Thermodynamics question

Faith & Science Conversation
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Thanks again! While the 2nd article seems to embrace the simple answer that yes - photons lose energy due to the expansion of space, I appreciate how the first article holds even that conclusion somewhat loosely. As in - the amount of energy a photon has can also still be seen as a function of perspective (my peculiar motion as I encounter that photon). The sorting of motion into two varieties: “co-movement” vs. “peculiar” motion (the more traditional kind we think of) was new to me. At first glance, that seems to me suspiciously like breaking another one of the taboos of relativity: the attempt to identify an “at rest” state of the universe in defiance of all motion (or alleged non-motion) being merely relative. After all if we can think of distant galaxies as having mere “co-motion” with us due to expanding space, it would seem to imply the existence of a “co-motion” bubble from which all peculiar motion could then be identified as present or absent. But I think I see the answer to this, in the form of the “co-motion” also being relative to whatever set of matter (galaxies & such) one is choosing to consider.

I also appreciated the admission that we can’t strictly rule out the possibility of the infinite universe (infinite energy) which inspired the idea of selecting a large arbitrary region of it (the ‘membrane’) and just examining within that to see how conservation laws might fare - and knowing that what’s true of one region ought to be true of all.

But I guess the main take-away I have is a confirmation that these are very much open-ended questions, and that our high-school level physics can very much be held as tentative at the cosmological level, even while it still functions as a rock-solid understanding for us in our little corner of activity and observation.

-Merv

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I certainly considered the infinite universe possibility before I made my previous reply, but it changes nothing and so it wasn’t worth mentioning. The problem is that an infinite universe doesn’t alter the expansion of the universe, because this expansion of the universe is not a global effect but a local one. In other words, the space is expanding everywhere even in our corner of the universe and that still means the heat density is decreasing. I just wanted to make sure you understood that part.

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Yes - and thanks for your responses too, Mitchell. I had read your first one too.

I don’t really think the universe is infinite, but was just making allowance for the fact that our telescopic eyes haven’t yet encountered anything we could call an ‘edge’ of it, right? Hence the open-ended nature of that query. But it seems to me that there are a lot of good reasons, mathematical, physical, theological or otherwise to rule it out. I probably can’t enumerate, much less explicate those as well as you could, but I’m just letting my intuition piggy back on my impressions gleaned from modern cosmology.

I’ve never understood how radiation could be prevented from leaving a finite universe, going out into … the void? Unless it be some transdimensional geometry that has “straight” lines just coming back over themselves (like a pacman just scrolling back onto the other side of the screen). I do like the oft-used image of the expanding surface of an inflating balloon. But it is just an analogy for something that my 3-D conditioned mind has not yet apprehended in any more direct form.

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Yes, if the universe is finite then if the universe wasn’t expanding so fast we would be able to see ourselves in the distance. But the expansion is faster than light so that more and more of the universe passes outside the visible limits, rather than being able see more of the universe as time goes on (which is what you would expect if it wasn’t expanding so fast).

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I know this is a long shot, but I thought I’d still ask a question. Awhile back I got into a long discussion with a person who claimed to have had a PhD in physics and that they earned a Nobel prize. I was skeptical. But they didn’t make a big deal about it and they seemed very knowledgeable about physics nonetheless.

At one point, as we wrangled about the impossibility for an infinite number of future events, they said something about the eventual heat death of the universe, to which I replied with the possibility of quantum particles coming into existence, to which they speculated on recombination. “But it’s still not an infinite number,” I said.

Are quantum fluctuations to be presumed upon in a dead universe?

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That’s another very good question for which we don’t know the answer.

Suppose you ignore quantum fluctuations, and just imagine an eventual “heat death” universe with particles and photons in thermal equilibrium, with a more-or-less constant energy density. Some physicists have argued that if you wait a very very very very very long time, eventually, randomly, some large but finite region of that universe will become locally low-entropy, and allow for the evolution of interesting things for a finite amount of time. And the spontaneous formation of such regions could happen again and again, infinitely. However, even if this did happen, each such region would be finite in time before going back to high entropy. And there are some significant objections as to whether or not this would ever really happen. I don’t think there is consensus among physicists on this question. And then, if you add in an expanding universe due to dark energy, such events become increasingly unlikely, and might never happen.

