Interstellar -the movie, planet with slower time

[Bob__]

Referring to all the people who have watched the movie, i got a question.
It is about one of the planets where time passes drastically slower (1 hour on the surface is 7 Earth years )
due to gravitational time dilatation.
Earth moves together with the sun with speed of circa 500 km/s trough space, so relativistic time does not differ very much from the rest of the universe.
standing on the surface of that planet means that people would observe the rest of the "normal" universe move circa 61320 times faster then standing on earth.
Because time runs slower on the planet, and the speed of light is universal regardless from which perspective it is observed, according to Einstein's theory of relativity. Any radiation ray that 's hitting the surface would have it's frequency increased 61320 times, and even the background radiation would turn into ionizing x-ray radiation, not speaking about the surrounding stars, or the black hole's radiation belt that is producing the light in that solar system.
Watching from "earth's perspective", it means that everything would move 61320 times slower on the surface of that planet , meaning physical processes such as heat distribution and thermal cooling would be 61320 times slower, so the anything on the surface of the planet would have no time to cool down from the energy that the universe is shining on it.

So the planet would be superheated plasma world, or at least the visuals would differ significantly (the sky would be more bright , the stars would be brighter and bluish...)
Or I am somewhere wrong?

 

[Matterwave]

Discussion of movie physics belongs in the Sci-fi forum. In fact, there is a thread in that forum already discussing this movie. :)

 

[Algr]

But that thread is so full of other stuff that another thread based on specifics might be warranted. I was thinking about a thread about the blight on Earth. Could environmental destruction really get so bad that we would have to leave the planet to survive?

Re Bob: It looks like the black hole has very uneven light projection - so two planets at the same distance might receive very different abouts of light from gargantua. That plus the clouds and an ionosphere could result in what we saw - but there would be no night on that world.

Also, given the size of Gargantua, it would probably take many centuries or millennia for a planet to orbit it. It would be like the sun orbiting the milky way.

 

[vemvare]

Except any object with such a significant time-dilation can be considered (from a non-rotating rest frame) to be moving at c, and, given that the event horizon of a black hole scales linearly with its mass, it really doesn't have to be a very long orbital period. At all.

100M solar masses = something like 300Mkm diameter, and from an outsiders perspective completing a close orbit around it should take something like 3140s, which in the perspective of the rotating object, like the water planet with a time dilation factor of 60 000 would be 0,052s? I might be screwing up my rest-frames.

 

[Algr]

That can't be right. Nothing with mass can move at C.

 

[DaveC426913]

That can't be right. Nothing with mass can move at C.

True.

It is moving at 0.9999999999 of the speed of light.

I'll hand wave it.Realtivity calculator:
http://www.1728.org/reltivty.htm
In the input field enter a number, then click [c=1].
Try numbers until the dilation factor reaches 61,000.

 

[QuantumPion]

According to Kip Thorne's book the orbital period of Miller's planet would have been around 1 hour. As for how the outside universe would appear from nearby or on surface, I don't know.

 

[Ken G]

It does sound reasonable that a dilation factor of 61,000 would turn 2.7 K background radiation into some 165,000 K ionizing radiation. I don't think it would be over much of the sky though-- seems to me the light rays would get very focused, so you'd just see a very bright blue spot in the sky, but the spot might be rather small. I don't know how to calculate how much flux it would be. It is all part of the general problem that people have pointed out-- that planet would be getting hit by all kinds of very energetic particles, hanging out near a black hole should not be terribly healthy. Putting the habitable planet near the black hole was really just a plot device to simplify the narrative-- it seems more likely that if the situation was at all plausible, the habitable planet would have been somewhere totally different. But you have to admit, the idea of exploring different planets in close proximity to a black hole offered a lot of pretty cool possibilities for action and suspense.

 

[Pete Cortez]

It does sound reasonable that a dilation factor of 61,000 would turn 2.7 K background radiation into some 165,000 K ionizing radiation.

Since local spacetime is more or less getting dragged around with you, you should expect your measurement of local background radiation to remain more or less the same.

