Redshift?

[Zas678]

Hey! This comment is for you physicists out there (pointed look at Chaos).

Technically speaking, when someone uses Bendaloy/Cadmium, would there be a redshift/blueshift at the bubble, so everything outside the circle looks either redder or bluer depending on the metal, and vice versa for outside the circle?

I was just thinking about how light doesn't speed up or slow down, it just changes colors depending on the speed of the object.

[Ryan]

That probably depends on whether or not relativity holds in the Cosmere.

But, well, I'd hazard to say that yes, you're probably right. Light emitted inside the bubble would find its wavelength compressed or elongated by the different flow of time outside. Same for light entering from outside. The energy for this would have to come from the Allomancer, which begs the question: does Bendalloy burn faster on a sunny day?

[Zas678]

Or under really, really bright lights. I could see a criminal making sure to work in the dark to minimize the effects of the Bendalloy.

[Eerongal]

interesting thought.

I gave it a few moments of thought, and i see no reason why that WOULDN'T be the case, given our physical laws are still in effect, as ryan said.

If they are indeed using our physical laws, then, in theory, to slow time, then, the metals could instantly rocket the individuals to some large percentage the speed of light!

[Beligaronia]

I disagree.

Light would not be altered unless the allomancer was moving, in which case due to the great speed the light would be blue or red shifted according to the normal laws of physics.

However this still depends on the scale factor the metal produces. Working on a hypothetical 10 times faster or slower there would probably be little to no red shifting. Suppose that an Allomancer on a pewter enhanced horse (a Mustang Misting) travels at 10ms^-1. Then the allomancer burns metal slowing time by a factor of 10, the horse is now traveling at 100ms^-1, about the speed of a bullet. (for a large value of -ish.) This is still only a minuscule fraction of light speed so there would very little red/blue shift.

(The 10 comes from a desire to keep the misting effective but not at god level.)

When passing through the walls of the time bubble there is no change in media, no physical properties that would cause the light to alter. The supposed change in speed would actually be compensated for by the change in time scale. The light would still move at 3*10^8 ms^-1 but the seconds would be shorter from the perspective of the outside world thus there would be no alterations to the properties of the light. Since the observer can only be on one side of the bubble they will see no change in the light since it will, to them, always be travelling at the same speed since they can't see the time shift itself.

Then again I may be wrong.

[Ryan]

I don't think motion has anything to do with it in this case. That's just how we create relativistic time dilation in our universe.

Let me preface this by saying that I am no physicist. I've taken the basic university-level course and quite a lot of chemistry, but I'll be the first to admit that I don't really understand relativity.

That said, doppler shifts in our universe are observer-depenedent too. If you're moving at the same velocity as a high-speed emitter, you won't observe any shift. You're in the same relativistic, time-dilated frame of reference, so emitted radiation looks just fine to you.

Observers in slower frames with less time dilation see shifts. The photons take energy from their emitter's velocity relative to the observer, but instead of kinetic energy, it is expressed as electromagnetic energy, i.e. increased (or decreased) wavelength.

Now, an allomancer burning a bendalloy or cadmium would create a bubble of time-dilated space. I imagine this functions a lot like relativistic time dilation, especially with regards to electromagnetic radiation.

Now imagine what happens to a photon at the boundary. To an observer outside the bubble, it stands to reason that a photon would appear to have traveled from its source to the boundary faster than the speed of light, but this is not how light works; even when dealing with light emitted from relativistically time-dilated frames of reference, all observers observe the same velocity regardless of their frame. What changes is the wavelength observed.

I'm sure it has something to do with the concept of space-time, which is something I don't really understand. But if time and space are interrelated, then stretching time must also distort space. Take a photon emitted in stretched space-time and cram it into normal space-time, and it stands to reason that its wavelength is going to be compressed.

Can someone who understands the physics better confirm or refute this line of reasoning?

[Silus - Shard of Flame]

I was playing Mass Effect and I thought of something along these lines.

