I've actually found something that I'm interested in. Physics, of all things. Go figure. The problem I have though, is that the more I read, the more questions I end up having. And as soon as I answer that question (hours of staring at the same paragraph, mind you), 4 more questions pop up off of that.
And believe me, the books I have and wikipedia aren't too Nathan-friendly.
So lets start at what I am currently thinking about. In reference to general relativity, why is space time curved, and what exactly does that mean?
I understand that "inertial observers can accelerate with respect to each other" and that to be considered inertial, you must be freefalling. What I don't understand is why this goes against Newtons first law of motion (an object in motion wants to stay in motion, an object at rest wants to stay at rest unless outside force acts upon it).
So anyway, back to the first question. What does it mean by saying spacetime is curved?
Posted by mr_porteiro_head (Member # 4644) on :
One thing that it means -- if the universe has enough mass to eventually collapse back on itself, then space is curved in such a way that if you travel in a straight line in one direction, you will eventually come back to the point you started at.
Of course, even if you travel at the speed of light, it will take you longer to do so than it will take t he universe to collaspe, but still...
Posted by Jim-Me (Member # 6426) on :
The short version is that, even though light is massless, it's affected by gravity. Others may embellish to their heart's content.
Posted by T_Smith (Member # 3734) on :
Now, when you say that, do you mean that I'd be pulled back to the starting location, or that I'll come out the other end, like Pacman going through the side of the maze and coming out the otherside?
Posted by fugu13 (Member # 2859) on :
Space time curves because a mass deforms it. This is an explantion for gravity; like a ball on a rubber mat with an indentation, things move towards other things.
The inertial frame of reference doesn't go against Newton's first law of motion, except by making it meaningless. Something in (non-accelerating) motion relative to you can be thought of as still, and something still relative to you can be thought of as in motion, all depending on your frame of reference.
Posted by mr_porteiro_head (Member # 4644) on :
Like pacman, or like walking around the earth.
In fact, it's a lot like the earth. The surface if the earth is a 2D space curved in 3D space. Likewise, the 3D space of the universe is also curved.
IIRC, A Brief History of Time explains this.
Posted by T_Smith (Member # 3734) on :
"The short version is that, even though light is massless, it's affected by gravity. Others may embellish to their heart's content."
Ok, that I understand, from the whole solar eclipse-stars thing. I guess then, that I'm not understanding space-time. I see it as a 3-d realm, with a parameter of time.
Which means that if space time is curved, then instead of a strait line of events, it means that gravity effects the speed of time, correct?
Posted by Bokonon (Member # 480) on :
More like Pac-Man, except there is no going "off screen".
-Bok
Posted by Bokonon (Member # 480) on :
Spacetime is 4-D (or perhaps a 4-D manifestation of an N-Dimensional) space. You can't untangle time from it, and treat it differently (I don't think).
-Bok
EDIT: There is no "speed of time" (or "speed of space") only matter/energy can have speed(/momentum/energy)
Posted by T_Smith (Member # 3734) on :
That's mostly an analogy. Just as if a 2D surface were curved like that, things would tend to "fall" toward the earth, the fact that 3D space is curved makes things tend to fall toward the earth.
Posted by El JT de Spang (Member # 7742) on :
The curvature is gravity. The more mass an object has, the bigger the indentation it causes in spacetime and the more gravity it has.
The way I've heard it explained is that if you rolled a marble across that surface, it would roll towards earth if it got into its gravitational pull (represented there by the dent in the image).
Posted by Jim-Me (Member # 6426) on :
quote:Originally posted by fugu13: The inertial frame of reference doesn't go against Newton's first law of motion, except by making it meaningless. Something in (non-accelerating) motion relative to you can be thought of as still, and something still relative to you can be thought of as in motion, all depending on your frame of reference.
To elaborate: Where it starts going wacky on Newton is that Newtonian Physics only works correctly for non-inertial frames of motion. For inertial frames, Newton's still pretty accurate for relative velocities much smaller than the speed of light, but technically incorrect. As relative velocity increases, so do measurable effects.
As far as the gravitational effect on time, yes, the curvature of space-time accounts for it (or perhaps I should say, "predicts it"), and yes, you are viewing it incorrectly. Space-time is 4 dimensional, with time being the 4th dimension.
Posted by fugu13 (Member # 2859) on :
Light is only massless at rest (which it never is). The mass it acquires due to motion means it is affected by gravity.
Oh, and mass and energy are equivalent.
Posted by Bokonon (Member # 480) on :
Well, the ultimate issue you have is that it's a [EDIT: 2d rendering of a 3d object in a 4d space]. And since we experience time differently from the other perceivable dimensions, it makes us think it is more different than it actually is.
-Bok
Posted by Jim-Me (Member # 6426) on :
Re: "speed of time" I suppose you could say it's normally 1s/s and that this rate is affected by gravitational differences between two observers.
Posted by T_Smith (Member # 3734) on :
Ok, so the answer to the question:
1) Spacetime is curved due to mass/energy. 2) This is what causes gravity.
Is that an adequate answer?
Posted by mr_porteiro_head (Member # 4644) on :
quote:Light is only massless at rest (which it never is). The mass it acquires due to motion means it is affected by gravity.
Actually, light is always massless. But even though it is massless, it manages to have momentum, which is usually defined as mass times velocity.
Posted by Jim-Me (Member # 6426) on :
quote:Originally posted by fugu13: Light is only massless at rest (which it never is). The mass it acquires due to motion means it is affected by gravity.
Oh, and mass and energy are equivalent.
Back in my day we used to talk about the "apparent mass" of light to delineate that, though it behaved as if it had mass, it didn't actually have it. Are they getting away from that now and saying that photons have actual mass, just no rest mass (and correspondingly no rest energy?) It wouldn't surprise me, it's just kind of intersting how much and how fast the prevailing view can change... I mean it's only been a decade or so since I studied this stuff.
Edit (to T-Smith): I'd be very leery of using the word "cause" anywhere in this discussion. I'd say the curvature of space time is a theory which explains gravity's effects, among other things. but you are entering a weird enough world that "cause" is a very dangerous thing to say and usually far too nebulous to establish.
Posted by mr_porteiro_head (Member # 4644) on :
quote:Originally posted by T_Smith: Ok, so the answer to the question:
1) Spacetime is curved due to mass/energy. 2) This is what causes gravity.
Is that an adequate answer?
Adequate for what? It's correct, AFAIK.
Posted by Bokonon (Member # 480) on :
Well, the whole "spacetime is curved" I think is [EDIT: only] part of it, particularly once you involve quantum mechanics (Gravitons (sp?) and all that). I would say, for 2), that "this is what predicts the behavior of gravity best".
-Bok
Posted by El JT de Spang (Member # 7742) on :
Adequate for a layperson without being in-depth enough to cause random brain a splosion, I'd guess.
