Redshift?

[Chaos]

As for timemaster's argument, it fails because it looks at light as only a wave.  But it's also a particle.  You wouldn't measure the wave peaks passing the bubble, but the photons.  The effective wavelength would be unchanged.

I'm not seeing your logic here. The fact that a photon has properties of particles like momentum does not invalidate Timemaster's argument, because a single photon will still have a particular wavelength.

So your argument basically boils down to "since it isn't gravity or velocity, relativity doesn't apply." I'd say, irrelevant of mechanism, if there is some time dilation, there must be a shift in frequency.

My understanding of Timemaster's argument is this (assuming a bubble in which time passes more quickly):

Light is emitted from within the bubble at a particular frequency.  The peaks of the wave hit the bubble boundary at a particular rate, 1/second to make math easy.  But outside the bubble, only 1 second passes for every 10 seconds inside the bubble.  So now 10 peaks are coming out of the bubble every second.

My argument is that light doesn't really work that way.  You don't count the peaks to measure how much light is entering or exiting a given space, you count photons.  Counting the waves is irrelevant.

The fact that light is also a particle doesn't mean it's any less a wave. That's like saying since an electron exhibits wave properties, it is no longer a particle.

I'll let Timemaster explain more He's a physics grad student (thus a few years ahead of me), and I'm sure he could elaborate on the subject.

Observable relativistic redshifts (for the doppler effect) kick in around 3,000 MPH (5,000 KM or so).

Edit: And, actually, that is the point where it would turn yellow to green (or orange, direction pending)

This is... not accurate.  From here we get a list of colors and their corresponding wavelengths.  Let's say we we wanted to go from yellow to green.  We'll make our emitted wavelength 572nm and our observed 568nm. That's a very slight difference, but still noticable.

z = (568nm - 572nm)/(572nm) = -0.007

From z = v/c, we get that the relative velocity would have to be about 4,690,000 mph.  5,000 mph isn't doing squat.

actually, i looked it up and realized my fault. It's KM/Miles per SECOND not HOUR.

It's been about 10 years since my college phsyics courses, so naturally my memory of such things can be a bit rusty.

However, a new though occurs!

As we all know (hopefully), the speed of light is constant only in a vaccum. As it hits new mediums it speeds up and slows down. I'm willing to bet that if we slow time, we also slow the emitted light because its going to take longer to get places. As such, when exiting/entering the medium of the time bubble, it's going to cause the usual refraction. When light moves through different mediums, and as its speed changes, it would actually get refracted similar to light passing through a prism.

So thinking about this, i'm actually gonna have to change my vote to a "no" on redshift, and instead flip over to saying that its going to refract light like looking into a crystal.

What says everyone?

Edit: i wonder what the angle of refraction would be on a time-dilation bubble?

I already noted that fact about Index of Refraction in my first post

[Eerongal]

I already noted that fact about Index of Refraction in my first post

So you did. I apparently missed that.

[Timemaster11]

On the wave and particle properties of light:

Alisto is only partially correct when he suggests that the amount of photons entering the bubble determines how much light enters the bubble.  (by the way, the number of photons entering the bubble is conserved across the boundary).  Not all photons are the same.  Individual photons have frequency, which cannot be determined simply by the number of photons. 

The frequency determines the energy of a photon through E=hf, where h is Planck's constant, and f is the frequency, and E is the energy of an individual photon. The number of photons acts to relate the frequency to the total energy, but does not in any way determine the frequency. 

For quantities such as wavelength and frequency, which are wave properties, the wave description of light is far more relevant.

(Interestingly, this means that, if frequency of light changes for the allomancer, so does the energy of that light proportionally.)

On the counting of wave peaks:

The peaks in a light wave are the peaks in the electric and magnetic fields.  Suppose we place a metal plate in the bubble, and shine a light on it.  Both outside and inside observers would agree on the moments when the absorption of energy by the electrons in the plate peaked (given that they had really good detection equipment), so both would agree on where and how many wave peaks are in the bubble at any moment. Through this method, the number of peaks hitting the plate could be counted.