In Mass Effect, the key technology for FTL travel is Element Zero, or eezo, which, when charged with an electrical current, increases or decreases a mass of space-time, depending on the current.

I thought that this sounded a lot like Cadmium/Bendalloy.  So I thought, is this the same sort of thing?  Could you, even theoretically, use these metals to create faster than light travel?  Is this how space travel will work on Scadrial?  I would love for it to be this way.

I doubt will get more than a RAFO for a question like this.

[Eerongal]

time dilation AND redshifts are also caused by gravity, not just motion.

From what i was thinking, in order for relativistic time dilation to happen (given our world's physics, that is), the allomancer is going to have to manipulate gravitons, either increasing or decreasing their pull, which would also cause a red/blue shift, similar to, but not the same as, the previously mentioned doppler effect.

This is the reason our sun looks yellow/red, because the light escaping its extreme gravity causes a redshift.

The reason im assuming we have to use gravitational means for time dilation (again, given our real world physics) is because my previously comment of jest using speed instead of gravity for time dilation would likely be not an ideal thing to do.

Edit: While i'm at it, i'll write up a sort of simple "primer" on relativity to see if it helps break down the thinking and whats going on.

Ok, think of the simplest "Clock" we can come up with. It's essentially two mirrored plates with a single photon of light bouncing between them. Every full up and down movement is some known, measureable unit of time, say 1 millionth of a second.

so every second, that photon moves up and down 1 million times. Said clock is perfectly accurate because the photon always moves back and forth at the same angle and the same speed.

so to draw it, we have something like this:

| .   |

where the two pipes are the surfaces, and the period is the photon. That photon is constantly moving back and forth.

Now, imagine if you will, two different people looking at this clock.

Observer A is sitting perfectly "still", that is, he isnt moving (at least from our perspective for this exercise)

Observer B, however, has the clock in his possession, and is moving PAST observer A, lets say on a train, or a space ship or something.

So assuming Observer A's viewpoint, I'm going to draw the movement of this photon. I'll only draw the surfaces when it hits.

|.

 .

  .

   .

    .|

Notice this creates essentially what is a diagonal line. This distance, however, is much LONGER than the distance if the photon simply moved up and down, because of the combination of the horizontal and vertical distance.

However, when it comes to observer B, this distance is NOT diagonal, which is hard to draw here, but would look kinda like this:

|.....|

This is because for observer B, the photon only needs to move one direction, creating a line straight in either horizontal OR vertical, not both.

Because of this, and because the speed of light is constant, meaning it has to hit these plates at exactly the same time for BOTH observers, and has a longer distance to go for one, this creates a time dilation, this is also the basic essence of relativity in as simple terms as i can think to explain it. EVERYTHING has to do with your frame of reference. Such as who is moving. For example, two astronauts in space, drifting randomly with no frame of reference. If they move past each other, to each one, only the OTHER one appears to be moving, while the one observing appears to be stationary without a reference.

This is what causes both time dilation AND redshift.

The blue/redshift happens because the wavelength of the light does NOT change, it moves up and down in its normal wave at its normal speed. However, when it moves diagonally to you (like observer , the wavelengths are observationally lengthened/shortened, causing the visible light it gives off to alter.

This very same time dilation and color shift is also caused by strong gravitational pulls

Does this help in any way those who don't really know much about relativity? I'm not a master of it, but i have taken advanced physics courses, and i understand it to some extent.

yet another edit:

Just a further note - If you really think about it, it makes sense, but its so out of proportion with how we are used to thinking it seems almost like a concept from sci-fi. Technically these things do affect us on a daily basis, but their effects are so minute, we can't tell.

To quote douglas adams:

"The fact that we live at the bottom of a deep gravity well, on the surface of a gas covered planet going around a nuclear fireball 90 million miles away and think this to be normal is obviously some indication of how skewed our perspective tends to be."

[Chaos]

I feel snarky, so I would like to bring up that in classical optics, an index of refraction can change the speed of light. c is the speed of light in a vacuum, not necessarily other mediums. I don't know how to exactly reconcile this with special relativity, however.