 

[Ken G]

Since local spacetime is more or less getting dragged around with you, you should expect your measurement of local background radiation to remain more or less the same.

Well I've been wondering about this, I guess there's no guarantee you'll get the 61,000 factor after all, because if you are falling into a nonspinning black hole, you shouldn't see blueshifted CMB that is falling in with you. But here you are not falling in, you are orbiting, so you have to be doing something more than just falling with the space, there has to be some Lorentz shifting going on there. So I think the CMB would be blueshifted in some rather beamed directions, I would imagine, but I'm not sure by what factor or over how much of the sky.

 

[phinds]

...
Earth moves together with the sun with speed of circa 500 km/s trough space, so relativistic time does not differ very much from the rest of the universe...

Just to be sure you are aware of it, you make that statement as though "moving through space" has some absolute meaning. It does not. All motion is relative and "space" is not something you can move relative to, it's just a framework in which things move relative to each other. I have no idea what the figure you mention represents, unless it is a gross approximation of the speed of the solar system relative to the CMB, which is 371km/s

Also, as a VERY minor aside, the term "circa" is normally only applied to dates, not speeds.

 

[AngelLestat]

Some data to help you in your math. Good question, I have some doubts too.

Millers planets moves at 0,55c at 1,5 Au from event horizon because is a very fast spinning black hole of 100 million sun mass (event horizon radius 1Au).
It has a time dilation of 1 hour equals to 7 years at earth.

This mean that seeing from the endurance, miller´s orbit gargantua in 1,7 hours, now from miller´s planet surface point of view, gargantua horizon seems frozen in time but if we look towards the endurance seems that miller´s is orbiting gargantua 10 times by second.

So what happens with all the falling matter and the blueshifted effect. Not sure.

 

[Pete Cortez]

Well I've been wondering about this, I guess there's no guarantee you'll get the 61,000 factor after all, because if you are falling into a nonspinning black hole, you shouldn't see blueshifted CMB that is falling in with you. But here you are not falling in, you are orbiting, so you have to be doing something more than just falling with the space, there has to be some Lorentz shifting going on there.

If you're orbiting relativistically, there's frame dragging, and incident radiation is subject to it as well.

 

[Ken G]

But an observer that is falling into the black hole, not orbiting it, will be moving at a very large speed relative to you, so they will see a rather different CMB than you will. In other words, if all your motion is due to frame dragging, you would fall into the black hole. To be orbiting, you need an additional relativistic motion to keep you from falling in, and that will blueshift the CMB seen over some narrow patch of the sky.

 

[AngelLestat]

:( I dint understand what pete cortez and kenG said.

For example the remaining of the accretion disk which has similar temperature than the sun´s surface in current "cooling process?", it has a time dilation of 2.400.000 vs 61000 from miller´s planet.

If miller´s planet receives the heat from this "hot disk", I can understand that this hot disk will remain like that for a really long time due to time dilation, so is able to heat miller´s planet much longer... But it seems a contradictions from the energy conservation perspective. How can the same hot disk provide more heat for longest periods of time? If in its own timeline the colling process takes the same time?

My english is not so good.. Sorry.

 

[Oysteroid]

[QUOTE="phinds, post: 4932100, member: 310841"All motion is relative and "space" is not something you can move relative to, it's just a framework in which things move relative to each other. I have no idea what the figure you mention represents, unless it is a gross approximation of the speed of the solar system relative to the CMB, which is 371km/s.[/QUOTE]

Given that CMB is connected to the origins of the Universe and the fact that you can determine speed relative to it, do you think there could be a possibility that it defines a special frame which we could treat as "space"?

Please understand what I'm driving at here: the GRT <i>posits</i> the absence of such a unique and special frame and proceeds to build a verifiable/falsifiable theory from that premise. That's all fine and dandy, but with the CMB, we seemingly have a phenomenon (directly linked to the Big Bang, no less!) that seems to contradict that premise. What gives?