Posted by fugu13 (Member # 2859) on :
Well, every observer observes time proceeding at the same speed for them (that is, in his or her frame of reference); this is a consequence of light going the same speed for all observers. From that person's frame of reference other frames of reference may be behaving as if time is different there (they really are behaving differently, perhaps even contradictorily to their own experiences, so in a sense time is different there, but you can never get to a place where time is going a different speed than it normally does for yourself).
Posted by T_Smith (Member # 3734) on :
I suppose the big thing here to help me conceptualize all of this is really understanding spacetime.
I keep trying to quantify it in a coodinate based system in my head, but that, I believe, is ruining it for me.
Posted by Jim-Me (Member # 6426) on :
Then, fugu, we get into the very neat but ultimately unanswerable question of whether that is strictly a function of the human perception, like being limited to 20hz-20khz hearing or viewing the visible spectrum.
I love talking about this stuff... it's been far too long Posted by fugu13 (Member # 2859) on :
Mass-energy equivalence is pretty much universally accepted; since photons have energy, they have mass. Furthermore, they're obviously affected by gravity, so why try to invent a fake mass that's affected by gravity just like real mass, but it isn't?
In some ways its strange anyone would talk about it as fake mass, when its a pretty clear consequence of (among other things) the equations for deriving E=MC^2.
Posted by Bokonon (Member # 480) on :
It can be seen as a coordinate system, but one with 4-axes instead of 3. Which is a bit hard to grok.
-Bok
Posted by Jim-Me (Member # 6426) on :
quote:Originally posted by T_Smith: I keep trying to quantify it in a coodinate based system in my head, but that, I believe, is ruining it for me.
If you can picture a coordinate system with 4 axes, you've got it.
I can't, though.
Posted by Javert (Member # 3076) on :
quote:Originally posted by T_Smith: I suppose the big thing here to help me conceptualize all of this is really understanding spacetime.
I keep trying to quantify it in a coodinate based system in my head, but that, I believe, is ruining it for me.
Which, unfortunately, is nearly impossible. We live in 3 dimensions, so the closest thing you could do (which is what the diagrams try to do) is reduce reality as we know it to 2 dimensions and imagining space time as a third.
At least, I think I know what I'm saying.
Posted by El JT de Spang (Member # 7742) on :
My favorite quote about relativity, the one I always think of when this discussion comes up, is the one from the British astronomer/astrophysicist Sir Arthur Eddington.
When asked by a journalist if it was true that he was one of three people alive that understood Einstein's relativity theories, he replied, "I am trying to think who the third person is."
Posted by Bokonon (Member # 480) on :
Jim, jinx!
-Bok
Posted by fugu13 (Member # 2859) on :
Its definitely not strictly a function of the human perception, the equations don't include any requirement of observation at all, and our observations correlate with the equations. Well, at least not any more than anything else; theoretically there could be some requirement that something be observed by a human before its really there, but that would require a lot of silliness, so why bother with it ?
Posted by mr_porteiro_head (Member # 4644) on :
For more headache inducing 4D goodness, check out the 4D cube, or hypercube.
Posted by Javert (Member # 3076) on :
"When you sit with a nice girl for two hours, it seems like two minutes. When you sit on a hot stove for two minutes, it seems like two hours. That's relativity."
-Albert Einstein
My favorite relativity quote. Posted by fugu13 (Member # 2859) on :
Yeah, its really amazing how far understanding of relativity has advanced. Now anybody who's taken a decent bit of college level physics can grok it pretty well, and lots of people have a lay understanding.
Posted by T_Smith (Member # 3734) on :
Yeah, how my brain is processing it is (x,y,z,t) where t is time.
So say Earth(x,y,z,t), where any of those are variables that can be changed. Say earth didn't move, but time kept going forward, that way we see x,y,z as the same, but t as a different value. So same place, different time. Now if we changed x,y,z and t we have different place, different time.
Thats pretty much the only what I'm going to be able to explain how I'm quantifying spacetime.
Posted by Bokonon (Member # 480) on :
That's more or less correct, but understand that the image you linked to really only (x,y) while faking (due to artistic tricks) (z).
-Bok
Posted by Jim-Me (Member # 6426) on :
I owe you a coke, Bok.
But Fugu, the equations don't explain our perception of time as passing at 1s/s or *why* that should be in the least. That's what I mean by "is this just a matter of human perception and it's limitations?"
Certainly a big effect of relativity is to show that time is not the absolute we thought it was. So why should there not be different ways to perceive time, not limited to 1s/s? Once you accept that time is a dimension, it is easier to suppose that things can move along that axis at different rates, though it's still just as hard to reconcile the paradoxes inherent in that.
Posted by Jim-Me (Member # 6426) on :
quote:Originally posted by fugu13: Yeah, its really amazing how far understanding of relativity has advanced. Now anybody who's taken a decent bit of college level physics can grok it pretty well, and lots of people have a lay understanding.
Thank you "Nova" and "Cosmos".
Posted by T_Smith (Member # 3734) on :
But then back to previous discussion, then, does that mean gravity effects parameter t?
Posted by Jim-Me (Member # 6426) on :
I was waiting for others, but the answer is "yes".
Probably.
Posted by Bokonon (Member # 480) on :
Jim, there are ways to observe different times... The stationary vs. orbiting atomic clocks, for instance. They measure time differently, empirically. So ultimately, each person perceives time slightly differently, but since we are moving relativistically slow, related to each other, it just seems like we observe it the same.
Also, remember that a "second" is ultimately an arbitrary measurement of time that is convenient.
T, I realized that I'm off a bit in my last response. the trick is to realize that based on what sort of energy/matter is nearby, the very axes at and around certain coordinates are warped.
-Bok
Posted by T_Smith (Member # 3734) on :
Ok, so say we have Earth(x,y,z,t) traveling in a straight line. That means that x is increasing, and t is increasing.
Suddenly, Earth encounters a strong gravitational field. This means x is still increasing, but now y is being effected. Is t still increasing at the same rate?
Posted by T_Smith (Member # 3734) on :
I need to go do dishes. Don't get too complicated without me. Posted by Jim-Me (Member # 6426) on :
T, an over-simplification, but if I understand you (and the subject) correctly, not only is t's rate of change affected (assuming an outside observer) but also x's, not due to gravitational acceleration but to Lorenz contraction... the whole axis would get shorter. Fugu, do I have this right?
Bok, I don't mean that we can't measure different rates of time passage, I mean that we can't experience them like we can, say, the color red or the note 'a below middle c'. Does that make more sense?
Posted by fugu13 (Member # 2859) on :
Bok: the amount of time that has passed is different, this doesn't mean the 'rate of experience' of it is any different.
Well, you're partly answering your own question. 1s/s is pure number, there is no unit. Travel through time is not like travel through other dimensions. And actually, that time progresses the same for any frame of reference we are in is an assumption -- Einstein's assumption that inertial frames of reference are indistinguishable.
