reference system."
-Albert Einstein
He was saying that the force of 1g near Earth's surface is indistinguishable from a force of 1g caused by an accelerating reference frame (like, say a magic elevator powered by the hand of God). He went on to say that this is only possible if the amount of "gravitational mass" a body has is identical to the amount of "inertial mass" a body has. Which everyone largely thought was rudimentary and went without saying.
He also said something like, "Let's assume that the conservation laws we observe are the same everywhere." Again, mostly nods of agreement.
Then he said, "So time dilation and space contraction, then, right?" That kicked the lid off, so to speak, of the steaming pile of ignorance that was waiting to be smelled (smelt?).
So, yeah... that's what the principle states. The implications are subtle and astounding, though.
Well, I'm a layman at full-scale GR calculations, first off. Actually, that kind of makes me sound like I have some understanding, which I do not. I have seen the equations, but I don't even know the math behind quaternions, which is the language of GR.Quote:
Originally Posted by Renton
My gut says that it would require infinite spacetime curvature to cause infinite time dilation.
Just like it would require infinite acceleration to cause the same.
Infinite spacetime curvature would imply infinite mass-energy density over some region, presumably infinitesimally small. This is the so-called singularity, which may or may not exist within a black hole. I am unsure of the current theories around singularities.
That said, I agree with your hyperbole of "trillions of years" as a nice work around. I have it in my head, though that it's the opposite, really. That the observer sees their own time passing as "normal" and that the "distant" times they observe are always slowed, never sped up.
Is Kingnat in the house? Any help here?
Yeah, man, in that case I really feel like its tiramisu. But I watched a Leonard Susskind vid and he said that the infinitely thin firewall black hole was the "classical" view and incompatible with QM. Then he said a bunch of weird shit that I had no understanding of, *shrug*.
It does seem to fit neatly that gravitational effects on mass have limits just as speed does, and that mass cannot exist at either extreme condition.
Much as I love a good lecture on physics, Leonard Susskind always leaves me feeling less informed than before I watched the video.
I still try to watch his lectures from time to time. He is among the most lauded physicists alive AND he's got YouTube videos, so that's ostensibly exciting for me.
However, I feel like he's too abrasive with his students. I watched a video where he was teaching a night class to adults. Right at the start of the series, he gets into a disagreement with one of the students about whether or not there is a net charge on a capacitor. The student is a man who works in electronics and knows the danger of a charged capacitor (it was a 1 F capacitor, so worthy of immense respect as a potential explosive). Susskind made the guy look stupid in front of the class and the guy knew it.
It was all a bullshit dialogue where the student says something like, "I know that I can put 1 Coulomb of charge onto that 1 Farad capacitor." Susskind says, "This capacitor will always have 0 charge." They argue and Susskind is a bit condescending. He never bothers to say, well, ONE plate of the capacitor will have a charge disparity from the other plate, but the those charges cancel out, leaving a net charge of 0 Coulomb. He never offers the student the dignity of having a valid viewpoint, but a misunderstanding of Susskind's statement.
It's like Susskind is so wrapped up in his own world that he failed to see the practicality of the electrician's view. Maybe that's part of what makes him great. Sounds like making an excuse for someone being a bit - not really being an ass, just not a great communicator.
This seems nitpicky, but I mean it as an example of how Susskind fails to empathize with his audience, which makes his presentations incredibly dense and hard to follow.
Also, Jibbers, he can be hard to follow just because he uses the jargon of QM so fluently and without pause. I mean... I know what a Hamiltonian is, and I know what a Hermitian matrix is, and a singular matrix... but calling to mind all of the properties and implications of those things takes my brain a hard pause to recollect. He just powers right through them so quickly that I'm quickly missing his lecture due to me falling behind in my listening and understanding skills.
Waitaminit now. My interpretation of gravitational time dilation:Quote:
Originally Posted by MadMojoMonkey
Person A observing the black hole from a weak gravitational field. Experiences time at 1 sec/sec.
Person B at 1 nanometer from the EH of a black hole. Experiences time at 1 sec/sec.
Person A observes Person B's clock ticking very slowly at 1/X B's seconds per A's seconds, where x is approaching zero.
Person B observes Person A's clock ticking very quickly at X A's seconds per B's second, where 1/x is approaching infinite.
Is this wrong?
