## Miscellaneous Science Questions

For the discussion of the sciences. Physics problems, chemistry equations, biology weirdness, it all goes here.

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

phlip wrote:...You do have to worry about time dilation, as that doesn't depend on direction...

Yikes.

phlip wrote:(ie when you move to A's reference frame, the clock at the station will slow down).

Wait, what? Doesn't the clock in the station, as seen by A, speed up?

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

No. From the point of view of A, in one second, a clock on the A train will advance one second (because, from the point of view of A, it's stationary), but a clock at the station will advance by 0.6 seconds. However, from the point of view of the station, in one second, a clock at the station will advance by one second, but a clock on the A train will advance by 0.6 seconds. They're both inertial frames that see the other as moving at 0.8c, so, by symmetry, their opinions of each other have to match.

Though this seems contradictory, it's just part of relativity of simultaneity... train A will see its clock hit 1s at the same time the station clock hits 0.6s, but the station won't see those events as happening at the same time... and this is correct, because "at the same time" is relative.

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

phlip wrote:No. From the point of view of A, in one second, a clock on the A train will advance one second (because, from the point of view of A, it's stationary), but a clock at the station will advance by 0.6 seconds. However, from the point of view of the station, in one second, a clock at the station will advance by one second, but a clock on the A train will advance by 0.6 seconds. They're both inertial frames that see the other as moving at 0.8c, so, by symmetry, their opinions of each other have to match.

Though this seems contradictory, it's just part of relativity of simultaneity... train A will see its clock hit 1s at the same time the station clock hits 0.6s, but the station won't see those events as happening at the same time... and this is correct, because "at the same time" is relative.

Δtimp = γΔtp where γ = 1/(1-v2)1/2

The frame in which events occur in the same place spacially (in this case, the moving frame, if we are saying the events are E1 occurs at (ti,xi) = (0,0) and E2 occurs at (tf,L) ) measures proper time. Because gamma is always greater than 1, the reference frame measuring proper time always measures time more slowly than all other reference frames.

What you're saying about symmetry makes sense to me (ie, when you say that the stationary frame sees the train moving slower and vise versa), but isn't the idea that you can view the reference frames symmetrically the basis of the twin paradox? That there is actually in inherent difference between the two frames, and that they cannot just be observed symmetrically by each other?

I'd venture to say, though, that i'm really just showing my misconceptions of the subject instead of actually saying something meaningful.

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

The twin paradox isn't a contradiction though... "Paradox" basically just means "unexpected". The A train sees itself as being older than the station, but the station sees itself as being older than the A train... you expect this to be contradictory, but the maths says it's not, hence "paradox"... in fact, the paradoxical thing is that you expect simultaneity to be absolute, since that seems "obvious"... yet it isn't.

The twin paradox also refers to what would happen if train A were to turn around and come back to the station... then they're in the same place, and relativity of simultaneity no longer applies... but for that to happen, the train has to turn around, so it's not actually an inertial frame. So the two frames are different, and symmetry doesn't apply. And the station will be, to all observers, older than the train.

Be careful referring to "the twin paradox", because those two situations above are different, the paradox is in a different place, and the resolutions are different. In one, the frames are symmetrical, and the differences between the ages is just a difference of opinion. In the other, the frames aren't symmetrical, and the differences between the ages are objective. Usually, just saying "the twin paradox" refers to the second situation... but this puzzle is the first.

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

Arrgh, I'm so confused. What about the thought experiment of sending a rocket to a different solar system (say, the one containing, alpha centari) at near speed of light? I was convinced that the rocket, according to us, would reach its destination according to how fast we measure its velocity (say, .98c) and we wouldn't measure any spacial contractions. The rocket clock, on the other hand, would barely move at all, because once near light speed is achieved, the travel time, according to the rocket, would be near instantaneous. Since there would be a measurable difference in time, I don't see how their observance of time is subjective, even if the rocket never returns back to it's beginning point.

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

I've already talked about that one futher up the page, though I didn't talk about simultaneity of relativity up there...

Talking about it again, with a different focus... also, we won't look at the rocket accelerating or decelerating... just say it's been going at 0.98c forever, happens to pass Earth, we synchronise clocks, and then it happens to pass Alpha Centauri and then keeps going.