Posted by Puppy (Member # 6721) on :
Whoah, Porter. I actually GET hypercubes now. Sort of. Thanks for the link!
Posted by Bokonon (Member # 480) on :
Yes, to earth, but to someone somewhere else in the coordinate system, their t may suddenly be different from earth's t (assuming their time was identical, which is impossible, since, in the words of They Might Be Giants, "simultaneous events don't happen, we are all isolated temporally").
-Bok
Posted by T_Smith (Member # 3734) on :
Ah, you bring up that Lorenz dude, another guy with concepts I can't understand.
Yes, I know x's would be changed as well, since if it were on a steady pace, then it would take longer, due to y's change, to get to the next x coordinate. If that made sense.
What I don't understand is why t's rate would be affected.
Posted by Bokonon (Member # 480) on :
Jim, I guess so, but it sort ends up nonsensical. Sort of like "what time was it before spacetime existed?" I guess I'm on the side that says we experience it as we are built to experience it.
-Bok
Posted by Jim-Me (Member # 6426) on :
quote:Originally posted by T_Smith: Yes, I know x's would be changed as well, since if it were on a steady pace, then it would take longer, due to y's change, to get to the next x coordinate. If that made sense.
That made sense, but it's not why x's rate would change. x,y,z,and t (and presumably other dimensions which probably exist) are all affected by the introduction of the gravity field. To an observer outside the gravitational field, one foot gets shorter and one second gets longer (if I have these right... I may be wrong about either one of them but they both definitely change) on your hypothetical earth in the new gravitational field.
Edit: as to why, it's kinda related to what someone else said about nothing being simultaneous.
Posted by fugu13 (Member # 2859) on :
*digs deep in brain* (I've had AP Physics plus some college level self-study, and that was a while ago, so I'm not necessarily the best person on this forum to ask for verification ).
In a sense the question is meaningless without an observer (though since gravity is indistinguishable from acceleration the frame is no longer inertial). If (as T seems to suggest) the gravitational field is perpendicular to the movement of the earth (and the earth's own gravitational field is taken as negligible), then there are several effects going on:
Any relative movement by the earth has already resulted in the earth's dimension in the direction of movement being distorted. Movement towards the gravitational source will have similar effects in that direction. Time will appear to go slower.
If the observer is coplanar with the earth relative to the gravitational source, then no change due to gravitation is observed. If he is closer, then their will be some gravitational effect making time on earth appear to go quicker to the observer, possibly counteracting the effect of speed differences.
If he is further, then there will be some gravitational effect making time on earth appear to go even slower to the observer.
*crosses fingers* I think that's correct.
Posted by fugu13 (Member # 2859) on :
Jim-Me: an observer outside the gravitational field? Posted by T_Smith (Member # 3734) on :
"one foot gets shorter and one second gets longer (if I have these right... I may be wrong about either one of them but they both definitely change) on your hypothetical earth in the new gravitational field."
Now, do you mean this in a way of "the earth is still traveled a foot, it only seemed shorter because it was moving along a different plane?
If so, then lets say the gravitational field moved the earth away from the person who was viewing it. At that point, it would appear that a second was longer, since it took longer for the light to reach the observer. But if it moved closer, it would appear that the second was shorter since it didn't take as long for the light to arrive.
Right?
Posted by Jim-Me (Member # 6426) on :
Well, I read him to mean some hypothetical device is generating a localized gravitational field which affects the earth but not other things in the relatively nearby area...
Posted by T_Smith (Member # 3734) on :
quote:Originally posted by fugu13: Jim-Me: an observer outside the gravitational field?
Yeah, I had the same thought. Posted by fugu13 (Member # 2859) on :
There is no seems, and no appears. These changes are. They are physical and real. However, they are also often contradictory. Fun, huh?
A foot for the earth got shorter. It really did. The people on earth would disagree, but that doesn't mean it didn't from your perspective.
Posted by T_Smith (Member # 3734) on :
What I meant was the people on earth still see it as travelling a foot, but the person who observed it saw it as, say, half a foot.
What I was asking about is if the people on earth saw it as a foot because instead of only x changing, now y is changing as well? And that the person observing saw it as half a foot, because from their perspective, the earth is still only traveling on x?
Or did a foot just really change?
Posted by Jim-Me (Member # 6426) on :
T,
I'm more familiar with doing this by motion, rather than by gravity well, but I know the gravitational effects are similar, so I'm going with that. I'm saying this as an addendum to the caveat that my last Modern Physics course was in the early 90's.
That having been said, you are correctly accounting for the effects of the earth starting to move in the y-axis because of the gravitational field.
*but*
There are other, similar, effects that occur merely from the earth's position in the gravity well... not from it's motion at all. as Fugu points out, though, it's not affecting all axes... that was my mistake, it only affects the axis in which the field pulls, in your example, I believe, the "y" axis.
And I do not mean "the earth still traveled a foot but it only seemed shorter because it was in a different plane. I meant that one foot on your hypothetical earth was actually shorter than one foot elsewhere. That a foot long hot dog on your earth, would measure less than one foot to someone away from it and observing from a (supposedly) non-inertial frame, though it would still be a foot long and measure one foot to someone on your earth. The actual, abstract length of "one foot" gets shorter.
Perhaps the best way I can put it is, a clock one foot tall in Death Valley is shorter and runs slower than an identical clock at the top of Mount Everest. *If* I don't have the equations upsde down because I only ever messed with moving objects, not gravity wells. I should add, though, it will still seem the same when viewed from nearby (i.e if you just pcik up the clock and move it, you won't see the difference because you are moving with it). It's only when comparing the two to each other that the differences become visible... to someone on Everest, the Death Valley clock looks to run slower and be shorter. To someone in Death Valley, the Everest clock looks to run faster and be taller, but if the person from Death Valley goes to Mount Everest, the clock will seem one foot tall and run "correctly".
Edit: apologies for using "seem". Fugu correctly points out that these changes are real... I was trying to emphasize that they are only measurable from other frames of reference. Tricky stuff... imprecise wording (a problem of mine) can get you all kinds of twisted in Modern Physics.
Posted by fugu13 (Member # 2859) on :
Yep, the more relative gravity (like the more acceleration), the slower a clock is to an observer, and vice-versa.
Posted by T_Smith (Member # 3734) on :
Ow... my head.
So lets say we have a clock at the bottom of Mt. Everest and one at the top. Both clocks running at the same rate. With both clocks seperated, the guy on the bottom and the guy on the top see their respective clocks hit Noon at the same moment. The guy on the bottom looks up at sees the clock at Noon, the guy on the top looks down and sees the clock at noon.
With that in mind, you're saying that after an hour passes, the clock on the top is going to be ahead of the clock on the bottom?
Posted by fugu13 (Member # 2859) on :
Well, they aren't running at the same rate, but we can say they're both considering the same number of oscillations of the spectral emissions of cesium atoms to be a second.
If they happen to both appear to show noon to someone down in death valley, then a bit later he'll look up and the one on everest will be ahead, yes. Very minutely, of course.
