RELATIVITY QUESTIONS! (and other common queries)

[Malconstant]

I love poking my nose into this thread every now and then. You're all doing god's work here.

[yurell]

I've a relativity question ... I have an object that I'm accelerating under constant power (it's not losing mass, though). I've calculated the amount of (proper) time it would take to accelerate to its maximum velocity, but I'm trying to figure out what this would be for another observer. We have that dt' = γ dt, but I've no idea how to integrate this, since velocity is time dependent. I know it's not that difficult to do if we assume constant acceleration, but I don't think it is (a = dv/dt = (dv/dE) * (dE/dt), only the latter of which is constant).

So does anyone know how I'd go about solving this?

[Yakk]

Sorry, maximum velocity what?

[yurell]

Oh, it stops accelerating once it's hit a certain speed relative to its target (which coincides to it being in the same location as its target), and begins its acceleration with zero speed relative to its target.

[Yakk]

So, in what frame of reference is the power "constant"?

How is the power being turned into delta-v? (Power is energy/time... you need to conserve both momentum and energy, so you need some mass to generate the acceleration you want. The same amount of power used in different ways will result in different velocities of your craft.)

[yurell]

The power is constant in the frame the accelerating object, and the delta-v is coming from photons being bounced off it (it's being assumed that it's 99% efficient at converting the energy to kinetic energy, the rest going into heat, which it's dissipating isotropically as blackbody radiation).

[gmalivuk]

The power is constant in the frame the accelerating object

Then acceleration is also constant, and you use these equations.

Note, however, that constant power in the accelerating frame means ever increasing power from the photon source.

[yurell]

Cheers, I'll read that!

[Twelfthroot]

I see there's already some discussion of relativistic mass in the thread, but I'd like to get a straight answer this question just as posed:

I see many arguments that relativistic mass is pedagogically unsound or somehow fictitious. But the people making these arguments generally do not have the same complaints regarding contracted length. Is a relativistic increase in mass in any way "less real" or different from a relativistic decrease in length?

The reasoning I've heard is that (rest) mass is a fundamental, invariant property of an entity and such properties should not and do not change just because the object is moving relative to the observer. But I don't see why you couldn't make the same argument about "rest length". A moving object isn't "really" decreasing the distance between its constituent particles -- it isn't changing from its own perspective -- but we measure it as shorter, so from our perspective it "really" is shorter. It seems to me analogous to say that a moving object's particles aren't "really" somehow becoming more massive -- it isn't changing from its own perspective -- but from our perspective we measure it as heavier, so it "really" is more massive. Is there some fundamental difference between the two I'm missing?

If on the other hand the reasoning is "momentum is the quantity that's actually significant and worth considering", that seems reasonable to me, but it doesn't make relativistic mass fictitious.

[PM 2Ring]

Relativistic mass isn't fictitious, but it can lead to misunderstandings, so the modern tendency is to avoid it and to prefer approaches that use momentum and energy instead.

A classic example of the kind of errors that arise if you use relativistic mass: consider two objects that are at rest with respect to each other but moving at relativistic speed relative to some observer. You need to use the rest masses of these two bodies to calculate the gravitational attraction between them, so if you use their relativistic masses you get the wrong answer.

There are some situations where the relativistic mass does come in handy, but because it has lead so many relativity newbies down the wrong path modern educators have generally developed an aversion to it. OTOH, there are people who do have some positive things to say about relativistic mass.

[Eomund]

In the movie the Hunt for Red October they talk about going 105% with their reactor. Is this just hollywood or what are talking about and how is it possible to go over 100%?

[doogly]

I think it actually is possible, mostly due to where they calibrate 100% at, which has more to do with safety than the theoretical limits of the reactor. But I am making this statement based on something I think I heard once. Do not trust me if it matters.

[eternauta3k]

I heard the same in a movie, can't remember if it was a plane taking off or a rocket from the Apollo missions. A quick search says 100% is the maximum rated speed/RPMs/heat output. So maybe it can be run hotter for a while.