If a rocket travels from here to Alpha Centauri at 0.98c. To us, it looks like it takes about 4 years (I'll call it exactly 4 years, to make the description nicer). However, we see the clock on the spaceship running slow, and it only measures the time as about 9 and a half months (again, to simplify the explanation, I'll just call it 9 months, since the actual value doesn't matter). So according to us, "launch time plus 4 Earth-years", an event that happens on Earth, is simultaneous to "launch time plus 9 rocket-months", an event that happens on Alpha Centauri, is simultaneous to "the rocket arrives", an event that happens on Alpha Centauri.

In the rocket's frame, the universe is moving at 0.98c, and thus has length contraction... the distance to the star is measured as only 9 light-months. So, conveniently, it'll take us about 9 months to arrive. But we'll see the clock on Earth running slowly, by symmetry... according to us, when we arrive, 9 months later, only 2 months has passed on Earth. So, in the rocket frame, "launch time plus 2 Earth-months", on Earth, is simultaneous to "launch time plus 9 rocket-months", on Alpha Centauri, is simultaneous to "the rocket arrives", on Alpha Centauri.

So we both agree that the two latter events happen at the same time... since they happen at the same time and at the same place, all observers will agree. But the time on Earth, we disagree on. Because we're talking about what's happening at the same time but in a different place. And that is relative. Neither the rocket's, nor Earth's, opinion about what events are simultaneous are wrong, and neither are absolute.

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

I think i'm beginning to understand some of these ideas on relativity of simultaneous events. One question, though, what would the person in the rocket frame observe when looking at alpha centari while speeding towards it? Would they observe all of the events that had taken place in the past 4 years scream by in the span of 9 months?

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

No, Alpha Centauri is in about the same frame as Earth (or near enough as makes no odds when compared to , so people in the rocket would also see Alpha Centauri as running at the same speed - they'd see 2 months pass on Alpha Centauri in the 9 months of their travels from Earth to the star.

So the events that, according the people on the rocket, are happening on Alpha Centauri as they pass Earth, are the events that, according to the people on Earth, are happening 2 months before they arrive. Relativity of simultaneity again.

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

*chokes self*

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### Re: So why can't an object go faster than light?

Think and Philip, remember that there is a difference between "see" and "observe". If we were to point a very big telescope at Alpha Centauri we would see events that took place four years ago, even though we are in the same frame and therefore agree on simultaneity.

If you were to move 4 lightyears away from earth at close to the speed of light and then stop again, you would see almost no time having passed at earth, but given that the light you see now has travelled for four years you would observe that four years have passed on the earth.

If I leave earth at newyear 2010, looking up I would see what happened in 2006 at AC, nine months later (my time) I arrive at AC, and it is september 2014. During my flight I see them living through 8 years and nine months, but I know it is just a doppler effect, so I still observe that their time is slowed.

Earlz wrote:Also, does that mean when aliens invade earth(and we wait for them to leave) that all we need to do is get in a really fast ship and travel for 100 light years somewhere and 100 light years back to earth and suddenly 200 years has passed while we are still about as young as before?

Yes.

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

Got bored and spent some time reading through this thread for the past couple of weeks... Some stuff from a while ago that I don't think anyone really addressed...

Charlie! wrote:Let's say we have a spaceship airline. Flight 1 sets out 1/1/3001 for alpha centauri at 0.98 c, and flight 2 follows exactly a year later... But [flight 2] should be able to measure the correct distance with respect to flight 1. So it sees alpha centauri engulf flight 1?

Immediately before flight 2 takes off, flight 1 is one fourth of the way to A.C. When flight 2 gets up to speed shortly thereafter, flight 1 is still one fourth of the way to A.C - but both are now closer...

ATCG wrote:In The Black Hole War [by] Leonard Susskind ... Alice experiences nothing in the least out of the ordinary as she crosses the event horizon. She might fall for a million years before the tidal forces exerted by the black hole's singularity become consequential to her... But what about Bob? He sees Alice fall toward the event horizon... Alice is progressively consumed by the "stretched horizon": ... [she] boils away as Hawking radiation... without ever having crossed the horizon.

According to GR, Alice falls through the EH unperturbed; Bob sees her simply slow to a halt and eventually fade to black. According to QM, Alice never crosses the EH - she boils away as she approaches. Don't know for sure what really happens, but it's hardly fair to compare Alice's viewpoint according to GR with Bob's viewpoint according to QM and then complain that they don't agree...

Also: it only takes a few minutes to reach the center of a galaxy-massed black hole after crossing the horizon.

Plamo wrote:My question is, what happens when the 1st mediator and his two clock bearing friends hop off the train, and meet the second mediator in the town between the two stations for some lunch and tea? Will the clocks be in synchronization, or will one be slower than the other?