On index of refraction:

In optics, the phase of a light wave does not change when it enters a material of differing index of refraction.  Thus, the number of peaks that reach the bubble must be the number that enter, regardless of the index of refraction.  Thus, to an observer outside the bubble, the frequency of wave peaks just outside the bubble equals the frequency just inside.  

To prevent a build-up of wave peaks, the number of peaks contained by the bubble must be constant, so the frequency at any point must be the same.  Thus, to the outside observer, the frequency of peaks striking the allomancer's eye equals the original frequency.  Then, as both observers would agree on the number of peaks that strike the allomancer's eye, the time dilation factor would shift the frequency of light accordingly for the allomancer.

Thus, the allomancer would find the frequency of the light to be shifted by the time dilation factor.

Note:  The index of refraction may still have an effect on the wavelength of light.  However, if to the allomancer in the bubble the light in the bubble has the standard speed of light, then the allomancer would detect a corresponding equivalent shift in wavelength, as well, since                                      (speed)=(frequency)*(wavelength).

[happyman]

Again, I have to say that Timewaster11 has it right.

I have a PhD in Physics, myself, and quantum mechanics is an important part of every physics curriculum I know and I've solved tons of problems in the fields.  The quantum mechanical effects of light are quite difficult to solve, but no theory we have for light invalidates the simple wavelength-counting Timewater11 is describing.  The fact that light is quantized as photons doesn't effect any of his arguments; each individual photon is also a nonlocalized wave with a wavelength that changes when traveling through a gravitational potential.  If you think this is bizarre, take it up with the universe; I'm sure it will listen to your complaints.

[trendkill]

Again, I have to say that Timewaster11 has it right.

Off topic (I seem to have a penchant for that in this thread :-\), but was calling him Timewaster intentional or a typo? Because I find it rather amusing. (Still give both of you mad props for knowing far more about light than I will ever know about... Anything really.)

[Eerongal]

@happyman and Timemaster:

You two are, apparently, more well versed in physics than i (ive only take up to a 200-level course) and timemaster's explanation goes a bit over my head in all, but not in so far that I can't understand him some.

So i put out this question: In regards to refraction, yes or no, would it indeed scatter light like a prism?

*--Off topic--*

so this is off topic as well, but i thought i would post it here for the physics-minded types. I thoroughly enjoyed it. Dunno if its true or not (likely is since its nothing too terribly crazy)

http://www.mycoted.com/There_are_many_correct_ways_to_answer_a_test_question

[Guest Alisto]

The fact that light is quantized as photons doesn't effect any of his arguments; each individual photon is also a nonlocalized wave with a wavelength that changes when traveling through a gravitational potential.

But there IS no difference in gravitational potential.  So what would cause the change in wavelength?

[Chaos]

so this is off topic as well, but i thought i would post it here for the physics-minded types. I thoroughly enjoyed it. Dunno if its true or not (likely is since its nothing too terribly crazy)

http://www.mycoted.com/There_are_many_correct_ways_to_answer_a_test_question

I was thoroughly entertained by that, however, I'd argue that "learning how to think" is the whole point of higher level physics (certainly, it shows in my upper division mathematics classes). Learning to think logically is the whole point.

The fact that light is quantized as photons doesn't effect any of his arguments; each individual photon is also a nonlocalized wave with a wavelength that changes when traveling through a gravitational potential.

But there IS no difference in gravitational potential.  So what would cause the change in wavelength?

The time dilation factor is what would cause it. Light will travel at the same speed regardless of reference frame. Here, inside the bubble, we're in a different reference frame than we would be outside of it. The only physics we're invoking here is that light will travel at the same speed (the speed of light postulate). It should fall out mathematically.

We know that c = λf. f = 1/T where T is the period of time between each wave peak. So, the frequency is a function of time. Because we are changing time, and not the speed of light (by the speed of light postulate), that means:

c = λf = λT, and if we have a time dilation factor (in special relativity, we call it γ), that means c = λ(γT).