Posted by Jim-Me (Member # 6426) on :
yeah, we're talking this effect wasn't measurable until the advent of the atomic clock, but they actually did an experiment with two of them and sure enough, Einstein was dead right on that one (though I gather Relativity is starting to show holes itself, now?)
Posted by fugu13 (Member # 2859) on :
Well, holes at the level of the sufficiently small, but its had those a long time. And people keep going back and forth over the cosmological constant (existence and possible interpretations).
Yeah, there was a cool experiment with airplanes.
Posted by T_Smith (Member # 3734) on :
What I meant by same rate is that if they were brought back at the same level, then both would be running a rate of 1s/s, regardless of what time each was showing.
The question I have, then, is why? And if there is no why, then fine. If we accept that as true, it means that the more gravity, the longer you live. Right?
Posted by fugu13 (Member # 2859) on :
The 1s/s thing is a bit of a misnomer.
There is a why, its because light always travels at the same speed for all observers and inertial frames of reference are indistinguishable. For why this is the why for gravitational differences, you'll have to have more math .
Posted by T_Smith (Member # 3734) on :
Since when has math ever been involved in physics? Posted by Bokonon (Member # 480) on :
fugu, Or notice that Faraday's Equations of Electro-Magnetism are referentially agnostic, therefore whether you are standing still, or going 1 million miles per hour, doing EM experiments will yield the same result.
EDIT: Of course the reason the results are the same is because c (the speed of light in a vacuum) is c is c is c.
-Bok
Posted by Dan_raven (Member # 3383) on :
Sasha is visiting his grandmother one time zone away.
I called him last night. When it was time to hand up the phone I told him it was bedtime.
He asked me, "What time is it? Really."
I said, without thinking, "Its 8 O'Clock here, and its 9 O'Clock there."
There was silence on the phone.
Then...
"No Papa. What time is real time?"
I had a bit of a mental melt down, my mind flashing everything from Relativity to Day Lights Savings to the all important Time Zones.
Luckilly Momma, with Sasha, answered.
"Its BED TIME!"
Posted by Dagonee (Member # 5818) on :
quote:Originally posted by fugu13: Well, holes at the level of the sufficiently small, but its had those a long time. And people keep going back and forth over the cosmological constant (existence and possible interpretations).
Yeah, there was a cool experiment with airplanes.
Does this indicate a possible different kind of hole?
Posted by fugu13 (Member # 2859) on :
Maybe, maybe not .
I suspect there may be other effects involved, but even if not I could see relativity being fairly easily reconciled with certain sorts of differences.
Posted by T_Smith (Member # 3734) on :
New question:
I am having trouble comprehending what exactly is causing gravitational forces.
I comprehend that gravity is the tendency for two objects to accelerate towards each other.
I understand the inverse square law.
I understand that 2 objects in freefall, or inertial motion, are not accellerating with respect to each other.
What I do not understand is what is causing the attraction. There is nothing in between them, there are no invisible strings pulling them together. I do not accept that forces are the end all "there is no explanation, they just are" answer. I can't wrap my head around how a curvature of spacetime is going to cause gravity, if gravity itself is causing the curvature of spacetime.
Posted by rivka (Member # 4859) on :
quote:Originally posted by T_Smith: I am having trouble comprehending what exactly is causing gravitational forces.
You are in good company.
The best demo I have seen to illustrate the theory of gravity warping space can be done at home. Take a sheet and stretch it tight (four people at the corners is the best way). Now place a bowling ball in the middle. See how the cloth dips towards it? If you now place a baseball near the edge of the sheet, it will most likely roll toward the bowling ball, (unless it is far enough away) because of the curvature of the sheet.
The theory is that mass somehow deforms the space around it in a 3-D manner similar to the 2-D effect of the bowling ball on the sheet.
Or there's string theory . . . Posted by King of Men (Member # 6684) on :
quote: I can't wrap my head around how a curvature of spacetime is going to cause gravity, if gravity itself is causing the curvature of spacetime.
Here's your problem. Gravity is not causing the curvature; gravity is the curvature. Personally, though, I find it very difficult to think of causality in this connection. I prefer to treat relativity as a highly accurate empirical model, something we use when we want answers on a large scale, and consider the causality as arising from the microlevel. (This may be a training bias, of course, as I am a particle physicist and not an astrophysicist. Perhaps if I'd gone the other way, I'd be happier with GR and consider it very difficult to think of what's 'causing' quantum mechanics to work.)
We usually consider forces as being caused by the exchange of messenger particles; in the case of gravity, it's called the graviton, and has not yet been observed, nor is it likely to be; gravity is so weak that stopping a mere neutrino is child's play by comparison. We know something about what properties it must have, though, just from looking at the large-scale behaviour. But I digress. Basically, all particles are constantly spitting out and re-absorbing force-carrying bosons. If you are visualising this as the bosons going out from the main particle, and then turning back, that's accurate but highly wrong. These are wave functions; essentially the carriers exist everywhere, and can be reabsorbed at will. Or you can consider them as not 'really' existing until they actually get absorbed by a different particle. Matter of taste.
Anyway, it's easy to see how this causes a repulsive force : Basically, you just throw a boson from one particle to another, and they'll repulse, right? Just like children on skates throwing snowballs at each other. (Who may also be repulsive for other reasons, but never mind.) What's harder to see is how this causes an attractive force; you almost have to visualise the bosons curving around like a boomerang to come at the target particle from the other end; and then what's causing them to curve? Fortunately, QM to the rescue again; the bosons are wave functions, and have a finite probability of existing everywhere in the universe. They can be going in direction X, and suddenly find themselves captured by a particle way off at minus X; but their momentum is still pointing at X, so the target particle gets a good kick in the direction towards the emitting particle.
Of course, this description is completely agnostic with respect to what kind of force you've got, so it works as well for gravity as for anything else. You just rarely see particle physicists talk about gravity because it's so weak, so unless they're wearing their cosmologist hats, examples usually use electromagnetism.
Posted by T_Smith (Member # 3734) on :
"The best demo I have seen to illustrate the theory of gravity warping space can be done at home. Take a sheet and stretch it tight (four people at the corners is the best way). Now place a bowling ball in the middle. See how the cloth dips towards it? If you now place a baseball near the edge of the sheet, it will most likely roll toward the bowling ball, (unless it is far enough away) because of the curvature of the sheet."
The problem I have with this, is that I begin to wonder what the blanket represents, since there isn't exactly anything for say, the moon to be rolling on. Just emptiness. I begin to see the blanket as physical plane, and the ball is rolling downwards because the plane itself is now tilted. I can imagine a theoritcal invisible plane, but my brain says "oh hey, its space, there isn't anything physical there" and I go crosseyed back to my original question.
I get what you are pointing out, though. I understand the concept, just the practicality of applying it to the earth and moon isn't working for me.