If you're at the front of a one light year long train deceleration at 1g (by your measurement), then both you and your friend in the back of the train agree that HIS clock ticks twice as fast as yours until the deceleration is complete. The harder the train decelerates, the faster the ratio. The longer the train, the faster the ratio. So yes, when you get off, your clocks don't match anymore - he's older than you.

doogly wrote:Certainly nothing happens at 15/8 the speed of light; you need to use the relativistic velocity addition law.

For the case that Plamo was quoting, the relativistic addition law does NOT apply. If YOU see a banana travelling west at 0.9c and a knit sock travelling east at 0.9c, then YOU measure their relative velocity to be 1.8c. The addition law would be used to calculate the speed of the sock IF AND ONLY IF we want to switch our measurements to the BANANA'S frame of reference; but YOUR measurement of their relative velicty is definitely 1.8c.

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

Fair nuff, usually that is not what is meant by relative velocity when I see the phrase, but I should have more closely read what was written before objecting.
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phlip
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### Re: RELATIVITY QUESTIONS! (and other common queries)

As I've seen it, "relative velocity" would involve the relativistic velocity addition formula... it's the velocity of one, as seen by the other. Which is a useful value, as everyone should measure the same relative velocity between two inertial (using SR "inertial") objects ("inertial" so that you don't have to worry about relativity of simultaneity messing up your measured velocities... the velocity is the same no matter what time you measure it).

But it depends exactly what you're trying to measure. It's certainly the case that, in one second, as measured by you, the ships would get 1.8 light-seconds closer, as measured by you. So a velocity of 1.8c is relevant to some calculations. I don't know if it has a useful name.

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

Would it be possible to accelerate so fast that a point exactly behind me doesn't move relative to me (due to Lorentz contractions)?
Last edited by Think on Tue Sep 29, 2009 11:42 am UTC, edited 1 time in total.

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

Goemon wrote:
ATCG wrote:In The Black Hole War [by] Leonard Susskind ... Alice experiences nothing in the least out of the ordinary as she crosses the event horizon. She might fall for a million years before the tidal forces exerted by the black hole's singularity become consequential to her... But what about Bob? He sees Alice fall toward the event horizon... Alice is progressively consumed by the "stretched horizon": ... [she] boils away as Hawking radiation... without ever having crossed the horizon.

According to GR, Alice falls through the EH unperturbed; Bob sees her simply slow to a halt and eventually fade to black. According to QM, Alice never crosses the EH - she boils away as she approaches. Don't know for sure what really happens, but it's hardly fair to compare Alice's viewpoint according to GR with Bob's viewpoint according to QM and then complain that they don't agree...

Also: it only takes a few minutes to reach the center of a galaxy-massed black hole after crossing the horizon.

I think the point is not to contrast their viewpoints with respect to some theory, but what is actually observed, and Susskind argues that a consistent theory of quantum gravity would create a universe that looks like this. As has been pointed out in other threads, horizons are frame-dependent.

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### Why is Work Force times Distance?

This probably sounds like a silly question, but I don't seem to be getting something. The work done on a system is the dot product of the force and its displacement. But why? Why is work defined as F*d?

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### Re: Why is Work Force times Distance?

Force is the - change in potential/distance. Rearranging, the force*change in distance=-change in potential. We define-change in potential to = work.

Edit: The definition of force above is more advanced than F=ma, but is entirely equivalent.

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

Think wrote:Would it be possible to accelerate so fast that a point exactly behind me doesn't move relative to me (due to Lorentz contractions)?

In other words, you're asking whether the squished universe you observe as you go faster might contract fast enough that the distance you observe between yourself and the object remains constant?
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### Re: RELATIVITY QUESTIONS! (and other common queries)

thoughtfully wrote:
Goemon wrote:. . . Don't know for sure what really happens, but it's hardly fair to compare Alice's viewpoint according to GR with Bob's viewpoint according to QM and then complain that they don't agree...
I think the point is not to contrast their viewpoints with respect to some theory, but what is actually observed, and Susskind argues that a consistent theory of quantum gravity would create a universe that looks like this. As has been pointed out in other threads, horizons are frame-dependent.