I've been on this for long enough to report in.Quote:
Originally Posted by Renton
I'm still a lot confused about the gravitational portion. I've even read some stuff that I don't fully understand about velocity transformations now... since the equivalence principle says that any force can be interpreted as a gravitational force, if that suits.
Here's the rub I'm dealing with. I am correct insofar as to say that an observer will always observe his own time as "normal." When observing things, if he's a clever physicist, he will know that what he observes can be different from what he calculates. This is because he's taking travel distances into account. He knows that everything he sees takes some amount of time between action and observation, and his calculations account for that.
OK. Some fuzziness around observations, but ultimately the calculations allow separated observers to agree on the cause of their observations.
Where I am lost is how an observer sees the other's clocks when the information is blue-shifted.
In the twin paradox, the blue shifted information arrives at increased frequency. The stationary twin sees his twin's clocks advance at a rapid pace, due to the fact that the traveling twin is approaching the stationary twin. There is a Doppler effect on the frequency.
So wait, what now? I thought that they would always see the other's clock tick more slowly, but this is not agreeing with the above information. So I have massive doubts.
I am trying to figure out where the notion that observers always see outside clocks tick more slowly is coming from. I thought it was tied to space contraction. I thought the dual effects of time dilation and space contraction served to make this effect.
I need to figure it out.
never to eat chocolate before you play poker , is my advice!!!
Why is there far more matter than antimatter in the observable universe?
Why does the zero-point energy of the vacuum not cause a large cosmological constant? What cancels it out?
What is the identity of dark matter? Is it a particle? Is it the lightest superpartner (LSP)? Do the phenomena attributed to dark matter point not to some form of matter but actually to an extension of gravity?
What is the cause of the observed accelerated expansion (de Sitter phase) of the Universe?
Does nature have more than four spacetime dimensions? If so, what is their size? Are dimensions a fundamental property of the universe or an emergent result of other physical laws? Can we experimentally observe evidence of higher spatial dimensions?
Why are there three generations of quarks and leptons? Is there a theory that can explain the masses of particular quarks and leptons in particular generations from first principles (a theory of Yukawa couplings)?
What is the mass of neutrinos, whether they follow Dirac or Majorana statistics? Is mass hierarchy normal or inverted? Is the CP violating phase 0?
What is the exact mechanism by which an implosion of a dying star becomes an explosion?
Is dark matter responsible for differences in observed and theoretical speed of stars revolving around the center of galaxies, or is it something else?
Fusion energy may potentially provide power from abundant resource (e.g. hydrogen) without the type of radioactive waste that fission energy currently produces. However, can ionized gases (plasma) be confined long enough and at a high enough temperature to create fusion power? What kinds of advances in material science must be made?
What causes the emission of short bursts of light from imploding bubbles in a liquid when excited by sound?
Are the branching ratios of the Higgs boson consistent with the standard model? Is there only one type of Higgs boson?
@ManchesterUnited: A quick glance through those questions leads me to believe that you looked up a list of unanswered questions on the cutting edge of understanding.
"What is the identity of dark matter? Is it a particle? Is it the lightest superpartner (LSP)? Do the phenomena attributed to dark matter point not to some form of matter but actually to an extension of gravity?"
If we had any other name for it, or explanation, we'd use it. The phrase, "Dark Matter," is a glorified "I don't know."
"What is the cause of the observed accelerated expansion (de Sitter phase) of the Universe? "
All the universe is distancing itself from humanity as fast as possible. The more humanity rises on Earth, the more rapid the rest of the universe scurries away.
(JK, obv.)
"What is the exact mechanism by which an implosion of a dying star becomes an explosion?"
I'm pretty sure this is just a trolly question. For "exact" you'd need the "exact" quantum state of the star, I suppose. With a unfathomable amount of time, perhaps some computation device could solve the "exact" solution - within the confines of quantum uncertainty.
"Is dark matter responsible for differences in observed and theoretical speed of stars revolving around the center of galaxies, or is it something else? "
Well, dark matter pretty much sums it up, whatever it is, so no... it's not something else.
Whatever it is, it is not interacting with the EM fields, therefore it is invisible (i.e., not made of atoms). It is transparent, and space is dark [citation needed], so it is dark. Whatever it is, it is causing masses to act in a way that implies that it (itself) has mass. So calling it dark matter is just a short hand for "I don't know what it is, but it's dark and acts heavy."