Anyways, on with the discussion of relativity.

I would like to note that I have not taken the 500 level General Relativity class here at MSU, because that has two 500 level prerequisites. So I don't know the math behind it. I do know it is extremely complicated

Hmmm, I actually know a physics grad student who loves Mistborn. I should link him into this discussion, because he is in General Relativity.

(A side note, there's a reason why one is "special" relativity and the other is "general" relativity. Special relativity came first, and it only works because the reference frames are moving at a constant velocity. Special relativity is very well tested and is essentially science fact at this point. General relativity is Einstein's method of generalizing SR to accelerating reference frames. There are other theories than GR, but GR works really well, so any alternative theory would need to return GR)

time dilation AND redshifts are also caused by gravity, not just motion.

I guess you could frame it like that. It's really because objects have mass, and that leads to a gravitational attraction. That means there's an acceleration, and it's that non-inertial reference frame of acceleration which creates the relativistic effects.

It's important to note that Eero's intro to relativity is special relativity. I guarantee you GR is much, much more complicated.

the allomancer is going to have to manipulate gravitons, either increasing or decreasing their pull, which would also cause a red/blue shift, similar to, but not the same as, the previously mentioned doppler effect.

Let's leave gravitons out of this

Okay, my gut reaction is that yes, we will see a shift in light's frequency. Beligaronia is kind of right, but there would actually be a large redshift for any large change in time.

Let's say that we're using Cadmium, so inside the bubble, time is moving slower. That means time outside is moving faster. So, let's call the time in the bubble the proper time. We get a super simple expression for the relationship between the time inside and outside:

t' = 2 * t

Where I'm calling t the proper time (inside the bubble), because that's a smart reference frame. Now, that factor of 2 is called a Lorentz factor by special relativity. It pops up all over the place, and it is made by a velocity of moving reference frames. I did some quick math, and a Lorentz factor of 2 means that the reference frame, by special relativity, is moving at .866c. That's... really fast.

If we can liken this example to special relativity, then yes, there will be a heck of a shift in light's frequency, both ways.

I suppose we could talk some GR here, but I don't think we need to go into that case. In order for time to dilate by a factor of two, we can make an easy conclusion: there's a lot of relativistic effects going on. This implies there will be doppler shifts from this effect.

(Short version: Ryan's physics is sound)

We run into some problems when an Allomancer flares metals a little, since that "acceleration" in burn rate will lead to some non-inertial analogs, but if we have an Allomancer burning at a constant rate, special relativity works perfectly fine. If I know the factor of time changing, then I can find the speed parameter Beta, which I can throw into an equation to calculate our shift of light's frequency, too.

So for all the talk about warped space time, my response is "shut up and calculate"

EDIT: I looked at some texts. The index of refraction has nothing to do with special relativity, because in that medium, there still can't be any signal which goes faster than light in that medium. Problem solved. Sometimes, doing high level physics (though SR isn't that mathy) makes you forget the easy stuff.

[Timemaster11]

Even if the person were standing still, light would still be severely redshifted or blueshifted.

To see this, imagine light as a wave, and imagine that 1 wave peak crosses the bubble boundary every second.  (Really low energy light)

Also, say that the light is aimed at the allomancer's eye.

In order to prevent a pileup of wave peaks, from the perspective of a person outside the bubble, the number of wave peaks crossing the bubble and the number entering the eye have to be the same for any given stretch of outside time.  The same holds for inside time.

Say time is 10 times faster/slower in the bubble.  Then the person in the bubble would say that either .1 wave peaks entered the bubble every second, or 10 peaks entered the bubble every second.  Thus, for them, either .1 or 10 wave peaks would enter their eye every second, so the frequency would be shifted by a factor of 10.

Thus, for a nonmoving allomancer in the bubble, the time dilation/speed up factor would equal the factor by which light was redshifted or blueshifted.  (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.)

(On a side note, in all actuality Special Relativity can deal with acceleration.  (Through Momentarily Co-moving Reference Frames.)  It just cannot deal with curvature of spacetime due to gravity.  (My physics professor for general relativity made it a point to stress this on more than one occasion.)