[eSOANEM]

It's also worth noting that a lot of devices/components are given with a "maximum" and "absolute maximum" rating. In general, exceeding the maximum rating for shortish periods of time isn't too bad and sometimes, you can even get away with exceeding the absolute maximums. My guess is that the 105% was referring to the "maximum" rating.

[Yakk]

You can run a CPU at 110% of rated GHz, why not a reactor?

[thoughtfully]

Maximum ratings are generally based on lots of criteria and operating assumptions, and then get a big cushion piled on for extra measure. You can pick and choose among what criteria really matter or change the operating conditions (immerse that motherboard in mineral oil) and extend your maximum in plenty of ways.

[Dr. Diaphanous]

OK I have some potentially n00by questions for the physicists out there?

1)Is there a maximum speed from the reference frame of the traveler? I mean, If you are travelling between two planets in a rocket with constant thrust, observers on the planets would observe it accelerate up to near the speed of light, then accelerate less and less so you never reach c, correct? But for the traveler, would time dilation balance out the reduced acceleration due to increased relativistic mass? So the traveler observes that constant acceleration is maintained up to infinite speed? Because you can cross the galaxy in a subjective second if you are going fast enough?

2) What is a light year? Surely photons do not age in travelling from one body to another, they hit your eye an instant after being emitted from the star you are looking at.

3) Why are the axes not labelled in pictures of a light wave?

4) Why are the axes not labelled in pictures like this of spacetime? Is one of the axes time?

Spoiler:

[eSOANEM]

1. Motion is relative and any observer always observes themself to be stationary. From the point of view of the moving person, the universe is moving towards/away from them and everyone else's clocks tick slower.

So the travelling observer sees everything in front of them accelerate and asymptotically approach c.

From the traveller's point of view, (when they cross the galaxy in what to a "stationary" observer appears to be 1 second of the traveller's clock) the stationary person's clock appears to tick 1 second which is slower than the clock in the traveller's ship. Each observer will see the other one as having a slower clock than their own.

2. Photons do not age correct, we see their clock as stopped and they see everything else's clock as stopped. A light year is defined in terms of the distance covered by a light ray in a a year as measured in a subluminal frame.

3. I'm not quite sure what you mean here. Do you mean the axes for the electrostatic and magnetic waves making up light or space and time axes?

4. Diagrams like this do not often represent actual bending of space, when they do, they tend to have the vertical axis being curvature rather than time IIRC. In this case, because the surface matches closely to the Newtonian well I suspect very strongly that this is the case here; the other two horizontal axes will be two spatial co-ordinates.

[doogly]

Yeah, that diagram in number is a schematic, a rough heuristic, a generally misleading one even. It can be a little perilous to take seriously.

[Goemon]

1. ...Because you can cross the galaxy in a subjective second if you are going fast enough?

For a little extra help here, in addition to what eSOANEM said: from the point of view of the traveller - someone who sees the galaxy flying towards them at a speed very close to c - length contraction makes the "depth" of the galaxy so tiny that it takes only a second to pass through it entirely. If they don't hit any stars on the way through.

[PM 2Ring]

1)Is there a maximum speed from the reference frame of the traveler? I mean, If you are travelling between two planets in a rocket with constant thrust, observers on the planets would observe it accelerate up to near the speed of light, then accelerate less and less so you never reach c, correct? But for the traveler, would time dilation balance out the reduced acceleration due to increased relativistic mass? So the traveler observes that constant acceleration is maintained up to infinite speed? Because you can cross the galaxy in a subjective second if you are going fast enough?

As eSOANEM said, the speed of a traveller in their own reference frame is always zero. It's very important to keep this fact in mind when thinking about relativity. However, when analyzing accelerated motion in special relativity we can't use accelerated reference frames, since they are not inertial. In other words, you can feel acceleration, and general relativity says that acceleration (locally) feels just like gravity. But we can still calculate things in special relativity for an accelerated traveller: at each instant we can associate an inertial reference frame to the traveller and perform our calculations in that frame. This can get tricky, since the frame is only valid for an instant.

For further details, see
http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html
and
http://en.wikipedia.org/wiki/Relativistic_rocket

Surely photons do not age in travelling from one body to another, they hit your eye an instant after being emitted from the star you are looking at.