King of Men- bosons? You'll find I have the need to repeat the already stated a lot when learning.
Ok- so we have particles, that I am, for the most part, are taking down the level of an individual atom. When you say boson, is that the previously mentioned messenger particle? Ok, so we have particles, spitting out and reabsorbing waves called bosons. Is a boson a wave or a particle?
So we have a particle that sends out a boson, say particle exists and 0, and particle boson is headed to is at 10. Boson gets to 5 and gets called back to particle at 0, particle at 10 then gets pulled in the direction of the particle at 0.
This then means that the more mass an object has, the more bosons it is emitting, and the more attraction it puts out.
Did I understand this, or did I totally flub this?
Posted by Mathematician (Member # 9586) on :
quote:Originally posted by T_Smith: "The best demo I have seen to illustrate the theory of gravity warping space can be done at home. Take a sheet and stretch it tight (four people at the corners is the best way). Now place a bowling ball in the middle. See how the cloth dips towards it? If you now place a baseball near the edge of the sheet, it will most likely roll toward the bowling ball, (unless it is far enough away) because of the curvature of the sheet."
The problem I have with this, is that I begin to wonder what the blanket represents, since there isn't exactly anything for say, the moon to be rolling on. Just emptiness. I begin to see the blanket as physical plane, and the ball is rolling downwards because the plane itself is now tilted. I can imagine a theoritcal invisible plane, but my brain says "oh hey, its space, there isn't anything physical there" and I go crosseyed back to my original question.
I get what you are pointing out, though. I understand the concept, just the practicality of applying it to the earth and moon isn't working for me.
King of Men- bosons? You'll find I have the need to repeat the already stated a lot when learning.
Ok- so we have particles, that I am, for the most part, are taking down the level of an individual atom. When you say boson, is that the previously mentioned messenger particle? Ok, so we have particles, spitting out and reabsorbing waves called bosons. Is a boson a wave or a particle?
So we have a particle that sends out a boson, say particle exists and 0, and particle boson is headed to is at 10. Boson gets to 5 and gets called back to particle at 0, particle at 10 then gets pulled in the direction of the particle at 0.
This then means that the more mass an object has, the more bosons it is emitting, and the more attraction it puts out.
Did I understand this, or did I totally flub this?
Woo! Mathematics to the rescue!
Suppose you have a penny and it's forced to stay on the surface of a basketball. Pick your favorite two spots on the basketball (for ease, don't let them be on opposite sides of the basketball). Suppose you want to pick the "shortest" distance between those two points, subject to the fact that the penny must stay on the basketball.
We're used to saying "the shortest distance between two points is a straight line". However, this really only works on flat things. To convince yourself of this, draw two dots on a piece of paper, draw the straight line between them. Now, bend the paper. You line bends!
While this isn't proof, it illustrates a point - on curved surfaces, the shortest distances between two lines is NOT a straight line, but rather a curve.
So, Mathematically, how do we determine if something is "straight"? For some decent reasons, the official mathematical definition of a "straight" line is one who's acceleration is 0. Note that this totally agrees with what you're used to in flat space.
What this means for curved things, however, is that you allow some "force" to stick the object to the curved space. But in the same way you don't feel a "force" keeping you in the universe, sticking an object to the curved space doesn't require a "force", it's something more natural in the geometry of the shape.
Here's where Einstein comes in. He says, what if what the universe REALLY is is a bunch of space-time everywhere/when, which is naturally flat. Further, suppose mass (and therefore energy) can force this spacetime to curve. What happens to straight lines? Well, they curve now.
We earlier said that that the shortest distance between two points is a line (and showed how this really doesn't capture the whole truth). There's another fact flowing around. An object, in the absences of forces, takes the shortest distance between 2 points.
Put these together, and what path do objects take when there's mass/energy around? A curved one. Einstein called this effect "gravity".
Hope this helps.
Incidentally, some people have been saying that the effects due to gravity and the effects to do velocity are the same. They work similarly, but they are NOT the same. The velocity effect is based solely on SPECIAL relativity, a much easier theory where you can (almost?) solve everything algebraically.
When we start talking about gravity, we're inherently talking about GENERAL relativity, a MUCH more complicated theory. You can solve ALMOST NOTHING algebriacally (it's all differential equations and something called tensor equations). What this means is the gravitational effects on position/time are in the same vein, but very different.
Finally, one more caveat.
Earlier in the post, you guys were talking about choosing coordinates (x,y,z,t). I want to stress that you can ALWAYS do this locally (meaning close to you), but they won't be globally defined. In otherwords, there will almost always be regions where your previous definitions of (x,y,z,t) will just break down, due to the curvature.
This is because general relativity involves things called "manifolds". These are math things with a few important properties. Up close, they look flat (and flat things are the only place you can put (x,y,z,t) on). But far away, who knows what shape they are? If from far away, they are INCREDIBLY well behaved, then your (x,y,z,t) will work everywhere. But if, for instance, if you manifold is a sphere such a thing won't work.
Posted by rivka (Member # 4859) on :
Nathan, empty space is actually not empty in the way you are thinking.
Even without string theory. Posted by Bokonon (Member # 480) on :
Also, remember that in essence, eferything at the subatomic level has wave-particle duality, That is, nothing is either one or the other, it just depends on the context.
KoM, the photon is the "carrier" boson (?) of EM, right? What are the matching entities for the Weak and Strong forces?
-Bok
Posted by King of Men (Member # 6684) on :
Weak force has W and Z bosons, and the strong force has gluons. I'm runninglate for work or I'd put a bit more work into re-explaining the force carrier thing.
Posted by T_Smith (Member # 3734) on :
Bok-
Like Einsteins gold sheet thingy, right? Or was that some other dude? Do particles with wave-particle duality travel in a straight line, or do they follow the wave itself, going from crest to trough?
I've gone and tried to attempt to show how my brain is now configuring how space time is curved. I decided to draw a circle representing a gravitational source, and then drew another circle comprised of different colors, where it is a spectrum from red to violet, violet representing faster rate of time, red representing a slower rate of time. Taking inverse square law into the equation, I showed how the rate of time changes correspondingly, to show that based upon location to a gravitational source, the rate of time changes.
There are 4 different scenes. Please be kind.
Posted by Nighthawk (Member # 4176) on :
/brain asplodes
Posted by Bokonon (Member # 480) on :
quote:Originally posted by T_Smith: Bok-
Like Einsteins gold sheet thingy, right? Or was that some other dude? Do particles with wave-particle duality travel in a straight line, or do they follow the wave itself, going from crest to trough?
I don't think it was Einstein. Your third sentence shows the misconception. There is no particle, only the entity that has wave-particle duality. Based on the qualities that a subatomic entity can have, they will behave more like what we consider as a wave (or particle), but in reality, they are both (or rather neither, they are an entity that we descibe as having these attributes).
quote: I've gone and tried to attempt to show how my brain is now configuring how space time is curved. I decided to draw a circle representing a gravitational source, and then drew another circle comprised of different colors, where it is a spectrum from red to violet, violet representing faster rate of time, red representing a slower rate of time. Taking inverse square law into the equation, I showed how the rate of time changes correspondingly, to show that based upon location to a gravitational source, the rate of time changes.