What if we include quantum fluctuations? I think (although I’m not sure) most physicists would agree that quanum vacuum fluctuations, creating (we imagine) virtual particle-antiparticle pairs for brief periods of times, could never lead to the creation of an interesting universe (or even an interesting sequence of real events) without the addition of some outside energy. So in a “heat death” universe, there might be an infinite sequence of such events, but none of them ever lead to anything interesting.

If you want to have an inifinite sequence of interesting things happening, you need some infinite source of orderly energy. The best candidate theory for that is something called “eternal inflation” – which has its own wikipedia page. There are observations in our own universe to suggest that some version of inflation theory might be true. There are several versions of inflation theory, and not all of them lead to multiple universes or eternal inflation. But some of the simplest versions of inflation theory describe an inflation field going forward in time eternally (but, interestingly enough, probably not backward in time indefinitely – this is still a subject of dispute), and this inflation field in turn gives rise to an infinite number of “bubble universes,” of which ours is one. Each bubble universe would be forever disconnected from the others, and each would have its own eventual heat death or in some other way be finite in time.

That, I believe, is the current thinking on those cosmological questions. Not a strong consensus on the answers.

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Thank you so much for the informative and interesting response

Gives rise to a number that may proceed to infinity without ever becoming actually infinite :wink:

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Using the balloon as a three dimensional metaphor for four dimensional spacetime, and since the balloon expands with time, how would we be able see ourselves, regardless of the rate of expansion? The metaphor also says that the interior of the balloon does not exist, just the ‘fabric’, and we cannot ‘see through it’. It sounds like you’re saying we would be in two places at once.

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After the initial cosmic inflation, it wasn’t always expanding faster than the speed of light. If it had been, we wouldn’t be able to see anything except our own galaxy, and maybe not even all of it.
 

So I was wondering when did cosmic expansion exceed the speed of light, and found this:

One of the most surprising facts about the Universe is that if you do the conversions and take the inverse of the expansion rate, you can calculate the “time” that you get out.

The answer? Approximately 13.8 billion years: the age of the Universe. There isn’t a fundamental reason for that fact; it’s just a fascinating cosmic coincidence.

Ask Ethan: How Does The Fabric Of Spacetime Expand Faster Than The Speed Of Light?

That may not be the answer to my question, but it looks like it might. Anyway, if it had been much sooner, we would be able to see way less.

It also fits nicely with these:

Have I ever mentioned that I like coincidences?

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Because if the balloon isn’t expanding too fast then light would be able to travel all the way around the balloon back to where it began.

I think what you are alluding to is the acceleration of cosmic expansion in inflationary theory which is far from uniform – high positive then high negative rapidly going to zero, then slowly increasing to positive again. The visible edge of the universe is the point at which things are receding from us at the speed of light (anything beyond that is receding from us faster than light). When the acceleration is positive, things pass beyond that edge and when the acceleration is negative then things are passing back into the visible portion again. But this doesn’t mean nothing in the universe is receding from us faster than light. So the universe is still expanding faster than the speed of light even when the acceleration of that expansion is negative. Though if the acceleration remained negative long enough, then if the universe is finite, eventually all the universe would pass into visible portion (and it wouldn’t be expanding faster than light anymore) – long enough and we would see ourselves in the distance.

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The universe is receding from us faster than the speed of light now, but it hasn’t always, is my point.

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If that is true, then…

It appears that it will have been fairly recently, in a cosmological perspective.

Physicists, others, weigh in? @DeborahHaarsma, @pevaquark, @glipsnort?

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Not my kind of physics, I’m afraid.

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There’s more than one kind?! :flushed::grin: Oh yeah, astronomy, cosmology, astrophysics, elementary and high energy particle physics, planetary science, geology, geophysics, physical geography, oceanography, meteorology, hydrology, climatology, chemical physics, molecular physics… (How many did I leave out? ; - )

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Thermodynamics

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If you consider objects at increasing distances from the Earth, to a decent first approximation, they follow Hubble’s law:

image

The equation for this is:
v=H_0d

Where v is the recessional velocity, H_0 is the Hubble constant and d is the distance of the astronomical object. The Hubble constant has a value somewhere around 70 (km/s)/Mpc. You will note that this has units of distance/time divided by distance (or inverse time). It is a slightly odd way to write the constant, but it can be quickly used to calculate how fast an object at a certain distance is receding from the Earth due to the Universe’s expansion.

