This is a really great post, and I’m glad that this post has raised these issues, because I’ve been interested in them for a while.
Could you clarify this for me?
all the cosmological observations we can possibly make come from a single slice of the universe—a 4-dimensional cone of spacetime. And as there are a finite number of events in this cone, cosmology has only a limited amount of data it can ever gather; in fact, the amount of data that even exists is finite.
Surely we constantly receive new data from the receding boundary of the observable universe? As we move through time our past light-cone follows us, swallowing up more events that will affect us.
Also, if we literally have all possible evidence, then we lose our motivation to care, as the theory can’t actually help us predict anything. When we really need these techniques is when we have all the evidence that is available at the moment, but it might make more predictions in the more distant future.
Surely we constantly receive new data from the receding boundary of the observable universe?
Yes, but the effect is so small I didn’t think it worth mentioning. Over the course of your natural lifetime, your past light-cone will extend by about 100 years. Since it already envelopes almost 14 billion years, you won’t get much new information relative to what you already know. If you have reason to believe that your lifespan will exceed 5 billion years, the situation is very different.
When we really need these techniques is when we have all the evidence that is available at the moment, but it might make more predictions in the more distant future.
Looking back, I implicitly assumed (without justification) that improving our understanding of the universe always has a positive utility, regardless of currently known predictive power. You may disagree if your utility function differs from mine. But you are correct in that a new theory may make predictions that we will only be able to test in the distant future, so thanks for making my post more rigorous :)
Over the course of your natural lifetime, your past light-cone will extend by about 100
years. Since it already envelopes almost 14 billion years, you won’t get much new
information relative to what you already know.
You are forgetting the impact of improving science. In fact, most of what we know about the 14 billion year light cone has been added to our knowledge in the last few hundred years due to improved instruments and improved theories. As theories improve, we build better instruments and reinterpret data we collected earlier. As I explained in a recent comment, suggesting new tests for distinguishing between states of the universe is an important part of the progress of science.
You are right about the growth rate of the accessible light cone, but we will continue to improve the amount of information we extract from it over time until our models are perfect.
Actually, since the Universe is accelerating, the past light cone effectively gets smaller over time. Billions of years from now there will be significantly less cosmological data available.
I don’t think so. Any events in the past now will still be in the past in a billion years. The past light-cone can only get bigger. (I think you might be misunderstanding my use of the word “past”. I’m using the relativistic definition: the set of all events from which one can reach present-day Earth while travelling slower than lightspeed.)
Without getting mathematical: there are galaxies moving away from us faster than the speed of light (and moreover every galaxy outside the Local Group is accelerating away from us). In the future these galaxies will not be visible to Earth-based observers. Similarly the CMB will be more redshifted and hence contain less information. So if you’re using a meaning of “event” such that every Planck volume of space produces an event every Planck time regardless of whether there are any atoms there or not, then yes, that number can only go up. But if you’re talking about actually interesting things to observe, then it’s certainly going down.
There are galaxies moving away from us faster than the speed of light (and moreover every galaxy outside the Local Group is accelerating away from us). In the future these galaxies will not be visible to Earth-based observers.
If they’re moving away from us faster than the speed of light, they’re not observable now either. As for currently observable galaxies, the event horizon between what we can observe and what we cannot is receding at lightspeed, relativity does not allow us to observe anything break the light barrier, therefore nothing observable can outrace the event horizon and become hidden from us. Black holes notwithstanding because Stephen Hawking is still working on that one.
Similarly the CMB will be more redshifted and hence contain less information.
I don’t think redshifting destroys information. Unless you mean that the information will be hidden by noise from within our own galaxy, which is perfectly true.
Anyway, I accept that the amount of data one can gather from current observations may go down over time. But, over a long enough time period, the amount of data one can gather from current and past observations will go up, because there is more past to choose from. Of course, even over millennia it will only go up by an insignificant amount, so we should be careful with the data we have.
Right, so this is the standard misunderstanding about what it means for space itself to be expanding. Thesetwo Wikipedia article might be a good place to start, but in brief: relativity forbids information to pass through space faster than light, but when space itself expands then the distance between two objects can increase faster than c without a problem. (The second link quotes a number of 2 trillion years for the time when no galaxies not currently gravitationally bound to us will be visible.)
I don’t think redshifting destroys information.
Well, technically I guess it just lowers the information density, which means less information can be gathered by observers on Earth (and less is available inside the observable universe, etc.) And then eventually the wavelength will be greater than the size of the observable Universe and thus undetectable entirely.
Thanks for the links. It all makes a lot more sense to me now (though at 2 trillion years, the timescales involved are much longer than I had considered).
One last quibble: Relativity does not forbid the space between two objects (call them A and B) from expanding faster than c, it’s true. But a photon emitted by object A would not be going fast enough to outrace the expansion of space, and would never reach B. So B would never obtain any information about A if they are flying apart faster than light.
But because the expansion of the Universe is accelerating, the apparent receding velocity caused by the expansion is increasing, and, for any object distant enough, will at some point become greater than c, causing the object to disappear beyond the cosmological horizon.
This, obviously, assuming that the current theories are correct in this respect.
But a photon emitted by object A would not be going fast enough to outrace the >expansion of space, and would never reach B. So B would never obtain any >information about A if they are flying apart faster than light.