Pretty neat. Just remember, there is no real "speed of time" Only "speed of time" as experienced by the observer. Also, remember space itself is also seemingly modified. Space and time are one and the (mostly) same in Relativity.
This is mind-bending stuff, which I wish I knew better, particularly the mathematics.
-Bok
Posted by Mathematician (Member # 9586) on :
quote:Originally posted by T_Smith: Bok-
I've gone and tried to attempt to show how my brain is now configuring how space time is curved. I decided to draw a circle representing a gravitational source, and then drew another circle comprised of different colors, where it is a spectrum from red to violet, violet representing faster rate of time, red representing a slower rate of time. Taking inverse square law into the equation, I showed how the rate of time changes correspondingly, to show that based upon location to a gravitational source, the rate of time changes.
It seems as if you've got a few misconceptions. First, the inverse square law for gravity has NOTHING to do with general relativity. It's a product of 2 facts: First, we live in 3 spatial dimensions. Second, gravity emanates equally in all directions from a single point of matter.
These 2 facts alone account for the inverse square law (which Newton came up with also, and he never even thought about space time, or whether or not it could be curved).
Second, the fact that gravity slows time down doesn't show that spacetime is curved, because, for instance, a body moving at a high velocity has the same effect occuring, and again, it doesn't depend on space-time or curvature at all. The curvature of spacetime slows time down, not the other way around.
Rather, when space time is curved, it's also stretched (it's not compressed because flat space time is mathematically the minimum surface area needed. In otherwords, maximum compression of space-time occurs during flatness, so no configuration of matter, etc, can compress it more). When the stretching occurs, in some since "distance" (even in the time direction) is lengthened. Thus, it takes *longer* for one second to pass (as measured by an outside observer). So, to an outside observer, it looks as if time has slowed down.
Hope this helps....
Posted by T_Smith (Member # 3734) on :
"Second, the fact that gravity slows time down doesn't show that spacetime is curved, because, for instance, a body moving at a high velocity has the same effect occuring, and again, it doesn't depend on space-time or curvature at all. The curvature of spacetime slows time down, not the other way around."
I remember that the faster one travels in relation to the speed of light, the more mass an object has, and of course, since E = mc^2, then mass, energy and speed are all tied in together.
If this is the case, then the curvature isn't gravity, the curvature is energy based upon mass, which also correlates to gravity, but not limited to gravity.
Posted by Mathematician (Member # 9586) on :
quote:Originally posted by T_Smith: "Second, the fact that gravity slows time down doesn't show that spacetime is curved, because, for instance, a body moving at a high velocity has the same effect occuring, and again, it doesn't depend on space-time or curvature at all. The curvature of spacetime slows time down, not the other way around."
I remember that the faster one travels in relation to the speed of light, the more mass an object has, and of course, since E = mc^2, then mass, energy and speed are all tied in together.
If this is the case, then the curvature isn't gravity, the curvature is energy based upon mass, which also correlates to gravity, but not limited to gravity.
The thing is, even if you didn't have E=mc^2 to fall back on, the velocity STILL effects time. Also, an particle DOESN'T effect itself. What this means is that if somethings moving faster, sure it has more energy (and thus, more mass), so things are attracted to it more. Fine. But it's own gravitational field doesn't effect itself. To talk about gravity effecting time, you have to be talking about at least 2 things - the object (or science fiction device) creating the gravitational field, and the object being acted on. (Some may argue we also need an observor, but whatever)
To make this clearer, consider this little thought experiment.
We have two objects, H (for heavy) and F (for fast).
Now, assume that F is moving quickly relative to H (and assume H is stationary, just makes everything easier).
From our perspective, F's time slows down for 2 VERY different reasons. For one, H is massive, so it has a large gravitatoinal field. This field effects the curvature of spacetime which stretches out the time component of F's space time, making time move slower for F. Notice no where did we talk about the gravitational field of F. F's gravitational field will effect H, but it WILL NOT effect F.
But F's clocks also slow down because F is moving fast. Note that this would happen even if H wasn't there. This isn't a bending of spacetime, rather it's an effect of the fininte speed of light.
Posted by T_Smith (Member # 3734) on :
I thought velocity itself is in correlation to C, which is the speed of light. Therein, spacetime is curved by energy due to either mass or speed of an object in reference to light.
Time = distance/speed of light
If so, I understand how gravity causes a curve in spacetime since it slows light. Velocity would change it then as well since light would appear to be going slower in reference to the object traveling closer to the speed of light.
All of this is back with spacetime, when I asked about gravity. Which I still don't get what is causing it.
Posted by Paul Goldner (Member # 1910) on :
" when I asked about gravity. Which I still don't get what is causing it."
The short answer is we don't really know yet. Special relativity has properties that lead us understanding how gravity works... but no one knows what creates gravity. Gravity is a distortion in space time, and space-time curves when a mass is introduced, and we understand this mathematically, but we don't know what causes this.
Gravity is a field. There are also electro-magnetic fields. These are caused by the attraction and repulsion of charged particles. But there's no corresponding understanding for why there is a gravitational field.
Posted by T_Smith (Member # 3734) on :
Is it foolish of me then to refuse to accept the answer "it just is and does?"
Posted by Paul Goldner (Member # 1910) on :
"Is it foolish of me then to refuse to accept the answer "it just is and does?""
For now, yeah. If you hold onto this too tightly, you won't let go.
Keep it filed away, though, for future analysis if you are so inclined. If you can tell the world what causes gravity, there's a nobel in it for you.
Posted by Mathematician (Member # 9586) on :
quote:Originally posted by T_Smith: I thought velocity itself is in correlation to C, which is the speed of light. Therein, spacetime is curved by energy due to either mass or speed of an object in reference to light.
Time = distance/speed of light
If so, I understand how gravity causes a curve in spacetime since it slows light. Velocity would change it then as well since light would appear to be going slower in reference to the object traveling closer to the speed of light.
All of this is back with spacetime, when I asked about gravity. :) Which I still don't get what is causing it.
In your initial paragraph, you state, "Therein, spacetime is curved by energy due to either mass or speed of an object in reference to light." This is an ok way to think about things. Energy curves spacetime and mass and speed are two ways (out of lots) of getting energy. Fine.
Time = distance/speed of light only if the following hold: 1. We throw out relativity (both special and general). 2. Something is moving at the speed of light.
The more general equation time = distance/speed is ALSO incorrect. It's just that at slow speeds/normal gravity, it's close enough.
Next paragraph, you state, "If so, I understand how gravity causes a curve in spacetime since it slows light. Velocity would change it then as well since light would appear to be going slower in reference to the object traveling closer to the speed of light."