 

[Ken G]

Yes, I've thought about that too. I think it depends on what we mean by a "preferred" frame. GR does not say there are no frames that offer special insights to us, like the CMB frame, it just says that physics has to work the same in all frames. So we are not forced to use the CMB frame, even if we have plenty of good reason to use it. Maybe someday we will find that the CMB frame is different, and the laws require that frame, but so far, the laws don't-- that frame is made special just by the initial conditions.

 

[AngelLestat]

About my question? Somebody knows the answer?
I'll rephrase the question:

If we have a laser emitting 1 TW by second close to a black hole with a time dilation of 2400000 (accrettion disk), then a receiver far from the black hole (no time dilation) will get 1 TW / 2400000 by second?
Because in other case will be violating the energy conservation in my opinion.

If that is correct, how the accretion disk may be enoght to heat the planets? Because is huge?

 

[phinds]

About my question? Somebody knows the answer?
I'll rephrase the question:

If we have a laser emitting 1 TW by second close to a black hole with a time dilation of 2400000 (accrettion disk), then a receiver far from the black hole (no time dilation) will get 1 TW / 2400000 by second?
Because in other case will be violating the energy conservation in my opinion.

If that is correct, how the accretion disk may be enoght to heat the planets? Because is huge?

I don't understand your question, but I did want to point out to you that your statement

receiver far from the black hole (no time dilation)

makes no sense. EVERYTHING is time dilated, it just depends on your frame of reference. You, right now as you read this, are MASSIVELY time dilated according to a particle in the CERN accelerator.

 

[AngelLestat]

Ok, what I want to said:

If we have a laser close to a black hole sending 1 TW by second, how much energy will get a receiver by second far away from the black hole if the laser not spread?

The time dilation between these 2 is 2400000, happy?

 

[Ken G]

About my question? Somebody knows the answer?
I'll rephrase the question:

If we have a laser emitting 1 TW by second close to a black hole with a time dilation of 2400000 (accrettion disk), then a receiver far from the black hole (no time dilation) will get 1 TW / 2400000 by second?
Because in other case will be violating the energy conservation in my opinion.

If that is correct, how the accretion disk may be enoght to heat the planets? Because is huge?

I see what you're asking, you are wondering why the redshifting of the light from the accretion disk as it rises out of the gravitational well of the black hole does not make it too cold to heat the planet. But we see accretion disks around supermassive black holes, sometimes from halfway across the universe (quasars). So the real problem is not that the accretion disk couldn't warm the planet, it is that it would fry the planet. But perhaps there are black holes we don't see because their accretion disks are much weaker, and that is what they are imagining.

Still, your question raises what I think is an error that I have wondered about also-- as I recall, Miller's planet is depicted as looking down on the accretion disk from a large distance away, yet its time dilation relative to us implies it should be close to the event horizon. That would put it inside most of the accretion disk, not outside it, it seems to me.

 

[AngelLestat]

Not, the accretion disk is closer to the event horizon than miller´s planet.
Accretion disk has a time dilation with respect to Earth of 2400000
Miller´s planet has a time dilation with respect to Earth of 61000

This mean that the accretion disk has a time dilation with respect to miller´s planet of (2400000/61000)= 40 aprox.

In the book it said that is a remainder of a old accretion disk in cooling process, which temperature is close to the sun surface, for that reason astronauts can see it at naked eye without radiation risk.

About my question not sure if you answered, so you said that we lost that energy in a redshift change.
So back to the laser example, if emit 1 Tw by second, this mean that the receiver (tune it for that frequency which is red shifted) will get only 1 TW / 2400000 by second?
So energy conservation applied this way?

 

[Ken G]

Not, the accretion disk is closer to the event horizon than miller´s planet.
Accretion disk has a time dilation with respect to Earth of 2400000
Miller´s planet has a time dilation with respect to Earth of 61000

An accretion disk does not usually have a single time dilation, that's why it's a "disk"-- it extends over a range of radii down to the last stable orbit. So even if the last stable orbit has a time dilation of 240000, there should be a lot of material in that disk with less time dilation, and much of it should be outside Miller's planet (the mass has to come from somewhere).