Already, we can see that our frequency f has shifted due to that γ factor. We don't have to know the mechanism for this simple math to work. This is basically the mathematical version of Timemaster's explanation.

[Timemaster11]

On energy:  (rough explanation)

From the outside observer's point of view, the frequency of the light does not change as it passes into the bubble.  Since frequency is proportional to energy, this says that the energy of the light is conserved.  

However, you could say that the allomancer is now moving in the time direction at a different rate.  In relativity, one finds that the energy is actually the time component of momentum.  

A speeding car normally is viewed as having a lot of momentum.  Drive at the same velocity as that car, however, and the speeding car will appear to have 0 momentum from your perspective.  As you change your motion in that direction, the car's momentum relative to you appears to change.

In the same way, as the allomancer changes his motion in the time direction, the time momentum (aka energy) of the light also changes from his perspective.

[Zas678]

So how much of a shift would there be if the bubble cut time in half? So for every second that happens inside the bubble, there's two outside.

I guess I'm saying is that there seems to be a consensus that there would be a redshift/blueshift. My question is, would anyone other than Lightsong be able to tell?

[Chaos]

So how much of a shift would there be if the bubble cut time in half? So for every second that happens inside the bubble, there's two outside.

I guess I'm saying is that there seems to be a consensus that there would be a redshift/blueshift. My question is, would anyone other than Lightsong be able to tell?

For cadmium, you'd just choose a different proper time. The cadmium redshift would be equivalent to the whole rest of the world except those in the cadmium bubble burning bendalloy.

And no, any significant shift in time would result in massive redshifting. As Timemaster said,

(Note that extreme blue and extreme red are separated by less than a factor of 2, so for even a time change of 2, the allomancer would cease to see visible light and would only see shifted infrared or ultraviolet light.)

[Guest Alisto]

The time dilation factor is what would cause it. Light will travel at the same speed regardless of reference frame. Here, inside the bubble, we're in a different reference frame than we would be outside of it. The only physics we're invoking here is that light will travel at the same speed (the speed of light postulate). It should fall out mathematically.

We know that c = λf. f = 1/T where T is the period of time between each wave peak. So, the frequency is a function of time. Because we are changing time, and not the speed of light (by the speed of light postulate), that means:

c = λf = λT, and if we have a time dilation factor (in special relativity, we call it γ), that means c = λ(γT).

Already, we can see that our frequency f has shifted due to that γ factor. We don't have to know the mechanism for this simple math to work. This is basically the mathematical version of Timemaster's explanation.

This doesn't really work, because the Lorentz factor is a number defined by velocity.  It only comes into play when we're talking about time dilation caused specifically by differences in velocity.

On energy:  (rough explanation)

From the outside observer's point of view, the frequency of the light does not change as it passes into the bubble.  Since frequency is proportional to energy, this says that the energy of the light is conserved.  

However, you could say that the allomancer is now moving in the time direction at a different rate.  In relativity, one finds that the energy is actually the time component of momentum.  

A speeding car normally is viewed as having a lot of momentum.  Drive at the same velocity as that car, however, and the speeding car will appear to have 0 momentum from your perspective.  As you change your motion in that direction, the car's momentum relative to you appears to change.

In the same way, as the allomancer changes his motion in the time direction, the time momentum (aka energy) of the light also changes from his perspective.

This, however, makes sense.  Kind of.  What you're saying is that the Allomancer is as the Allomancer travels more quickly through time, the energy of the light would appear to drop, and therefore become redshifted?  I get that, but doesn't that assume that the light itself is unaffected by the bubble?

Brandon said, "As soon as you get close enough to change it, it

[Chaos]

The time dilation factor is what would cause it. Light will travel at the same speed regardless of reference frame. Here, inside the bubble, we're in a different reference frame than we would be outside of it. The only physics we're invoking here is that light will travel at the same speed (the speed of light postulate). It should fall out mathematically.