You just mentioned that ENERGY curves spacetime. energy is NOT the same thing as gravity. So this doesn't logically follow from what you just told me. Also, VELOCITY only changes space time if we're considering multiple object interactoins (this is what I tried to explain in my above post). In otherwords, if we're only interested in a single object (and the effects of the graviataional field on it), then the velocity of the object has NOTHING to do with the calculation curvature of spacetime.
Finally, your statement "Velocity would change it then as well since light would appear to be going slower in reference to the object traveling closer to the speed of light" is incorrect in what it argues. You're saying "if I move closer to the speed of light, then light will appear to move slower" This is exactly what Einstein's denied by postulating special relativity. That's what gives all these weird effects we're talking about now. Now matter HOW fast you are moving, if I shine a light at you, you ALWAYS meausre the speed of light to be 186,281.6 miles per second, even if you're moving 186,281.5 miles per second.
Posted by T_Smith (Member # 3734) on :
quote:Next paragraph, you state, "If so, I understand how gravity causes a curve in spacetime since it slows light. Velocity would change it then as well since light would appear to be going slower in reference to the object traveling closer to the speed of light."
What I was saying is since mass curves spacetime, and gravity is a direct effect of the level of mass, that gravity is curving the space time. I suppose it is a bit innacurate to say that gravity itself is, then. More the mass that is creating the gravitational pull is curving spacetime, yes?
Posted by Paul Goldner (Member # 1910) on :
"More the mass that is creating the gravitational pull is curving spacetime, yes?"
Yes.
Posted by King of Men (Member # 6684) on :
quote:Did I understand this, or did I totally flub this?
Well, not totally. Say 50% flubness.
quote:Ok - so we have particles, that I am, for the most part, are taking down the level of an individual atom.
Atoms, nothing. Atoms are HUGE. Only boring nuclear physicists talk about atoms - well, actually, even they at least manage to concentrate on the nucleus. You practically have to talk to a chemist to hear about atoms, and who would want to do that? The action is at the level of quarks and electrons; quarks are the components of protons and neutrons, which make up the atomic nucleus.
However, none of this actually matters for the argument; my particle snobbery aside, you are perfectly at liberty to consider atoms.
quote:When you say boson, is that the previously mentioned messenger particle?
Yepyepyep. All messenger particles are bosons, that is to say, they have integer spin.
quote: Ok, so we have particles, spitting out and reabsorbing waves called bosons. Is a boson a wave or a particle?
Yes please, both, if possible.
quote:So we have a particle that sends out a boson, say particle exists at 0, and particle boson is headed to is at 10. Boson gets to 5 and gets called back to particle at 0, particle at 10 then gets pulled in the direction of the particle at 0.
Flubbity starts here. In the scenario you describe, there is no attraction; the boson has to actually reach the target particle to exert any influence on it. This, incidentally, accounts for the 1/r^2 strength of gravity and electromagnetism; basically, the further away a particle is, the less likely it is that the bosons manage to travel that far before getting reabsorbed.
Now, if the boson was travelling from 0 to 10 and got absorbed, that would be a repulsive force; it has to push the target particle in the direction it is going. So to account for attractive forces, we have to invoke QM; the boson can travel from 0 to 10, and still be absorbed by a particle sitting at -10. (This is not intuitive, and I realise that it contradicts what I said above about having to make contact. This is basically Heisenberg. Because the boson has a well-defined momentum, it doesn't really have a location. So we can say that it is going in the direction of 10, from 0; but at any given time, its position is best described as 'anywhere you like'. Therefore, it really is touching the particle at -10.) That pushes the absorbing particle in the positive direction, since that's the way the boson was going, which means it gets closer to the emitting particle - attraction, in other words.
quote:This then means that the more mass an object has, the more bosons it is emitting, and the more attraction it puts out.
Yepyepyep. Or in the case of electromagnetism, the more charge it has, the more bosons (in this case photons) it puts out. For the weak force, it's "the more hypercharge...", and the strong force is described in terms of two different charges collectively referred to as 'colour'. For the general case, we say the more "coupling to X" the particle has, the more bosons it puts out, where X is the kind of force in question.
Posted by rivka (Member # 4859) on :
quote:Originally posted by T_Smith: Like Einsteins gold sheet thingy, right? Or was that some other dude? Do particles with wave-particle duality travel in a straight line, or do they follow the wave itself, going from crest to trough?
I think you mean Ernest Rutherford, but I have no idea what connection to mass or gravity you are making.
Waves and wave-like particles do not zig up and down. The wave represents the energy/intensity of the light/sound/particle, not its path.
Posted by rivka (Member # 4859) on :
quote:Originally posted by King of Men: You practically have to talk to a chemist to hear about atoms, and who would want to do that?
HEY! Posted by T_Smith (Member # 3734) on :
Ok, two questions this time.
First, in the idea of time in the sense of general relativity, what exactly is time defined as, if not Distance/Speed of Light?
Second, what exactly is light?
Posted by T_Smith (Member # 3734) on :
Ask what causes gravity, you get 5 responses in an hour, ask what time is, and you stump them all.
Posted by Mathematician (Member # 9586) on :
Sorry about the delay in response (my in-laws are in town, gotta spend time with them!)
In GR, time (or more technically, Speed of Light * time) is simply another direction you can travel in, with one restriction - you can only go one way through time (no backwards time travel!).
As far as light (at least in the classical, non-quantum mechanics sense), light is a moving perterbation in an electromagnetic field. Think of it like this. If you're holding the end of a rope and you snap it really fast, a wave will travel down it. In this example, the rope represents the electromagnetic field and the wave represents the light.
In the quantum mechanics view, I know very little about what light is. I know they tend to model it more as a point particle, but in quantum mechanics, the rules of common sense are more or less thrown out, so a point particle of QM doesn't behave like an intuitive point particle does. I imagine photons still have something to do with fluctuations in an electromagnetic field, but at this point, I'm out of my league.
Posted by Eldrad (Member # 8578) on :
If you're looking for a good book on relativity and a number of other things, The Elegant Universe comes highly recommended from a number of my friends (I've not yet had a chance to read it, personally).
Also, another interesting tidbit: Einstein did not originally come up with the theories of special and general relativity. A Frenchman named Henri Poincaré published a paper detailing special relativity about five years before Einstein did, and he published a paper on general relativity a few weeks before Einstein. This is the same man who's famous conjecture was recently proven by Grigori Perelman, a Russian mathematician, and is considered to be one of the most important landmarks in the history of mathematics (since it's supposed to help to explain the nature of the universe, though I don't know enough details to explain more).
I find that with GR it's not usually good to try to answer questions of the form 'What is X?' I much prefer just to plug the numbers into the equations. An intuitive understanding won't really help you anyway.
For the QM view of light, it's basically the same as in the classical view, except that the field is quantised and has to obey SR. Stick with photons and you'll be ok; the differences are highly technical and don't really matter unless you're doing actual calculations with the theory.