Sort of. Photons are useful when discussing the interaction of light with matter, they aren't so useful when discussing the propagation of light, which is better modelled using waves.

3) Why are the axes not labelled in pictures of a light wave?

Sometimes they are. The electric and magnetic components of an electromagnetic wave are perpendicular to each other, and if a diagram only shows one component it's generally the electric component, since the plane of that component is the plane of polarisation. IE, a vertically polarised light wave will pass through a polarising filter whose crystal are aligned vertically. See http://en.wikipedia.org/wiki/Polarizing_filter#Wire-grid_polarizer

4) Why are the axes not labelled in pictures like this of spacetime? Is one of the axes time?

Spoiler:

What Doogly said.

1. ...Because you can cross the galaxy in a subjective second if you are going fast enough?

For a little extra help here, in addition to what eSOANEM said: from the point of view of the traveller - someone who sees the galaxy flying towards them at a speed very close to c - length contraction makes the "depth" of the galaxy so tiny that it takes only a second to pass through it entirely. If they don't hit any stars on the way through.

Or interstellar gas and dust. Hell, at that speed even the CMBR would be severely blue-shifted into very hard gamma.

[KrO2]

This is probably not a common query, but it didn't seem like it deserved its own thread. Anyway.

My understanding of the Boltzmann brain thought experiment is that it assumes a universe that lasts forever at high entropy. Some of the random fluctuations involve low enough entropy for observers to be present, and most of the observers (by a very large margin) are the simplest possible self-aware entities. If any of this is wrong, that probably answers my question.

My question is, why shouldn't we be Boltzmann brains? It's obvious that we aren't, but why not? According to current best guesses the universe will eventually have a heat death and will go on forever at high entropy. If there is a nonzero probability of an entropy fluctuation that involves an observer, then given an infinite amount of time it will happen. A lot. The pre-heat death universe should be statistically insignificant just because that's the part that doesn't go on forever. And the post-heat death universe sounds a lot like the cosmology assumed by the thought experiment. Does this mean that the universe must eventually have an endpoint, instead of just asymptotically running down?

Possible other answers:
The likelihood of getting an observer by random chance is literally zero instead of being infinitesimally small.
There is some significant difference between our universe post-heat death and the universe assumed for the brain thing. (This is kind of the one I'm expecting.)
I've completely misunderstood the brain hypothesis or the forecast for the end of the universe or both.

[Xanthir]

This is probably not a common query, but it didn't seem like it deserved its own thread. Anyway.

My understanding of the Boltzmann brain thought experiment is that it assumes a universe that lasts forever at high entropy. Some of the random fluctuations involve low enough entropy for observers to be present, and most of the observers (by a very large margin) are the simplest possible self-aware entities. If any of this is wrong, that probably answers my question.

All of this is correct.

My question is, why shouldn't we be Boltzmann brains? It's obvious that we aren't, but why not?

No, it's *not* obvious that we aren't, and that's the point. It would be problematic if most conscious entities across time were short-lived randomly-formed minds, sure. But Boltzmann's argument is worse - even if you just look at conscious entities who think they live in an long-lived, orderly universe with physics like ours, the brains still vastly outnumber the number of observers who are actually *in* such a universe. Memory is just a neural pattern, and can be reproduced by a random fluctuation as easily as anything else.

The Boltzmann Brain idea is Last Tuesdayism writ large. You can't prove that the universe wasn't created last Tuesday with the mere appearance of being a few billion years old. Boltzmann just formalized this, showing that, within the confines of his hypothetical, *most* universe were created last Tuesday, so to speak.

According to current best guesses the universe will eventually have a heat death and will go on forever at high entropy. If there is a nonzero probability of an entropy fluctuation that involves an observer, then given an infinite amount of time it will happen. A lot. The pre-heat death universe should be statistically insignificant just because that's the part that doesn't go on forever. And the post-heat death universe sounds a lot like the cosmology assumed by the thought experiment. Does this mean that the universe must eventually have an endpoint, instead of just asymptotically running down?