We know that c = λf. f = 1/T where T is the period of time between each wave peak. So, the frequency is a function of time. Because we are changing time, and not the speed of light (by the speed of light postulate), that means:

c = λf = λT, and if we have a time dilation factor (in special relativity, we call it γ), that means c = λ(γT).

Already, we can see that our frequency f has shifted due to that γ factor. We don't have to know the mechanism for this simple math to work. This is basically the mathematical version of Timemaster's explanation.

This doesn't really work, because the Lorentz factor is a number defined by velocity.  It only comes into play when we're talking about time dilation caused specifically by differences in velocity.

I was simply calling any cadmium/bendalloy shift with the variable gamma. I could have called it any letter I want, because never did I use the word "Lorentz factor" or its mathematical definition. I used gamma because that would signify to the community of physicists that there is time dilation.

I could name it alpha, beta, zeta, epsilon, mu, B, n, box, heart, or cow. It's notation. I chose the most practical one.

[Timemaster11]

In both special and general relativity, the speed of light does not change in a local frame.  Thus, from the point of view of the allomancer, the light will be travelling the true speed of light.  (It is possible that to the outside observer the light in the bubble will be travelling at a different speed, which is fully allowed by General Relativity.  However, locally relativistic effects do not change the speed of light.)

[Chaos]

So I decided to tweet Brandon asking this, and he gave me a three tweet answer! Short version, yes to redshifts. Here's how it went.

EricLake: In M:AoL, will bendalloy's time dilation result in redshifting of light going in/out of the bubble? #weescience

BrandonSandrson: I've been working on the science of it. Basically, I've been treating it as a gravitational time dilation.

BrandonSandrson: But only focused inward, and equally, on those inside the bubble. It's making my brain hurt a bit, but I think I've got it working

BrandonSandrson: I think this means yes to a gravitational redshift. But...it gets wacky. Trying to decide just what it would do is tough.

[Eerongal]

I've been treating it as a gravitational time dilation.

Score one for eero's random assumptions.

[Chaos]

I'm not surprised the math's confusing him, though. He's very scientific, but at least from Writing Excuses, he isn't super math-inclined.

[happyman]

Heh.  He could always ask one of us to do it.  It'd be a nice break from the kinds of problems I do at work.  Unfortunately, the fully correct answer may be unworkable as a magic system, so some tweaking and handwaving may be in order.

[SOM1else]

can someone explain what a red shift is and why it would happen (try to explain it to me like I'm 5)

[Eerongal]

can someone explain what a red shift is and why it would happen (try to explain it to me like I'm 5)

I can do my best, though some others here may be able to explain it simpler than i.

I'm going to explain a doppler red shift, because it's probably a bit easier to wrap your mind around, if you ask me.

First off, all light moves in a wave, or an "up and down" motion. A red (or blue) shift occurs when an object is moving toward or away from you. This is because the objects speed in either direction influences HOW the light moves up and down. I.E. if it's moving towards you, the distance between the top of each wave is shorter. If it's moving away, it's longer. In effect, this either "crunches" or "expands" the size of the light's wave.

The visible color of the light is determined by the size of its wave. Because of this, the visible color changes when moving towards or away from you (note that it has to be at high speeds, someone walking or even driving the fastest vehicle is going to be so minute you cant see it)

Something very similar to this happens with area of high gravity. It causes the size of the wave to change.

The exact reasons for the redshift are what's been being debated in this thread, but brandon himself stated that he's treating it as if it were a gravitational redshift.

Clear as mud?

[PeterAhlstrom]

OK guys, help me out on this.

Let's take a bubble where time is sped up inside, maybe to 10x, maybe to 100x. I'm thinking that if there is no light source inside the bubble, but all light comes from the area outside the bubble, to an observer outside the bubble all light that goes inside and gets redshifted will get blueshifted back the same amount when it exits the bubble. So the outside observer won't see a color change at all. (I'm ignoring refraction for the purposes of this post, but someone else may elucidate.)