Posted by T_Smith (Member # 3734) on :
"In GR, time (or more technically, Speed of Light * time) is simply another direction you can travel in, with one restriction - you can only go one way through time (no backwards time travel!)."
I suppose the better question is "how do we measure time?"
To say that "time is a direction" is all good, if I new it was a direction in correlation to something. The only way, I suppose to measure time if not by the speed of light, is by comparison to things that happen, and the rate of experience observers have between the two things.
Since what people observe is going to be different, it therefore means that time is relative to the observer. Correct?
Posted by T_Smith (Member # 3734) on :
OK, so, I'm in a Physics-y mood. Anyone want to start a subject for my own learning?
Posted by T_Smith (Member # 3734) on :
Ok, a bit of a question, which should be easy, and I believe I know the answer, but wanted to double check.
Hypothetically:
I created a box with unlimited air supply and pressure, is completely sealed, with no windows, and put a gerbil in it. I take said box into space. I attach a 10 foot pole to the box and swing it around over and over again in a 360 degree spin.
First) is the gerbil experiencing any centrifugal force and being pushed against a wall, or is it free floating. I believe it is free floating.
Second) would time be moving slower for it compared to a gerbil outside staring at the box?
Posted by Bokonon (Member # 480) on :
I believe it will feel neither centrifugal force (which is an imaginary "convenience" force) nor is it floating. It is subjected to the centripetal force. The box is pushing in on the gerbil.
Space is no different than Earth in this regard. Just like those amusement rides that spin fast, creating forces on you, so would the spinning cardboard box. Now it may depend on the speed of the rotation exactly how much it is feeling, but it's still there, I believe. ---
Probably, but at such a minute level as to be inconsequential.
-Bok
Posted by King of Men (Member # 6684) on :
To answer the question without reference to abstruse arguments that only physicists and pedants care about, yes, the gerbil will feel centrifugal force. And yes, time would slow down for it, but obviously not very much.
That said, really, there is no centrifugal force. Trust me.
Posted by King of Men (Member # 6684) on :
On a vaguely related note, here's a thought experiment which bothers me a bit. Suppose I have a sphere of unobtainium, which is perfectly reflective on the inside. It is filled with vacuum. Now, using my handwavium drill, I open a tiny hole in the unobtainium, let in some arbitrarily large amount of photons, and close the hole, leaving the unobtainium unchanged except that there are now photons in the cavity. We know that the gravitational mass increases, since I've increased the energy of the system; my question is, what happens to the inertia, both linear and angular? And, given some answer based on the theory of GR, what is the relevant experiment showing this particular result to be correct?
Posted by Dan_raven (Member # 3383) on :
Centrifigual Force is in reality the Dark Side of "The Force" so the Hamster in the box would be a Sith Hamster, while the Hamster watching, uninfluenced by the Dark Side, would be a Jedi Hamster.
(Pictures two hamsters with tiny hamster-sized light sabers, battling to the death. Admit it. Light Saber Weilding Hamsters is why you went into physics in the first place.)
Oh, and if you put an infinite amount of atmosphere in a box you would crush the poor hamster into a singularity.
Posted by El JT de Spang (Member # 7742) on :
What up, Nate?
Posted by Bokonon (Member # 480) on :
It's not (that) pedantic! I learned it in high school physics!
-Bok
Posted by Mathematician (Member # 9586) on :
quote:Originally posted by King of Men: On a vaguely related note, here's a thought experiment which bothers me a bit. Suppose I have a sphere of unobtainium, which is perfectly reflective on the inside. It is filled with vacuum. Now, using my handwavium drill, I open a tiny hole in the unobtainium, let in some arbitrarily large amount of photons, and close the hole, leaving the unobtainium unchanged except that there are now photons in the cavity. We know that the gravitational mass increases, since I've increased the energy of the system; my question is, what happens to the inertia, both linear and angular? And, given some answer based on the theory of GR, what is the relevant experiment showing this particular result to be correct?
Can the rotation of the sphere "drag" the photons along? In otherwords, if I have a sphere filled with fluid, the fluid begins to spin as I spin the sphere (due to frictional effects, I believe). Would photons get dragged around in the same way?
More generally, what does GR predict about the angular inertia of solid objects? That is, the inertia depends on the mass density and the shape. I can see how GR messes with the mass density, but doesn't SR also predict shape changes (I mean, length contracting/etc must change at least one dimension). So, does the calculation of the moment of inertia depend on ones perspective? (I guess this shouldn't be surprising since everything short of ds^2 is dependent on the observation, this one I've just never thought about before).
For the linear question, I have NO idea. I'm invisioning a photon starting at the back of the sphere moving forward as the sphere moves forward. But relative to the forward edge of the sphere, the photon is moving c, so this is really screwing with my head ;-), Thus, from an outside observor, the sphere should contract a bit in the direct ion of motion, so now we have an ellipse? But I distinctly remember reading something that said that spheres ACTUALLY contract to spheres (though, as usual, I could be wrong)
So, instead of answering, I pose more questions ;-)
As an aside, I'm taking a quantum field theory course. So far, there has been NO physics :-) It's great.
Posted by Alcon (Member # 6645) on :
T_Smith, I think I know what you're getting at. If you put the gerbil in the center of a torus and set that to spinning then it wouldn't feel a force. The gerbil wouldn't be set to moving with the torus and the torus would just cheerfully spin around it. It wouldn't effect the gerbil unless the gerbil made contact with any of the walls, in which case it would start moving with the torus and begin to experience a simulated gravity force. It's hard to explain with out diagrams, so I hope that makes sense.
In the case of a box, well think about it. At first it'd be freefloating, but the wall of the box would quickly smack into it. Once that happened the gerbil would be accelerated with the box and would feel the simulated gravity force (centripedal is the actual force in question there).
Posted by King of Men (Member # 6684) on :
About the linear inertia, I convinced myself (and another grad student, so maybe there's something to it) that you would get extra inertia from Doppler effects. At any rate, you would get an additional resistance to acceleration. Whether the resistance would be at the correct rate, ie whatever extra energy you pumped in would show up as F=(m+dm)a where dm=dE/c^2, well, that's another matter entirely.
But the angular moment is puzzling me. I suppose you'd have to say that there's enough interaction between the photons and the unobtainium to create a drag, since otherwise you're basically just manipulating the original unobtainium sphere, but I don't know if it makes sense to say that a fluid of photons is rotating.
Basically, though, the whole subject of rotating objects in GR is strictly for experts; I was hoping one would come along. Mere particle physicists should fear to tread here, and I do.
![[Wink]](wink.gif)
![[Smile]](smile.gif)
I'd say the curvature of space time is a theory which explains gravity's effects, among other things. but you are entering a weird enough world that "cause" is a very dangerous thing to say and usually far too nebulous to establish.
![[Big Grin]](biggrin.gif)
![[Razz]](tongue.gif)