What thoughtfully said. Susskind's insight allowed him to consistently reconcile the apparently contradictory viewpoints of Alice and Bob.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

thoughtfully wrote:I think the point is not to contrast their viewpoints with respect to some theory, but what is actually observed, and Susskind argues that a consistent theory of quantum gravity would create a universe that looks like this. As has been pointed out in other threads, horizons are frame-dependent.

hang on, horizons are frame dependent? Earlier in this thread I posed a question that was only resolved by stating that horizons are frame-independent.

The problem was as follows:

imagine a massive object travelling down the centre of the cross-section of a tunnel at a high velocity (enough that its mass as observed by someone on the tunnel would be sufficient to cause a horizon to exist) now imagine an observer in the centre of the cross-section of the tunnel that is stationary relative to the tunnel. Then imagine an observer matching the object's velocity that is also in the centre of the cross-section of the tunnel.

One last imagining, imagine a photon travelling down the tunnel such that its path would (in the absence of any forces acting upon it) take it through all 3 points. As the object's horizon only exists for the platform and not the moving observer, surely this means that the moving observer will see the photon and the platform will not. Furthermore the moving observer would observe the photon even if it was previously observed (by the platform) to not have existed.

please can somebody help me understand horizons more.
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Think
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### Re: RELATIVITY QUESTIONS! (and other common queries)

gmalivuk wrote:
Think wrote:Would it be possible to accelerate so fast that a point exactly behind me doesn't move relative to me (due to Lorentz contractions)?

In other words, you're asking whether the squished universe you observe as you go faster might contract fast enough that the distance you observe between yourself and the object remains constant?

Yeah, that's exactly what i'm asking.

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

eSOANEM wrote:hang on, horizons are frame dependent? Earlier in this thread I posed a question that was only resolved by stating that horizons are frame-independent.

I think there's been some confusion over two different types of horizon. The event horizon associated with a black hole (for example) is frame independent. But there's some kind of horizon for constant (and similar enough) accelerations too. That horizon just applies to the observer accelerating though. I suppose one might call it frame dependent, but that would be rather confusing because it's not even associated with a single inertial frame.

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

No, a black hole's horizon is also frame-dependent. It's not there if you're the one falling in, for example.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

gmalivuk wrote:No, a black hole's horizon is also frame-dependent. It's not there if you're the one falling in, for example.

It's still there, but it's not a singularity in the coordinate system you'd be using.

The definition of the event horizon is purely geometric: something along the lines of a surface separating spacetime into two regions, one of which no future-pointing light ray can leave. Since observers will agree on the path of light rays this is frame independent.

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

That definition seems to rule out a number of different event horizons I've seen described. The one bounding the observable universe, for one thing. And the one that follows an accelerating frame at a distance of c2/a, for another.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

There's more than one definition tossed around. I do prefer the global definition, which if you want to free up the word 'horizon' you could specify as a null trapping surface. (
Or trapped surface? Google is suggesting I mean trapped, but I didn't think so...)
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### Re: RELATIVITY QUESTIONS! (and other common queries)

gmalivuk wrote:That definition seems to rule out a number of different event horizons I've seen described. The one bounding the observable universe, for one thing. And the one that follows an accelerating frame at a distance of c2/a, for another.

I'd want to exclude the second of those two, it's just one ship's crazy path and nothing the rest of the universe should care about. Not so sure about the first, it's possible my definition was too specific but on the other hand each point has an observable universe so I'm disinclined to be worried.

Certainly all three are horizons. The black hole one is definitely called an event horizon (and is coordinate independent); when I learned terminology the ship one was definitely not (apparent horizon seems to be wikipedia's choice and rings bells) and I never did much cosmology. Perhaps there are different conventions flying around.

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

thoughtfully wrote:I think the point is not to contrast their viewpoints with respect to some theory, but what is actually observed, and Susskind argues that a consistent theory of quantum gravity would create a universe that looks like this. As has been pointed out in other threads, horizons are frame-dependent.

Well it certainly doesn't sound consistent to me, but I guess I can't pass judgement based on a one paragraph description

I think I've heard the Event Horizons associated with acceleration and the expansion of spacetime referred to as virtual or coordinate horizons, as opposed to the "real" horizon around a black hole. Not really sure about the right terminology, but they're definitely different animals...
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Question, once in event horizon, even light cant escape Black Hole's gravity, right? But closer i get to the black hole, faster i fall into the canter of the black hole? In the middle my speed is for example 2* the speed of light, and very near to the center of black hole my speed can be multiplied many times?
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### Re: RELATIVITY QUESTIONS! (and other common queries)

okay, here is my understanding of relativity and some issues surrounding it, please point out the faults and enlighten me some more! maybe it will even help someone else figure things out. =]

Everything is governed by relativity(except for quantum stuff, it will wait for another note). Everything we see, touch, smell, or even think of exists in four dimensions. Just go with it, you got up/down, left/right, forward/backward, and the all important time.