The person inside the bubble will see a redshift of all light coming into the bubble--but will also see far fewer photons per second, so the world will go dim or even black.

At low time-speedups, the person in the bubble will see UV light shifted into the visible range, so will start effectively seeing in UV. At very fast speeds he can see X rays or even gamma rays. (I don't know from Brandon what the max speedup is.)

If the person inside the bubble turns on a flashlight, this will be shifted into the UV or X-ray range when it leaves the bubble. You can fry everyone around you with deadly radiation this way.

When you have a bubble that slows time, the opposite happens. People inside can see in infrared or radio waves. And if they go slow enough, visible light from the outside is shifted into the X-ray or gamma-ray range and the person inside gets fried by radiation. If they turn on a flashlight, people outside get cooked.

Can anyone point out flaws in this analysis? Does anyone have magical suggestions for why any of these things wouldn't happen?

For practical reasons it looks like there will need to be a lot of handwavium burned.

[mycoltbug]

Peter, I don't know all the science behind it but I as for apart of the magic system I may be able to provide some ideas...

Brandon has always stated that the DNA of the beings on his planets are different and that is what allows them to use magic. Maybe the DNA change also makes them able to handle the negative effects of the light shift or that the bodies of them adapted from being so close to the sun during the lord rulers reign that it litterally forced an evolution, or even Sazed knowing all saw this potential and made a change in the human physiology to account for this. It is hinted that Sazed made some changes (at least from what I remember from when I was reading a few years ago.)

[happyman]

OK guys, help me out on this.

Let's take a bubble where time is sped up inside, maybe to 10x, maybe to 100x. I'm thinking that if there is no light source inside the bubble, but all light comes from the area outside the bubble, to an observer outside the bubble all light that goes inside and gets redshifted will get blueshifted back the same amount when it exits the bubble. So the outside observer won't see a color change at all. (I'm ignoring refraction for the purposes of this post, but someone else may elucidate.)

The person inside the bubble will see a redshift of all light coming into the bubble--but will also see far fewer photons per second, so the world will go dim or even black.

At low time-speedups, the person in the bubble will see UV light shifted into the visible range, so will start effectively seeing in UV. At very fast speeds he can see X rays or even gamma rays. (I don't know from Brandon what the max speedup is.)

If the person inside the bubble turns on a flashlight, this will be shifted into the UV or X-ray range when it leaves the bubble. You can fry everyone around you with deadly radiation this way.

When you have a bubble that slows time, the opposite happens. People inside can see in infrared or radio waves. And if they go slow enough, visible light from the outside is shifted into the X-ray or gamma-ray range and the person inside gets fried by radiation. If they turn on a flashlight, people outside get cooked.

Can anyone point out flaws in this analysis? Does anyone have magical suggestions for why any of these things wouldn't happen?

For practical reasons it looks like there will need to be a lot of handwavium burned.

Peter,

I think you've got it right in every major point.  And yes, I suspect that for practical reasons, the powers will have to be tweaked.  I suspect there would be refraction, but it's hard to say.  Gravitational redshifting is a mess, and as far as I know the only people who really learn it well enough to give a definitive answer are those who decided to study general relativity for a living.  Space bends as well, after all.  (Rather, space-time picks up a non-Minkowskian metric, but that's about as far as I can say anything without sounding like a complete newb to the real General Relativists.)

As for handwavium---I don't know, really.  Maybe the metals change the bodies so they can adapt to the odd light effects?  Maybe (for whatever reason) metal time-bending doesnt' affect light in the same way, but just affects matter?  (Brandon might not like that one, though, if it's meant to really grab time by its essence and push or pull.)  That's all I've got.

[Eerongal]

So the other day i ran across this and i think it may be slightly relevant to this discussion. Note that it's, obviously theoretical at this point, but the same sort of thinking could apply. What does everyone else think?

[mycoltbug]

It's a very very interesting concept to say the least.