(Also, the requirement that the amount of wave peaks passing into a surface must equal the amount leaving the surface -- equal flux in and out -- should hold true also in SR and GR.  Plus, at the end of the day, when the bubble was collapsed, the person inside the bubble would have to agree with the person outside the bubble on how many wave peaks reached him.)

[Chaos]

(On a side note, in all actuality Special Relativity can deal with acceleration.  (Through Momentarily Co-moving Reference Frames.)  It just cannot deal with curvature of spacetime due to gravity.  (My physics professor for general relativity made it a point to stress this on more than one occasion.)

Well, Jeremy, you would know that much more than I would, that's for sure.

But you know what's awesome? If you're the bubble, and you see infared light. Heat vision practically for free.

Now I'm going to be a little upset if Brandon didn't think of having a redshift, because that's just too cool.

[Ryan]

(Short version: Ryan's physics is sound)

I actually find that somewhat surprising. ;D

(I was trying to cast it into an energy balance problem. This is the half-trained chemical engineer in me talking; chem-e's always try to make everything an energy (or mass) balance problem, because those are relatively straightforward to solve.)

[Finallity]

Also, if one allomancer burned cadmium, and another bendalloy (at an equal rate) while standing twenty feet from each other, each creating a bubble with a fifteen foot radius, would the overlap cancel out the time change? In application, you could use that to comabat the effects.

That or it'd be a purple bubble, and break the space time continuum.   :'(  I wuv'd that continuum.

[Zas678]

Also, if one allomancer burned cadmium, and another bendalloy (at an equal rate) while standing twenty feet from each other, each creating a bubble with a fifteen foot radius, would the overlap cancel out the time change? In application, you could use that to comabat the effects.

That or it'd be a purple bubble, and break the space time continuum.  :'(  I wuv'd that continuum.

It'll be the Duraluminum Atium of the second series.

Plus, at the end of the day, when the bubble was collapsed, the person inside the bubble would have to agree with the person outside the bubble on how many wave peaks reached him.

I can imagine. After a huge allomancer fight, both sides meet together.

Criminal-"I got 1.32*10^20 waves. How about you?"

Police-"I only got 1.31*10^20!"

Criminal-"Did you account for the reflected light off the pavement?"

Police-"Ahh. That would do it."

[Chaos]

Also, if one allomancer burned cadmium, and another bendalloy (at an equal rate) while standing twenty feet from each other, each creating a bubble with a fifteen foot radius, would the overlap cancel out the time change? In application, you could use that to comabat the effects.

That or it'd be a purple bubble, and break the space time continuum.   :'(  I wuv'd that continuum.

There'd still be a horizon where you would get redshifts.

[happyman]

I was going to weigh in, but Timemaster11 made the most important points for me.  I endorse his explanation.

I would add to his addendum that Special Relativity *can* handle acceleration quite simply, but it does require an extra postulate beyond the famous two, known as the Clock Postulate, which states that you can treat an accelerating system as having an infinite series of constant velocities for infinitesimally short times, with no other side effects.  This postulate has been confirmed experimentally many, many times and the techniques to handle acceleration in Special Relativity are used all the time by particle physicists.

Also, I would say that the behavior of Cadmium and Bendalloy as described by Brandon are much more like gravity in general relativity than velocity in special relativity, and finding a corresponding velocity to special relativity doesn't mean much.  The fact that Timemaster11's explanation is independent of mechanism is it's best feature, by far!

[Guest Alisto]

I'm going to go against the consensus and say that there would be no red/blueshifting.  To state the obvious, redshifting is caused by two things: the Doppler Effect and gravitational effects.  (There's also expansion of space-time, but that's irrelevant here) 

Gravity: In the case of a black hole, which is what probably comes to mind when most people first approach this topic, time dilation and redshifting are separate effects caused by gravity.  Time dilation itself does not cause the redshifting.  Since there are no gravitational differences between people inside and outside of the bubble, we get no shifting.