I think that was the point, but since the expansion is accelerating this was not always the case.
A and B are retreating faster than light now (in our reference frame), so the light they are emitting now will not reach each other.
However, the A and B are far apart, say 5 billion light years. 5 billion years ago A and B were receding more slowly—perhaps half the speed of light, so the light emitted 5 billion years ago from A is now reaching B. Hence, B currently sees light from A.
Five billion years in the future this will not be the case. Sometime in the next 5 billion years B will observe A to redshift all the way to zero and wink out.
This is a really great post, and I’m glad that this post has raised these issues, because I’ve been interested in them for a while.
Could you clarify this for me?
Surely we constantly receive new data from the receding boundary of the observable universe? As we move through time our past light-cone follows us, swallowing up more events that will affect us.
Also, if we literally have all possible evidence, then we lose our motivation to care, as the theory can’t actually help us predict anything. When we really need these techniques is when we have all the evidence that is available at the moment, but it might make more predictions in the more distant future.
Yes, but the effect is so small I didn’t think it worth mentioning. Over the course of your natural lifetime, your past light-cone will extend by about 100 years. Since it already envelopes almost 14 billion years, you won’t get much new information relative to what you already know. If you have reason to believe that your lifespan will exceed 5 billion years, the situation is very different.
Looking back, I implicitly assumed (without justification) that improving our understanding of the universe always has a positive utility, regardless of currently known predictive power. You may disagree if your utility function differs from mine. But you are correct in that a new theory may make predictions that we will only be able to test in the distant future, so thanks for making my post more rigorous :)
You are forgetting the impact of improving science. In fact, most of what we know about the 14 billion year light cone has been added to our knowledge in the last few hundred years due to improved instruments and improved theories. As theories improve, we build better instruments and reinterpret data we collected earlier. As I explained in a recent comment, suggesting new tests for distinguishing between states of the universe is an important part of the progress of science.
You are right about the growth rate of the accessible light cone, but we will continue to improve the amount of information we extract from it over time until our models are perfect.
Actually, since the Universe is accelerating, the past light cone effectively gets smaller over time. Billions of years from now there will be significantly less cosmological data available.
I don’t think so. Any events in the past now will still be in the past in a billion years. The past light-cone can only get bigger. (I think you might be misunderstanding my use of the word “past”. I’m using the relativistic definition: the set of all events from which one can reach present-day Earth while travelling slower than lightspeed.)
Without getting mathematical: there are galaxies moving away from us faster than the speed of light (and moreover every galaxy outside the Local Group is accelerating away from us). In the future these galaxies will not be visible to Earth-based observers. Similarly the CMB will be more redshifted and hence contain less information. So if you’re using a meaning of “event” such that every Planck volume of space produces an event every Planck time regardless of whether there are any atoms there or not, then yes, that number can only go up. But if you’re talking about actually interesting things to observe, then it’s certainly going down.
If they’re moving away from us faster than the speed of light, they’re not observable now either. As for currently observable galaxies, the event horizon between what we can observe and what we cannot is receding at lightspeed, relativity does not allow us to observe anything break the light barrier, therefore nothing observable can outrace the event horizon and become hidden from us. Black holes notwithstanding because Stephen Hawking is still working on that one.
I don’t think redshifting destroys information. Unless you mean that the information will be hidden by noise from within our own galaxy, which is perfectly true.
Anyway, I accept that the amount of data one can gather from current observations may go down over time. But, over a long enough time period, the amount of data one can gather from current and past observations will go up, because there is more past to choose from. Of course, even over millennia it will only go up by an insignificant amount, so we should be careful with the data we have.
Right, so this is the standard misunderstanding about what it means for space itself to be expanding. These two Wikipedia article might be a good place to start, but in brief: relativity forbids information to pass through space faster than light, but when space itself expands then the distance between two objects can increase faster than c without a problem. (The second link quotes a number of 2 trillion years for the time when no galaxies not currently gravitationally bound to us will be visible.)
Well, technically I guess it just lowers the information density, which means less information can be gathered by observers on Earth (and less is available inside the observable universe, etc.) And then eventually the wavelength will be greater than the size of the observable Universe and thus undetectable entirely.
Thanks for the links. It all makes a lot more sense to me now (though at 2 trillion years, the timescales involved are much longer than I had considered). One last quibble: Relativity does not forbid the space between two objects (call them A and B) from expanding faster than c, it’s true. But a photon emitted by object A would not be going fast enough to outrace the expansion of space, and would never reach B. So B would never obtain any information about A if they are flying apart faster than light.
But because the expansion of the Universe is accelerating, the apparent receding velocity caused by the expansion is increasing, and, for any object distant enough, will at some point become greater than c, causing the object to disappear beyond the cosmological horizon.
This, obviously, assuming that the current theories are correct in this respect.
I think that was the point, but since the expansion is accelerating this was not always the case.
A and B are retreating faster than light now (in our reference frame), so the light they are emitting now will not reach each other.
However, the A and B are far apart, say 5 billion light years. 5 billion years ago A and B were receding more slowly—perhaps half the speed of light, so the light emitted 5 billion years ago from A is now reaching B. Hence, B currently sees light from A.
Five billion years in the future this will not be the case. Sometime in the next 5 billion years B will observe A to redshift all the way to zero and wink out.
Agreed. Thanks.