This mean that the accretion disk has a time dilation with respect to miller´s planet of (2400000/61000)= 40 aprox.

Yes, for that last bit of accreting material. But just for the sake of argument, let's imagine that this disk is in a transient state where all the mass in the disk is at that same time dilation, and maybe it can last that way for a long time (because of the time dilation itself). Then you are asking, why doesn't it badly redshift, by a factor of 40? Maybe it does-- the temperature of that gas would be highly relativistic, it should be radiating in the x-rays if not the gamma-rays if not for the redshift.

In the book it said that is a remainder of a old accretion disk in cooling process, which temperature is close to the sun surface, for that reason astronauts can see it at naked eye without radiation risk.

OK, so it does sound like they are imagining some transient state for the disk, for some reason all mass feeding to the disk has turned off and we are just watching the final embers of the disk fall into Gargantua. In that case, their meaning that it glows in the visible must include the redshift you talk about. Unfortunately, that would only work for Miller's planet-- on Mann's planet, and the planet they eventually decide to settle, the redshift would be much worse, and it would not serve to warm those planets too. Dramatic license, they wanted more than one planet to be potentially habitable, but it just doesn't work.

About my question not sure if you answered, so you said that we lost that energy in a redshift change.
So back to the laser example, if emit 1 Tw by second, this mean that the receiver (tune it for that frequency which is red shifted) will get only 1 TW / 2400000 by second?
So energy conservation applied this way?

I don't think the power shifts by a single power of the time dilation factor, because you have both the redshifting and the time dilation. In other words, a distant observer thinks that photons are being emitted at a slower rate, and they are also lower energy photons, so the power should scale like the square of the time dilation factor-- making the problem even worse. This is further complicated by the Doppler shift due to the orbit of the accretion disk-- they left that out, I'm not sure why. (It seems to me the orbiting disk would show Doppler shifts on opposite sides, even for a rapidly spinning black hole, but perhaps I'm wrong about that-- they were very proud of the visual appearance of the disk.) But note the power can be whatever you want at anyone planet, because the disk could have any temperature you need in its own frame, but the real problem is getting it to work for more than just one planet.

 

[AngelLestat]

Yeah about the time dilation differences between the disk.. I knew it, There are just things that I want to avoid to not complicate the question.

So light comming from far from the black hole to mille´s planet is blue shifted? This mean that they gain energy? Or is just about time frames, and when the light reach miller´s planet seems normal?

All this seems logic about the red/blue shift and energy conservation. But is weird that Kip Thorne never mention this issue in his book. So I wonder if we are right.

Also when other physicists talk about what it will happen when we cross the event horizon, they never said death due blue shift radiation.

 

[Ken G]

Yes, the issue is whether the huge spin of the black hole is changing everything. Certainly there is frame dragging, but it still seems to me that gas, to be in orbit, must have a very significant Doppler shift, relative to something that is falling in, or relative to something that is in orbit farther out. But the disk is never depicted as Doppler shifted, so perhaps Kip Thorne knows something about spinning black holes that I do not, which was alluded to by Pete Cortez. It also seems like it would be very hot when you got into its frame, so the light from the accretion disk should fry anyone falling into the black hole, if it can keep Miller's planet warm. It's hard to tell if these are science mistakes that were left in because the story required it, or if Kip Thorne would have some answer to them. He certainly could be forgiven for saying that there were just some things the director wanted to happen, so he had to fit the science in around that the best he could.

 

[Matterwave]

Yes, the issue is whether the huge spin of the black hole is changing everything. Certainly there is frame dragging, but it still seems to me that gas, to be in orbit, must have a very significant Doppler shift, relative to something that is falling in, or relative to something that is in orbit farther out. But the disk is never depicted as Doppler shifted, so perhaps Kip Thorne knows something about spinning black holes that I do not, which was alluded to by Pete Cortez. It also seems like it would be very hot when you got into its frame, so the light from the accretion disk should fry anyone falling into the black hole, if it can keep Miller's planet warm. It's hard to tell if these are science mistakes that were left in because the story required it, or if Kip Thorne would have some answer to them. He certainly could be forgiven for saying that there were just some things the director wanted to happen, so he had to fit the science in around that the best he could.