Doppler Effect: While this could cause some shifting, the effect probably wouldn't even be noticeable.  Let's say that someone burns Bendalloy and as a result speeds up time around them.  They run directly at someone standing still outside of the bubble.  They would appear to be moving quickly and they would, to the person outside, appear blueshifted.  But for the effect to be noticable... well, let's do math.

z = v/c.  (z is shift, v is velocity, c is speed of light) Let's say that the Allomancer is effectively moving at... oh, 5000 mph.  Well the speed of light converts to 670,616,629 mph.  So z = 0.000007.

What does that mean?  z is the percentage of increase (or decrease) of wavelength.  In this case, the wavelength will increase 0.0007%  Not exactly turning someone's yellow shirt green.

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.

Honestly, the more important question is what would happen to objects passing through the bubble.  If the bubble has a hard boundry, a bullet passing through would destroy itself.  It would either be ripped apart as it entered a region of faster time or compress/obliterate itself when moving a region of slow time.  And a person passing that boundry?  Well, that could get messy.  So really, I guess we'll just have to say, "It's magic!" and enjoy the book.  ;D

[Eerongal]

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)

[trendkill]

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)

I assume you mean KM/h, right?

[Eerongal]

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)

I assume you mean KM/h, right?

Psh. Nope. When you go 5,000 KM total, ever, you instantly get a permanent redshift.

(yes )

[trendkill]

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)

I assume you mean KM/h, right?

Psh. Nope. When you go 5,000 KM total, ever, you instantly get a permanent redshift.

(yes )

So if I go say... 10,000 KM, does that double the redshift?

[Chaos]

I was going to weigh in, but Timemaster11 made the most important points for me.  I endorse his explanation.

I would add to his addendum that Special Relativity *can* handle acceleration quite simply, but it does require an extra postulate beyond the famous two, known as the Clock Postulate, which states that you can treat an accelerating system as having an infinite series of constant velocities for infinitesimally short times, with no other side effects.  This postulate has been confirmed experimentally many, many times and the techniques to handle acceleration in Special Relativity are used all the time by particle physicists.

Also, I would say that the behavior of Cadmium and Bendalloy as described by Brandon are much more like gravity in general relativity than velocity in special relativity, and finding a corresponding velocity to special relativity doesn't mean much.  The fact that Timemaster11's explanation is independent of mechanism is it's best feature, by far!

I had a good discussion with Timemaster about accelerations in SR, which I certainly didn't know before. Good deal.

I'm wondering if we ran a time factor of two into SR, would GR return the same values for a predicted redshift?

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.

Honestly, the more important question is what would happen to objects passing through the bubble.  If the bubble has a hard boundry, a bullet passing through would destroy itself.  It would either be ripped apart as it entered a region of faster time or compress/obliterate itself when moving a region of slow time.  And a person passing that boundry?  Well, that could get messy.  So really, I guess we'll just have to say, "It's magic!" and enjoy the book.  ;D

Well, Brandon has said that it's not a hard boundary.

And sheesh, when has "it's magic" stopped us before

[Guest Alisto]

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.

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.

More random thoughts:

-Assuming an Earthlike planet, the surface of the planet could be rotating as fast as 95,000 mph.  If you affected time in a bubble, wouldn't everything in that bubble end up moving relative to the planet?  I mean, if you're moving at 95,000 mph relative to the center of the planet, but now all of a sudden you've messed with time your momentum would throw you in all kinds of unpleasant directions at pretty dramatic speeds.

-Even with a soft boundary to the bubble, how do you avoid compression or spaghettification when passing through it?

-What if someone is right on the boundary as you create the bubble?  Part of their body would be moving through time faster than the other parts.  That would likely not do good things for blood flow.

Sorry if these things have been discussed on TWG already, but with the forums down (and I was avoiding WoK spoilers), I haven't been over there lately.

[Emeralis00]

What if someone is right on the boundary as you create the bubble?  Part of their body would be moving through time faster than the other parts.  That would likely not do good things for blood flow.

or your brain...

[Eerongal]

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?