The second thing that not many people realize is that c is not merely the speed of light, it is the fundamental speed limit of everything, and no I don't mean that nothing can travel faster than that(although that is true, there is more to it). What you have to remember is that there are four dimensions, not just three. All EM radiation travel at this velocity. That is because they have no mass, or no rest mass, we will get to that later.

Now since these 'massless' particles are have no mass, they are pure energy, and this causes them manifest all of that energy into moving in one or any combination of the first three dimensions mentioned above, and since they are only moving in space, and not time, their velocity is at a constant value, which happens to be c.

The appearance of time is also governed by a sense or relativity. All frames of reference are different and time as well as space can be observed as quite different depending is this frame. So there has to be something that brings it all back together or you end up with paradoxes everywhere and nothing would make sense. As you approach c in one dimension, your velocity in any other must vary directly. This means that if you are going 'forward' at .5c, the sum of the velocities in any other direction(including time) must add up to .5c. This causes time to be 'slower' at higher velocities. The only way to travel as fast as possible, c, through time is to be absolutely still in space. If you could travel at c in space, time would be moving at a velocity of zero.

Through the equation E=mc², it is shown that mass means energy. Due to this, a massless particle, such as a photon, would have no energy. This is solved by the fact that a photon has zero rest mass, but once moving it gains kinetic energy through momentum. Anything with momentum must have mass. A photon has mass when traveling at c, and can not exist if its not traveling at c, therefor removing the issue of it having no rest mass but having mass while moving.

The fact that you can not accelerate any mass to c is due to the increase in inertia. As you put more energy into accelerating the mass, since c is constant in E=mc², the only thing left to change is the mass. As it travels faster, it has more mass and takes more energy to accelerate by the same amount. Therefor requiring an infinite amount of energy to accelerate to c.

Thanks,

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

It looks roughly true, although it seems to lack emphasis on the key point of relativity--which is the "relative" part. The key point of it all is in Maxwell's Equations, which define a speed of light based on two fundamental constants--the permittivity and permeability of space, which control how empty space resists EM fields. So, we have to square this with Einstein's two postulates:

First Postulate: The laws of physics are the same no matter how fast you're going. This is absolutely critical for science to work at all--the Earth keeps changing velocities as it orbits, and all our science is done on the Earth or in Earth orbit. So it stands to reason that, since we never notice anomalies caused by, say, speeding up in the winter because we're closer to the sun, that the first postulate is true. Really, it generalizes to "nobody is more correct than anyone else in defining a velocity". I'm standing still right now, but if a bus flew past my window at 30 m/s, they'd observe me as going at 30 m/s. You can always call yourself stationary. So the dilemma now is that Maxwell's equations have a predefined speed built into them, based on the properties of empty space. Either Maxwell's equations don't apply at different speeds (which wouldn't make any sense considering what we've observed) or the permittivity/permeability of space changes as you speed up or slow down, which would also break the universe. This leads us to the second postulate:

Second Postulate: All observers measuring the speed of light will measure the same value -- c. I hope you can see how this follows from the above.

It's the consequences of the second that make things really trippy. If I'm going .9c relative to you, and you shine a flashlight outward at the same time, you'll observe me as going at .9c and the light as going at c. The critical thing, however, is that I measure the light's velocity to also be c, even though from your point of view I'm nearly catching up to it. This requires completely transforming how we look at space and time. You're right about "spacetime velocity" adding up to c at all times--mathematically, you have a four-vector momentum which has to remain constant. (Although I haven't really dealt with relativity in a school setting and so don't remember the math exactly.) If I remember correctly, moving essentially rotates your frame of reference relative to someone else, as far as space and time goes.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

I think the answer might be that you can get out, but it's going to take an infinite amount of time, or something. Ignoring the tidal forces. Actually, this answer isn't backed up by math at all, it's just something that sounds right, so.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Meteorswarm wrote:conservation of energy seems to say you should have enough energy to overcome the black hole's pull, since you have your speed + whatever GPE you'd lose in approaching it. What gives?

Doesn't matter how much energy you have: if it's finite, it's not enough to overcome the black hole's pull.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

YoungStudent wrote:Question, once in event horizon, even light cant escape Black Hole's gravity, right? But closer i get to the black hole, faster i fall into the canter of the black hole? In the middle my speed is for example 2* the speed of light, and very near to the center of black hole my speed can be multiplied many times?