Kip mentions in his book that the relative doppler shifting between the two sides of the accretion disk was left out in order to not confuse the audience (i.e. why is one side blue and the other side red?).

 

[Ken G]

OK, that helps, though it's a bit distressing-- seems to me the great feature of that movie was avoiding "dumbing down the physics" just so that audiences would not be confused. I liked that it treated them like they could handle the truth! After all, it is the first movie to ever include time dilation, but simple Doppler shifting would confuse the audience?

 

[tionis]

The companion book is very revealing. Director Nolan was pretty much in charge of everything with a major case of 'My way or the highway' attitude. Kip stood no chance of realizing his true vision for the movie.

 

[AngelLestat]

So the red/blue shift is not so big?

Kip throne change in some cases things that Nolan want it in his movie, one of this things was faster than the speed of light, thorne said.. forget it.. that would not happen. Then nolan has to change the script.
Kip Thorne was the executive producer of the movie, I guess is the first time that a real scientific has an important role in a movie.

One thing that I don't understand very well, why accretions disk are so flat?
This is due how matter fall, or by the black hole spin?
If its due the spin, what happen with things that are falling from a different direction or they have different orbit.

 

[Ken G]

One thing that I don't understand very well, why accretions disk are so flat?

They aren't always, but in cases where you have a thin disk, it is because the temperature is low compared to the orbital kinetic energy. There is a lot of dissipation that removes heat, but it cannot remove angular momentum as easily, so it tends to come close to the minimum orbital energy for a given amount of angular momentum-- that amounts to a thin disk and a relatively lower temperature than you might expect in a relativistic flow.

 

[Pete Cortez]

The companion book is very revealing. Director Nolan was pretty much in charge of everything with a major case of 'My way or the highway' attitude. Kip stood no chance of realizing his true vision for the movie.

You must have read the wrong book.

 

[tionis]

I beg to disagree, Pete Cortez. Kip's discontentment and frustration with Nolan and how he handled the science of Interstellar is palpable throughout the book * (I'm on page 163). You just have to read between the lines. Kip soon realized what he was getting into when Chris took over, but being the humble man that he is, preferred to collaborate rather than bicker with Nolan. Either way, I'm glad Kip is setting the record straight.

*
'' That shook me up a bit'' (page 9)
''Chris backed off'' (page 9)
''I was shocked" (page 59)
''It is non-negotiable,'' Chris insisted.'' (page 59)
''Christopher Nolan knew that Brand's argument was wrong'' (page 100)
''For me, Chris's decision was painful'' (page 151)

 

[Matterwave]

OK, that helps, though it's a bit distressing-- seems to me the great feature of that movie was avoiding "dumbing down the physics" just so that audiences would not be confused. I liked that it treated them like they could handle the truth! After all, it is the first movie to ever include time dilation, but simple Doppler shifting would confuse the audience?

There are a few other instances of "we don't want to confuse the audience" or artistic license as discussed in the companion book. Gargantua looks far too small from Miller's planet as well as far too small from Endurance in it's parking orbit, it should have taken up roughly half the sky of Miller's planet (or the entire sky if you were on the face of the planet facing it), and about 50 degrees arc from Endurance, but having such a dramatic visual effect so early on in the movie would have spoiled the climax, so Nolan reduced the size of Gargantua in both cases. The accretion disk should have been farther out than Miller's planet, because Miller's planet occupies basically the inner most stable orbit possible. The only orbits possible below Miller's planet are unstable, critical orbits, or photon orbits. But it would look weird to be "inside the accretion disk", so it was not shown as such. Lastly, they slowed down the spin of Gargantua significantly, from something like 99.999999999999% maximum to 60% maximum because the spinning would have made the black hole appear too lopsided - the lensing effects would have been too different between the two sides of Gargantua and they feared that would have also confused the audience.

