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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?
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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...
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The short version is that, even though light is massless, it's affected by gravity. Others may embellish to their heart's content.
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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?
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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.
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"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?
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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)
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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.
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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).
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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.
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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.
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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.
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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.
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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.
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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".
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Adequate for a layperson without being in-depth enough to cause random brain a splosion, I'd guess.
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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).
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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.
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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 Posts: 3846 | Registered: Apr 2004
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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.
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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.
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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."
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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 ?
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"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. Posts: 3852 | Registered: Feb 2002
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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.
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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.
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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.
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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".
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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.
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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?
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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?
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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.
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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").
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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.
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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.
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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.
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