Possible other answers:
The likelihood of getting an observer by random chance is literally zero instead of being infinitesimally small.
There is some significant difference between our universe post-heat death and the universe assumed for the brain thing. (This is kind of the one I'm expecting.)
I've completely misunderstood the brain hypothesis or the forecast for the end of the universe or both.

Your second one (some significant difference) is correct.

[KrO2]

No, it's *not* obvious that we aren't, and that's the point.

I didn't mean obvious because what we see must be true. I had been thinking that if the brain hypothesis were true, then I should be much simpler than I would have to be to believe myself to be in a complex universe. Most people should be just brains appearing long enough to think "I exist." Those should outnumber brains that believe themselves to be in an orderly universe by, well, infinity. Since the brain hypothesis says that we should not have the observations we do, it gets falsified. I'm not sure how convincing this is, but I do believe I'm not a spontaneously appearing mind and I'm guessing so does everyone else.

I think the more important question is, what is it about the eventual fate of our universe that would prohibit random fluctuations that potentially contain Boltzmann brains?

[Xanthir]

You're still not quite getting it. Even after applying anthropic filtering (wiping out all the possibility-space that doesn't result in something like our observations), we're *still* vastly outnumbered by Brains in Boltzmann's scenario. You simply cannot falsify the assertion that you're a Brain who came into existence a moment prior with fully-formed memories of living a life in an orderly universe.

Yes, the Brains that are convinced they're us are vastly outnumbered by the Brains that are conscious, but don't have memories of an orderly universe. That's irrelevant, because they still dwarf real-us.

The way around this is to posit that the universe doesn't end up in an infinite maximum-entropy state. The Big Crunch was one way around this, as our universe had a finite lifetime. Another way around it is to assume that inflation will continue forever, where in finite time every quantum of energy will be separated from every other by a cosmological horizon, so Brains can't ever develop.

I'm not sufficiently familiar with this area to come up with any more, though I suspect there are some.

[gmalivuk]

Since the brain hypothesis says that we should not have the observations we do

But it says no such thing.

[Yakk]

The way around this is to posit that the universe doesn't end up in an infinite maximum-entropy state. The Big Crunch was one way around this, as our universe had a finite lifetime. Another way around it is to assume that inflation will continue forever, where in finite time every quantum of energy will be separated from every other by a cosmological horizon, so Brains can't ever develop.

Another way around that is to posit that there is a reasonably likely way for a region of space to experience a big-bang like event (high matter density, ridiculously low entropy, massive expansion of space-time). It has to be unlikely enough that universes where only one of these events has occurred in their visible past lightcone are common enough, yet common enough that Boltzmann Brain's are outnumbered by "real-universe" beings.

If this process is somehow destructive of the flat space-time in which Boltzmann's Brains appear, "real" universes can outnumber Boltzmann's Brains. But I don't think you need that -- you just need for child-universe generation to outpace Boltzmann Brain generation. Which means outpacing it over the infinite tail end of the universe as well, or eventually Boltzmann's Brains win out: the process to seed a big bang needs be possible (and more likely than a Boltzmann's Brain) in the nearly flat, nearly zero entropy "end-game" universe.

[PM 2Ring]

This recent thread in Fictional Science has some good discussion on Boltzmann brains: Things a Perfect logician would Discover.

A few years ago we had a great thread here discussing life and the universe in the far distant future (eg > 1 googol years). Can anyone find a link to it? I think this might be it: Stupid Theory About Universe. I thought the thread was a bit longer and more elaborate, but that might just be my memory playing trickses.

[tomandlu]

Reading the Boltzmann's Brain article on wikipedia led me to the Swampman article (http://en.wikipedia.org/wiki/Swampman). Nerd question (in case anyone knows). Alan Moore's Swampthing #21 came out in 1984, and the Swampman thought experiment is from 1987. There are several similarities* - does anyone know if Davidson has ever acknowledged whether it was the comic that prompted this idea?

* for anyone who hasn't read it, it's the issue where Swampthing discovers that he's not a reanimated human, but a plant that has replicated the conciousness of a (dead) human.

[PM 2Ring]

Some previous xkcd forum threads that mention Swampman:
The Problems with Teleportation and ethics of artificial suffering
I particularly like Charlie's comment:

Oh snap it's like a pzombie sailing on theseus' ship.