"Fusion energy may potentially provide power from abundant resource (e.g. hydrogen) without the type of radioactive waste that fission energy currently produces. However, can ionized gases (plasma) be confined long enough and at a high enough temperature to create fusion power? What kinds of advances in material science must be made?"
(I'm assuming you mean in a "laboratory" on Earth.) Probably.
Materials that can create immense magnetic fields without being crushed and/or melted by the reaction forces they create.
Materials that become superconducting at "high" temperatures would sure be a help, too.
"What causes the emission of short bursts of light from imploding bubbles in a liquid when excited by sound?"
Water is made of atoms, which have their own dipole moment, as well as the induced dipole of the water molecule, H2O.
Maxwell's Equations say that changing magnetic fields create electric fields. When you shake a magnet, some of the vibrational energy is dissipated through the emission of electromagnetic quanta, aka photons.
Sound is many orders of magnitude lower in frequency than light, so it could be a resonance setting up in the compressed atoms. I wonder if the pressure is great enough to induce a temporarily crystalline state. It could also be blackbody radiation from the localized extreme heat caused by the localized high pressure region.
(I'm guessing. Given the nature of the other questions, this answer may be based on a false assumption about the question.)
TL;DR:
I have an undergrad degree, and I'm guessing that you don't even know what you're asking me in these questions.
E.g. zero-point energy, de Sitter phase, CP violations... come on... I know where to look to find those definitions, but I'm not a PhD, so ... sorry.
I'm happy to take all questions, but if you don't even know what you're asking, then I hardly see the point.
On the other hand, if you do understand these concepts, then please take over the thread for a few posts and educate this monkey.
Ugh. I'm so out of practice these days.Quote:
Originally Posted by Renton
You are correct. The Lorentz transformation goes both ways and the inverse transformation has a '+' sign, where the forward transform has a '-' sign.
The clocks on the ISS require re-synching with ground-based clocks, due to the combined effects of both special and general relativity.
Clocks in greater gravitational fields run more slowly, as you've said, than clocks in lesser gravitational fields.
Personal derp. Sorry it took so long to correct it, but I really wanted to be certain of why I was confused before I stated anything more on the topic.
No they don't, they just appear to from another frame of reference!Quote:
Clocks in greater gravitational fields run more slowly, as you've said, than clocks in lesser gravitational fields.
*smug grin*
Yes, they really do.Quote:
Originally Posted by OngBonga
Not just clocks, but all processes. The dilation of time is inherent to the universe.
You, whatever "you" means, will never perceive this because all of the constituent particles which are "you" are experiencing the time dilation. Your "now" always appears "normal" to you, because you inhabit that spacetime. The changes to your environment ARE changes to you.
In general, when I say, "clocks" run slower... what I mean is that time flows at a different rate. It has nothing to do with the macroscopic clock. It has to do with the (imaginary) internal clock which mediates particle interactions.
The (actual, real world) clocks on the ISS would not ever need to be re-synched if the difference was only apparent. They would just use a bit of math to correct for the discrepancy. However, the discrepancy continually grows, so they need to re-align them. The only way to not have the clocks slowly drifting out of synch with each other is if they run at different rates. I.e. they must have a different definition of a second and therefore a different definition of the speed of light.
X approaches infinity in both observations. I think you got my meaning but I thought I'd fix the glaring typos here in case anyone else reads it and it confuses them.Quote:
Originally Posted by Renton
Yes, the relativistic time dilation would affect the clocks in the way you describe, with appropriate handling of infinities, that is.Quote:
Originally Posted by Renton
(The following is based on a loose understanding of the effects of relativistic velocity. I'm assuming they apply to gravitational effects as well.)
When the relativistic factor becomes high enough, atomic interactions become somewhat impossible.
Imagine a single molecule of water, H2O. Assume that by some un-described means, it experiences a constant accelerating force.
At some speed, the exchange of photons which mediates the attraction of the covalent bonds will be left behind. Meaning that the molecule of water will just be one atom of Hydrogen and another atom of Hydrogen and an atom of Oxygen speeding along, moving too quickly to "catch" the photons that are "thrown" by the other atoms. They outpace the exchange particles.
E.g. Assume 2 capable people are playing catch with a beach ball. They keep throwing the ball back and forth as the wind slowly but unfailingly picks up. No matter what angle the 2 people stand at, relative to the wind, eventually the wind will become so strong that they can't play catch anymore. Either the wind will blow the ball too far off coarse to be caught, or the wind will be too strong for the person downwind to throw it upwind without it coming straight back to them.