Measuring your speed as (change in Schwarzchild radius coordinate) per (tick of your wristwatch), yes, you travel at a speed greater than 300,000 km/sec.

To understand what's meant by the Schwarzschild radius coordinate: imagine building a series of thin hollow concentric spheres in empty space. You build one that's a meter in radius, then another one around it that's one more meter in radius, and another, like one of those doll-inside-a-doll thingys. Now imagine somebody sneaks in to your creation in the midddle of the night and places a black hole at the very center. The spheres are strong enough so that the ones outside the event horizon don't change shape or stretch in any way. If you carefully measure the circumference of each sphere, you find it hasn't changed before / after the black hole was inserted. The distance between spheres DOES change - space gets stretched by the black hole. The spheres - imaginary ones now inside the event horizon, since real ones would collapse - represent the Schwarzschild r coordinate. So you fall through more than 300,000,000 successive imaginary spheres per one tick of your wristwatch after you cross the EH, approaching infinite velocity at the singularity.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Sir,

Thanks for your reply, and most of that post was assuming that the reader already has most of the basics down and is looking for further understanding. I know I should have not assumed anything but that was my own thought process with it

rofl

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

Meteorswarm wrote:
gmalivuk wrote:
Meteorswarm wrote:conservation of energy seems to say you should have enough energy to overcome the black hole's pull, since you have your speed + whatever GPE you'd lose in approaching it. What gives?

Doesn't matter how much energy you have: if it's finite, it's not enough to overcome the black hole's pull.

But shouldn't you gain precisely as much energy as you'd need to get out by falling in in the first place?

That's an awfully Newtonian way of thinking, and it just doesn't apply here.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

The energy goes into the mass of the black hole (as apparent to people outside).
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### Re: RELATIVITY QUESTIONS! (and other common queries)

This is a homework assignment to do with the relativity of simultaneity.

"In a frame of reference S two events occur simultaneously at two different points which are seperated by 3x10^8m. Using special Relativity find (as a fraction of the speed of light c=3x10^8m/s) the velocity of the inertial frame S' in which the two events are seperated by 0.1s, where the frame S' is moving with constant velocity along the x axis with respect to S"

So far I've tried it a couple of different ways, one time getting the result "0.1=0" and another time getting "V=c", which makes me think something's horribly wrong with my method. The main problem seems to be that I've been using the equation:

(delta)t' = (delta)t/(1-(u^2)/(c^2))

But (delta)t=0, which just complely writes off the right hand side of the equation. If anyone could just point me in the right direction on how to do this problem I'd be very grateful.
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### Re: RELATIVITY QUESTIONS! (and other common queries)

burningcowsrule wrote:This is a homework assignment to do with the relativity of simultaneity.

"In a frame of reference S two events occur simultaneously at two different points which are seperated by 3x10^8m. Using special Relativity find (as a fraction of the speed of light c=3x10^8m/s) the velocity of the inertial frame S' in which the two events are seperated by 0.1s, where the frame S' is moving with constant velocity along the x axis with respect to S"

So far I've tried it a couple of different ways, one time getting the result "0.1=0" and another time getting "V=c", which makes me think something's horribly wrong with my method. The main problem seems to be that I've been using the equation:

(delta)t' = (delta)t/(1-(u^2)/(c^2))

But (delta)t=0, which just complely writes off the right hand side of the equation. If anyone could just point me in the right direction on how to do this problem I'd be very grateful.
Cheers.

Explain this equation to me: Is one side supposed to be one frame and the other the other frame?
And the dt is the observed difference between the two events in each frame?
Is then there some special reason you are assigning the S' time to the t' side? Can they work the other way around?
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### Re: RELATIVITY QUESTIONS! (and other common queries)

Mr_Rose wrote:
Explain this equation to me: Is one side supposed to be one frame and the other the other frame?
And the dt is the observed difference between the two events in each frame?
Is then there some special reason you are assigning the S' time to the t' side? Can they work the other way around?

The dt' is the time interval between the two events as measured in frame S', and the dt is the time interval measured between the two events in frame S (in this case, 0). I'm assigning S' to the t' side because t' is the time as measured from the frame S'. I've no idea if they'd work the other way around, I'm about to try the problem from the point of view of an observer in the frame S' though to see if that helps at all.
Hope that that clears it up.