[drewder]

So my question is do pilots age at a different rate because they spend so much of their time at high altitude (less gravity)

[douglasm]

So my question is do pilots age at a different rate because they spend so much of their time at high altitude (less gravity)

Yes, but the difference is so small no one would ever notice without timing things with atomic clocks.

[eSOANEM]

So my question is do pilots age at a different rate because they spend so much of their time at high altitude (less gravity)

Yes, but the difference is so small no one would ever notice without timing things with atomic clocks.

An atomic clock in the plane will tick slightly faster than one on the ground and so the pilot will seem to age slightly more. The fact the pilot is moving will produce a twin-paradox type effect as well which will result in the measured difference in the time the clocks measure as having elapsed being slightly less than you'd expect just due to gravitational effects however as even the fastest passenger jets are much slower than a millionth of c, any difference from the gravitational effect will only be noticed at the 13th significant figure or so so I suspect this effect wouldn't be noticed even with atomic clocks.

[Xanthir]

Well, it will definitely be noticed by atomic clocks, since we used atomic clocks to measure it as a verification of relativity. ^_^

But since humans don't age with the necessary precision, you wouldn't ever notice it.

[eSOANEM]

Well, it will definitely be noticed by atomic clocks, since we used atomic clocks to measure it as a verification of relativity. ^_^

You're quite right. I suspect the bigger problem would be that it would be that variations in the potential the pilot flies at are probably sufficiently large effect to mask any special relativistic effect.

[Twistar]

Quantum spin:

So every time it's taught the teacher (be it a professor or book) always goes on about how we shouldn't think of spin as the electron actually spinning since it has no extent (i.e. it's a point,) and that it is just some intrinsic quality. I see so many issues with this explanation.
First of all: Even with the L operator (regular angular momentum) I don't think of the electron as actually spinning around the proton with a certain classical angular momentum. I think that this is the operator that helps us figure out parts of the angular dependence for the wavefunction of the electron. an electron revolving around the proton is a classical picture. All we have in quantum mechanics is wavefunction

Next: What do you mean the electron has no extent? Particles are HARDLY defined in quantum mechanics. In Classical mechanics a particle is a pointlike object. in quantum mechanics a particle is just something that corresponds to a specific Hamiltonian. I mean, you could argue that if there is a pontential then a quantum particle is only acted on by one specific point in the potential at a time but I don't think that's right. The way I see it there is a set of eignenwavefunction corresponding to any Hamiltonian. This doesn't really depend on the particle at all.
I'm not as well versed in the language for wavefunctions for multiple particles, but from what I can tell you're never really treating the particles as a point.

So the way I see it.. There's no such thing as particle electrons. Instead an electron just corresponds to a wavefunction and spin is just a property of that wavefunction. Now there's the other issue which is that I've never been given a good way to think about the spin part of the wavefunction in any concrete way. As far as I can tell it lives in some sort of tensor product with the regular Hilbert space that tells us about the spatial wavefunction.

So here's a pretty relevant question. Do protons have a radius? Or gluons? As far as I can tell it's all wavefunctions down there and we need to entirely abandon the particle picture. Now, there are entities which correspond in some way to wavefunctions and that is sort of a confusing concept so I need to think about that.

[doogly]

Nothing has a radius, the way that they do classically. Things do have a cross sectional area for the purposes of collisions, and it depends on what you are shooting, what energy you are shooting at, etc.

In general, all the notions of a reality that is nice and cozy and real and that you happen to check in on when you do experiments have to perish. So, what is "a particle?" A particle isn't a thing, it's an event -- a particle is when a particle detector goes *click.*

It's tricky, yeah.

[Twistar]

ok. That makes sense, doogly. The problem is bigger than spin being non-intuitive. The whole idea of particles needs to be revisited.

[thoughtfully]

The whole idea of particles needs to be revisited.

No more so than any of the other "lies we tell children". It's the lies we tell ourselves that raise my bristles

[Robert'); DROP TABLE *;]

Are there any particles which are both massless, and affected by a force other than gravity? (e.g. charged, has net colour...) Is such a particle existing forbidden by any current theory?