In the analogy, the beach ball is the exchange particles between the atoms, and the wind is the spacetime that the atoms are rushing through.
At some speed, the atoms are no longer a molecule.
At some greater speed, the same thing happens to the atoms. The electric fields emanated by the protons and electrons become shaped like an elongated tear drop behind them. When this deformation reaches a tipping point, the atoms are no longer really atoms. They're just a bunch of fundamental particles whizzing along near eachother, completely oblivious to each other's existence.
Yeah, relative to someone in a "static" frame of reference. But ten seconds flows at exactly the same rate from your pov regardless of the velocity you're travelling at. The slower clock thing, it's other people who see your clock going slower. Time always flows at the same rate from your pov, a second is always a second.Quote:
In general, when I say, "clocks" run slower... what I mean is that time flows at a different rate.
That's my understanding anyway. Please feel free to tell me I'm wrong, I'll believe you!
I think you should reread the post you quoted. I affirm your notion of perceiving your own time as 1s = 1s. I called it "normal" time. (Assuming your perception is tied to physical particles doing physics stuff... and things.)Quote:
Originally Posted by OngBonga
"Static" is relative. As long as 2 objects aren't accelerating, then they are static in some inertial reference frame.
The thing is that sometimes you both see each other's clock ticking slower, and sometimes not. In the case of gravitational time dilation, a person on the space station sees clocks on the surface of the Earth ticking slower, and clocks on the surface of the Earth see the clocks in orbit ticking faster.
The twin paradox is real. If two identical twins travel on different space-time paths, then they will age at different rates. So much so that it "could" be possible that one twin ages much more rapidly than the other twin, and when they are brought back together after their separation, one of them could be years older... or his body will have aged much more... than the other.
For the record, it's not a paradox at all. The only thing is that we are so used to traveling on nearly identical space-time paths with everything around us that we fail to notice that the rules in the universe act differently on different scales.
If you zoom in on a curve close enough, it will look like a flat plane - unless it's a fractal. You go fractals!
(Actually, an infinite, flat plane is a fractal. Even more win for fractals!)
I'm saying that life on the surface of Earth sees only the barest of minutiae when it comes to differences in gravitational field or differences in velocity. It's easy to falsely assume that the flow of time is constant under these conditions.
I feel like I've watched 100 youtube videos about the wave-particle duality and I still don't really get it.
I'll contrive a probably retarded example and ask you how it behaves:
Say you have a perfectly straight, slender, tube made out of a material that is a perfect black body that absorbs all photons that interact with it. The inner-diameter of the tube is 1mm. One end of the tube is closed with the same material, and has a source that emits a beam of single photons in the direction of the tube.
1. In a tube of length X meters, what is the probability that the photons would escape from the tube?
2. Would the part of the wave that travels outside the tube then propagate in an ever-widening cone? What is the angle of that cone, and for a few different lengths of the tube, what does the probability distribution look like? It seems to me that with a very short tube there would be a larger gap in probabilities from the edge of the cone to the center than if the tube were very long.
Bonus question: is it even possible to direct electromagnetic waves or are they omnidirectional?
I'm not clear on what you're describing.
A brief description of blackbody radiation:
Blackbody radiation is the physical process that describes why hot things glow. E.g. Molten metals usually are red-orange to yellowish in color. Everything which is made of atoms emits blackbody radiation according to its temperature. Humans emit blackbody radiation with a peak frequency in the infrared range. If you hold your hand under an infrared lamp, you immediately feel the heat. The frequency of the IR light is in a resonance tuning with the thermal vibrations of the atoms in your body (or at anything near room temperature).
There are other Quantum Mechanical effects which alter a thing's (possibly apparent) color.
The tube is a perfect blackbody, so it absorbs 100% of photons which are incident on it. It neither reflects nor transmits any photons through it. I'm assuming the tube does not have any holes in it, so that any photon which is inside the tube will definitely be absorbed by the tube in some amount of time.
Ignoring any weirdness from the tube's length being very short, the answer to question 1 is straightforward. None of the photons which are inside the tube will ever make it to outside the tube without having been absorbed by the blackbody. The blackbody will emit photons via its "heat glow."