Disclaimer: I agree with all of the dramatic changes that Nolan made, e.g. the shrinking of Gargantua. If the climax of your movie is falling into the black hole, you can't have them basically fall in halfway through the beginning of the movie lol. I think they should have kept the Doppler shifting and the lopsided black hole though.

 

[Ken G]

I agree-- I never mind artistic and dramatic license, this is a movie after all. But let the reason be that there is some effect they are shooting for, or some dramatic episode, not simply that they didn't think the audience would get it. These kinds of things set the bar-- the next time we see a black hole, it will have to look like Gargantua, so let's get what we can right! Until eventually a movie comes along with the courage to show a Doppler shift, and who knows when that will be.

 

[Pete Cortez]

I beg to disagree, Pete Cortez. Kip's discontentment and frustration with Nolan and how he handled the science of Interstellar is palpable throughout the book * (I'm on page 163).

Again, we must have read different books.

You just have to read between the lines.

No, I don't. I don't have an inexplicable axe to grind that would require me to do so.

Kip soon realized what he was getting into when Chris took over, but being the humble man that he is, preferred to collaborate rather than bicker with Nolan. Either way, I'm glad Kip is setting the record straight.

Considering Kip and Nolan bickered over several points, and won every single one except one, you're wrong on both points. In any case:

You:

That shook me up a bit'' (page 9)

Thorne:

"In that first meeting, I laid on Chris my proposed science guidelines: Nothing will violate firmly established laws of physics; speculations will all spring from science. He seemed positively inclined, but told me that if I didn’t like what he did with the science, I didn’t have to defend him in public. That shook me up a bit. But with the movie now in postproduction, I’m impressed how well he followed those guidelines, while making sure they didn’t get in the way of making a great movie.”

You:

''Chris backed off'' (page 9)

Thorne:

“Chris’s ideas occasionally seemed to violate my guidelines but, amazingly, I almost always found a way to make them work, scientifically. Only once did I fail miserably. In response, after several discussions over a two-week period, Chris backed off and took that bit of the film in another direction.”

This, by the way, is in reference to Nolan and Thorne's two week argument on faster-than-light travel. Nolan conceded.You:

'I was shocked" (page 59)
''It is non-negotiable,'' Chris insisted.'' (page 59)

Thorne:

“When Christopher Nolan told me how much slowing of time he wanted on Miller’s planet, one hour there is seven years back on Earth, I was shocked. I didn’t think that possible and I told Chris so. “It’s non-negotiable,” Chris insisted. So, not for the first time and also not the last, I went home, thought about it, did some calculations with Einstein’s relativistic equations, and found a way.”

And let's face it. Nolan was right. The diversion to MIller's planet is a critical component for pacing the plot.

You:

'Christopher Nolan knew that Brand's argument was wrong'' (page 100)

Thorne:

“This is one of the few spots in Interstellar where the characters get the science wrong. Christopher Nolan knew that Brand’s argument was wrong, but he chose to retain these lines from Jonah’s draft of the screenplay. No scientist has perfect judgment.”

Nolan's job isn't to give you characters who are unerring in dialogue. And given the direction the story is taking at this point, the less reliability the better.

You:

''For me, Chris's decision was painful'' (page 151)

Thorne:

“For me, personally, Chris’s decision was painful. I cofounded the LIGO Project in 1983 (together with Rainer Weiss at MIT and Ronald Drever at Caltech). I formulated LIGO’s scientific vision, and I spent two decades working hard to help make it a reality. And LIGO today is nearing maturity, with the first detection of gravitational waves expected in this decade.
But Chris’s reasons to jettison gravitational waves were compelling, so I didn’t utter even a whisper of protest.”

Personally, I don't understand this need to imagine "discontentment and frustration" where none exists. Thorne doesn't need your help defending his point of view.