Side note: to calculate this more precisely, you should use the Friedmann equation, which describes how the Hubble expansion changes as a function of the density of stuff inside the universe, but that is beyond the scope of my post here.

Back to our estimate, we want to know at what distance does:
H_0d>c

where c is the speed of light. Doing a little aligning of units gets you d>4.3 GPc which is 4.3 gigaparsecs or about 14 billion light years which is what you found in the article posted above. Put another way, an object that is presently at or more than 14 billion light years away is presently receding away from us faster than the speed of light (assuming a constant Hubble expansion rate). This cutoff point wouldn’t necessarily change for most of the universe’s history. However, with a now accelerating expansion (unless dark energy is more interesting than a cosmological constant), this number will gradually start decreasing. In principle, the most distant galaxies that we can presently observe (now further thanks to JWT) will gradually become more and more redshifted until they disappear from our sight entirely.

None of this answers your questions per se about when did cosmic expansion exceed the speed of light, but here is a short video that talks about some of these things:

To answer your question can also be done I suppose to a first (very simple) approximation by asking this question, now that we found the magic distance of about 14 billion light-years where we then say how long would it take with an object’s speed continually increasing as it moved away from us (or the location where Earth would someday be) to reach this magic cutoff point of 14 billion light years away. Maybe we could write something like this:
dx(t)/dt=H_0x(t)

The main idea here is that the velocity is turned into the first time derivative of distance from Earth, and the distance from Earth changes as a function of time.

Edit: usually this is done via the scale factor of the universe, but a plot of this distance (also called the Particle Horizon) is shown here:

image
image335×643 7.11 KB

Source explaining this in more detail:

So @Dale, it looks like to answer your question the universe first passed the Hubble radius about 8 billion years ago.

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In my abyssal ignorance:

If space expands already intrinsically expanding universes forever then the wavelength of all photons and force particles would tend to the infinite? From 10^100 years OOM? In the Dark Era? During which no work can be done? At what wavelength do photons etc become ‘useless’? Yet…

(To your second para) There seems to be a need to factor in an energy value for the volume of space itself to maintain conservation? In the pinhole experiment you are describing black body radiation. In the moving walls scenario, if the walls expand due to an external force, then the energy is still conserved in the total expanding volume. The density decreases but the particles’ speed does not (universes have no walls). But in an ICE piston the gas particles lose energy by driving the mechanical expansion. Which seems to be an analogy for the expansion of space (but not universes).

If universes expand but space itself does not, do photons intrinsically attenuate? I was told not by a Ph.D. physicist. Newton’s first law. I infer. But, space itself is expanding, only exists where there is matter, even worse it is accelerating… so photons’ and force particles’ wavelengths must be increasingly stretching, attenuating, decaying, their frequency must be decelerating, to conserve energy?

In a perfect mirror wall box of photons there can be no expansion from within, so any externally driven expansion will not affect the photons’ frequency, just dim the light intensity. But space itself is expanding, so the photons must intrinsically redshift. Acceleratingly.

We have no warrant for breaking conservation.

Is that coherent?

Space itself has an intrinsic energy value.

And can expand faster than light when what it is transporting has a high enough density. Whence inflation.

All of which may be rationalization too far, but does make some of the ineffable strangeness of existence probably illusorily less so. It’s still stranger than God.

Hmmmm. So at what wavelength would photons become incapable of driving the expansion of spacetime (for some reason I’d either picked up or made up that it was driven by conservation breaking increasing in dark energy)? And what would happen if they did?

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@Dale updated my post to answer your question more specifically. Will try to respond to a few things @Klax in next few days unless someone else beats me to it.

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Thanks for your work in that. It seems that Earth (and the humans on it) are in kind of a sweet spot for being able to observe the universe, including in time.

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