The rate and frequency of emitted photons will be a direct result of the temperature of the blackbody. Photons carry energy, and their introduction into the tube (a test volume) means that the total energy of the test volume has increased. If you add photons, you add energy, and that energy will manifest as heat. The glow will come from the inside walls of the tube as well as the outside walls, and all photons emitted inside the tube will ultimately be re-absorbed by the tube. This could happen many times before the photon's energy escapes the tube.
So... if you mean does "this" photon ever escape the tube?
NO. The photon will be absorbed by one of the atoms in the tube's wall. That atom will emit a photon which may or may not be of the same frequency as the original incident photon, and could be emitted in any direction.
If you mean, does the energy carried by this photon escape?
YES. The photon will change form many times, and its energy could be split up into any number of bits, but that energy will escape the tube.
Number 2 is a bit trickier. Assuming the blackbody is made of atoms and is thick enough to be called "perfect," then it doesn't change anything. I don't even think the interior volume of the tube is entirely relevant, but that feels odd to say. At some point, there will be uncertainty as to whether the photon is inside the tube or merely near the tube, but outside. Seems like a discussion for another day.
If the walls of the tube are too thin, then the tube ceases to function as a perfect blackbody, in that some of the interior photons can pass through the wall of the tube.
In this case it becomes a question of the atomic structure of the tube. The photons will scatter off of the atomic lattice, and will experience self-interference at the various angles of scattering. At angles where the interference is destructive, there will be no photons. Those photons will be displaced to the angles where there is constructive interference.
Bonus Question: There are these miraculous things called "conductors" which can be used to direct EM waves in all kinds of potentially insane ways. I even heard they've gone brazenly public and are marketing things like digital watches.
Wait, I think you may be misunderstanding the setup. The tube is only closed on one end. All I meant to set up is that there can be no reflection that focuses photons in the direction of the open end of the tube. i.e. all photons that escape the tube will have traveled directly from the source. In ASCII cross-section:
______________________________________________
|S ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
|_____________________________________________
Where S is a source of photons, and ~ is the path of a photon exiting the tube.
Also, re: the bonus question, what I mean is that whenever a wave is originated, does it then propagate omnidirectionally by default or is there a bias where the probability is stronger?
If the photons are coherent, i.e. the source is a laser, then the cone with have a minimal spread.
There will always be a cone. Even a laser has a cone and a narrow frequency band. It is not a "single" frequency, nor is it perfectly coherent. Within the confines of almost any experiment, it can be considered both, though.
This is all due to the fact that the photons carry momentum. The momentum is slight in comparison to the mass of the atom, but conservation of energy says that the atom MUST receive an equal and opposite change in momentum. This means that the emitted photon is slightly off "perfect."
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A lot depends on the "sharpness" of the tube's end, and what percentage of photons go "near" it. Photons that pass roughly 1 wavelength from a sharp edge will be diffracted. This diffraction will induce "banding" due to constructive and destructive interference.
This is easy to test at home. If you have a laser pointer and anything with a straight, opaque corner. If you set both up on stands, such that the laser beam is pointed at the corner, then the projected "shadow" will have bands of light and dark at the boundary of the spot where it is "cut off."
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If the photons had a wavelength of near 1 mm... probably even 0.5 mm or o.25 mm... then they could be diffracted into the wall and absorbed quite easily. Or they could be diffracted "through" the wall. (For reference, microwaves have wavelengths in the ballpark of centimeters. This is one reason they don't pass through the tiny holes in the shielding on your microwave oven's door.)
I'd need to actually crunch some numbers as to the spread of the cone... it would be a function of the wavelength of the photons.
FWIW, any photons diffracted into the blackbody would eventually be re-emitted in a random direction, and with a random number of photons. Random within the limits of the thermal excitations of the electrically charged atoms.
The blackbody emissions are merely the excitations of the EM fields by moving, charged particles.
Oh, bonus question.
Short answer is that it just depends on the electric permeability of the surrounding medium. Clearly there is a wide spectrum of conductors and semiconductors and insulators. Each propagates the EM fields at a different strength.
In any case, if the charge source is embedded in a uniform volume, then the fields it emits will be spherically symmetrical.
If the charge source is, say an electron in a piece of copper, then the fields it emits will favor the "easy" path in being confined to the conductor. At the balance where the "compactness" of the field lines inside the conductor means adding one more is just as hard as adding one more to the volume outside the conductor, then the field lines will penetrate.
This is all a bit hand wavy to give a quick summary. Electric field lines are an imaginary construction to help visualize the intensity of the field, but they are not really anything you could measure (As in counting the lines. Obv. we can measure the electric field). They are the gradient lines of the electric field, and are infinite in number over any region. We pretend to "count" them when we talk about the intensity of the field.
These are the lines you might see drawn between a positive and negative charge in a text book. They are always at right angles to the equipotential lines, which go around the charges, but do not touch them. The electric field lines are like longitude, making a path to each pole. The equipotential lines are like latitude, going around, but not touching. All longitude lines intersect all latitude lines at right angles.
who needs ascii when I know how to use autocad?
http://i.gyazo.com/816b5a08466a1b18e27e3767e33e699a.png
http://i.gyazo.com/578581b171e1cd0186834dcb98f6a0c1.png
The green object is a cross section of a tube of inside diameter 1 unit and length 5 units. The cyan arcs represent the propagating EM wave, the dashed grey arcs represent the part of that wave that has been blocked by the tube, and the red radials show the density of the probability. Unless I'm doing it wrong, it appears that the photon only has about a 4% chance of escaping the tube.
More silly questions. If a photon is absorbed, does its wave disappear? Say one photon was created in a vacuum in an area of space that was completely devoid of energy. The wave from that photon could propagate for light years without encountering anything. Say you had an array of detectors that provided complete coverage of half of the sphere of 1 light year radius from the source of the wave. Would those detectors have a 50% likelihood of seeing the photon, and then would the other half of the wave disappear if they did?
Just to be clear to anyone following the thread: This question was erroneously posted to the Randomness thread - which is appropriate from time to time, I think - and I answered the questions there.Quote:
Originally Posted by Renton
Short answer is that this is exactly the kind of picture I was visualizing and it sums up the classical situation perfectly well.
It falls short for the Quantum Mechanical effects. The photons which pass "near" the edge of the tube will be diffracted and will experience constructive and destructive interference. This will make a "rippled" boundary to the spot this device would project on a wall.
Also, it misses the fact that the tube absorbing the photons is absorbing their energy. This will cause the tube to heat until it's glowing and radiating an equal amount to it's intake.
How dare you suggest these are silly questions!Quote:
Originally Posted by Renton
Ummm. Words.Quote:
Originally Posted by Renton
Disappear? :/
Dis-appear... yeah. A photon being absorbed is exactly that. Dis-appearing. Oh wait. Actually it's the fact that the photon was absorbed which allowed it to "appear" to the observing particle. :/ words.
A photon being absorbed means before there was 1 photon and now there are 0 photons. So yes, the wave of the photon collapses. The energy carried by the photon will be transferred to the particle which absorbed it, in accordance with the Law of Conservation of Energy (and accepting that mass may be one expression of energy).
We really need at least 2 photons to have any hope of preserving said conservation law, and all his stern-looking friends, who are giving me the stink-eye and waving their fists,Quote:
Originally Posted by Renton
but I'll play along.
Given a perfectly random initial trajectory of the photon, then yes, 50%... assuming the detector has 100% efficiency.Quote:
Originally Posted by Renton
Other half? You lost me.
At any rate, the entire wave packet that is the photon is absorbed.
Think of the single slit experiment. The rippled pattern looks like wave interference. It is also true that when a photon is detected, it always has the energy of exactly 1 photon. Never half a photon here and the other half over there.
This is the meaning of "quantum." They come in discrete bits. They act like waves in many ways, but they act like particles, all the same.
Yeah I still completely don't get it. How can a wave be an omnidirectional sphere propagation that has the same amount of energy even as it gets exponentially larger? I just don't understand what the wave is aside from being an expression of the probability of the locations that the photon could be detected.
The magnitude of the wave gets exponentially diminished as the wavefront grows. The integral of the probability function over all space is always equal to 1 for each particle.Quote:
Originally Posted by Renton
There is a mathematical step called "normalization" that is required to solve for the wave function explicitly. This is because there is a need to eliminate a variable from the equation in order to determine its magnitude. It amounts to saying that for each particle, there is exactly 1 particle and it's definitely somewhere in the universe.
The problem is that there is simply no well-defined position function for massless photons.Quote:
Originally Posted by Renton
It's quite complicated to visualize at this stage. A photon is a quantum of the electromagnetic fields, in a measurable sense. That quantum is expressed with a certain momentum, which is proportional to its electromagnetic wavelength.
Note that the electromagnet fields are indeed waving. The propagation of light is explained by Maxwell's equations quite well.
What is confusing is just what you said. The probability function expands with diminishing probability as it spreads out. Yet, the particle is somehow only ever in one place. NOT spread out.
It's a mind bender, and we're jumping beyond physics to try to explain "why" anything is how it is. Physics is primarily aimed at explaining what something is and does, but struggles at why after a certain point.
can more than one photon comprise the same wave?
It could well be that the reason there is no well-defined position function goes back to the relativistic effects of extreme velocity.
In the limit of velocity approaching the speed of light, the time dilation approaches an infinitely large value, as does the space contraction.
I don't know what this means exactly, but it seems to imply two things.
1) At the limit of infinite time dilation, all clocks have slowed to stopping, except for the photon's, which is perceived as "normal" in its comoving reference frame (if that's meaningful at this stage).
2) At the limit of infinite space contraction, the universe is an infinitely thin sheet in the direction of travel for the photon. The space in front of and behind the photon, in its direction of travel has contracted to a nothingth of width... the photon could be thicker from front to back than the entire universe in which it exists.
All this is WTF, obv.
I may be misunderstanding some exception or loophole around the massless photon and these relativistic effects.
My primary assumption is that I'm thinking of a particle with mass accelerating ever faster and somehow, despite the physical impossibility of the feat, reaches the speed of light.
Yes, in that case each photon's wave would have a total probability of 1.Quote:
Originally Posted by Renton
Hmmm.. as I type that I realize that there could be such a case that the two waves are indistinguishable, and only the combined wave packet will be measurable. I think the normalization step is still required, but we're talking quite generally.
In this case, the information of both would be contained in the packet, and the packet would be treated as a single pair... if that makes sense.
The number of photons is conserved in all reference frames. I believe this even comes up in Max Plank's original derivation of blackbody radiation.
I think you have a good enough picture of my ignorance level wrt QM, what resources would you direct me to learn more at this point? Keeping in mind that the source needs to be dumbed down to a certain degree.
I think you are on the brink of a completely intuitive understanding of blackbody radiation. Max Plank and Albert Einstein developed the explanation of blackbody radiation at the dawn of the revelation of QM.
Another important phenomenon to study is the photoelectric effect.
This is a new physics YouTube channel that I just found. It looks excellent based on this one video:
https://www.youtube.com/watch?v=GUyo5U20fd4
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At some point you may want answers that are more than qualitative. You will need to be familiar with a few disciplines of math if you want a more full understanding.
A) Lots of algebra*
B) Matrix mathematics offers a huge toolbox for (A)
C) Partial Differential Equations, which comes with a boatload of calculus
D) Probability theory*
*My guess is that you already have (A) and (D) covered.
Just picked up Einstein by Walter Isaacson. I know he didn't like some things about quantum physics - will probably have some questions related to the book at some point.
Can you explain in 100 words or less why we can't use quantum entanglement for faster-than-light-speed communication?
Simply put, the entanglement is too sensitive to alter without first observing. The act of observing one particle from an entangled pair collapses the entangled wave function, dis-entangling them. Any change made after than will not have any consequences on the other particle.Quote:
Originally Posted by Eric
Bear in mind that by 'observation' I mean any interaction with anything.
Note that wave function collapse is a poorly understood phenomenon on very small time scales. As in... it seems like a sudden, discontinuous change, but if we could watch it in slow motion, then maybe we would understand it better. As far as I know, there is no mathematical description of the collapse.
To my knowledge, there is no way to alter the entangled wave function without first collapsing it into a non-entangled group of waves.
So the information carried by the entangled partner is "chosen" by the observation, and can not then be changed.
Let's use heads and tails for simplification. It is my understanding that as soon as we observe one entangled particle as heads then the other entangled particle must be tails.Quote:
Originally Posted by MadMojoMonkey
Suppose that before I leave for Mars, I take one entangled particle with me and leave the other one here with you.
We agree that I'll observe my particle once I've found a certain mountain on Mars. I find the mountain and observe heads. At that moment your particle must be tails.
Is the problem that you can't know when your particle becomes tails because you'd have to be monitoring it the whole time to know that? In other words, the second you start monitoring your particle then they are dis-entangled?