I love reading io9, it’s such a fun mixture of science fiction, entertainment, and pure science. So I was happy to respond when their writer George Dvorsky emailed to ask an innocent-sounding question: “Why is the scale of the universe so freakishly large?”
You can find the fruits of George’s labors at this io9 post. But my own answer went on at sufficient length that I might as well put it up here as well. Of course, as with any “Why?” question, we need to keep in mind that the answer might simply be “Because that’s the way it is.”
Whenever we seem surprised or confused about some aspect of the universe, it’s because we have some pre-existing expectation for what it “should” be like, or what a “natural” universe might be. But the universe doesn’t have a purpose, and there’s nothing more natural than Nature itself — so what we’re really trying to do is figure out what our expectations should be.
The universe is big on human scales, but that doesn’t mean very much. It’s not surprising that humans are small compared to the universe, but big compared to atoms. That feature does have an obvious anthropic explanation — complex structures can only form on in-between scales, not at the very largest or very smallest sizes. Given that living organisms are going to be complex, it’s no surprise that we find ourselves at an in-between size compared to the universe and compared to elementary particles.
What is arguably more interesting is that the universe is so big compared to particle-physics scales. The Planck length, from quantum gravity, is 10^{-33} centimeters, and the size of an atom is roughly 10^{-8} centimeters. The difference between these two numbers is already puzzling — that’s related to the “hierarchy problem” of particle physics. (The size of atoms is fixed by the length scale set by electroweak interactions, while the Planck length is set by Newton’s constant; the two distances are extremely different, and we’re not sure why.) But the scale of the universe is roughly 10^29 centimeters across, which is enormous by any scale of microphysics. It’s perfectly reasonable to ask why.
Part of the answer is that “typical” configurations of stuff, given the laws of physics as we know them, tend to be very close to empty space. (“Typical” means “high entropy” in this context.) That’s a feature of general relativity, which says that space is dynamical, and can expand and contract. So you give me any particular configuration of matter in space, and I can find a lot more configurations where the same collection of matter is spread out over a much larger volume of space. So if we were to “pick a random collection of stuff” obeying the laws of physics, it would be mostly empty space. Which our universe is, kind of.
Two big problems with that. First, even empty space has a natural length scale, which is set by the cosmological constant (energy of the vacuum). In 1998 we discovered that the cosmological constant is not quite zero, although it’s very small. The length scale that it sets (roughly, the distance over which the curvature of space due to the cosmological constant becomes appreciable) is indeed the size of the universe today — about 10^26 centimeters. (Note that the cosmological constant itself is inversely proportional to this length scale — so the question “Why is the cosmological-constant length scale so large?” is the same as “Why is the cosmological constant so small?”)
This raises two big questions. The first is the “coincidence problem”: the universe is expanding, but the length scale associated with the cosmological constant is a constant, so why are they approximately equal today? The second is simply the “cosmological constant problem”: why is the cosmological constant scale so enormously larger than the Planck scale, or event than the atomic scale? It’s safe to say that right now there are no widely-accepted answers to either of these questions.
So roughly: the answer to “Why is the universe so big?” is “Because the cosmological constant is so small.” And the answer to “Why is the cosmological constant so small?” is “Nobody knows.”
But there’s yet another wrinkle. Typical configurations of stuff tend to look like empty space. But our universe, while relatively empty, isn’t *that* empty. It has over a hundred billion galaxies, with a hundred billion stars each, and over 10^50 atoms per star. Worse, there are maybe 10^88 particles (mostly photons and neutrinos) within the observable universe. That’s a lot of particles! A much more natural state of the universe would be enormously emptier than that. Indeed, as space expands the density of particles dilutes away — we’re headed toward a much more natural state, which will be much emptier than the universe we see today.
So, given what we know about physics, the real question is “Why are there so many particles in the observable universe?” That’s one angle on the question “Why is the entropy of the observable universe so small?” And of course the density of particles was much higher, and the entropy much lower, at early times. These questions are also ones to which we have no good answers at the moment.
Sean carol
At one point, you have stated
“But the scale of the universe is roughly 10^29 centimeters across”
At other point, you are stating
“The length scale that it sets (roughly, the distance over which the curvature of space due to the cosmological constant becomes appreciable) is indeed the size of the universe today — about 10^26 centimeters.”
There is difference in 10^26 and 10^29 by a factor of 1000 which is very high. So what is the size of universe : 10^26 cm or 10^29cm?
Obviously, both these scales of 10^26b and 10^29 should be within observable universe. Can it be that after every 10^26 cm, new lengths of scales appear in universe even though lying beyond observable universe
Sean carol
At one point you stated size of universe is 10^29 cm
Than you also stated
The length scale that it sets (roughly, the distance over which the curvature of space due to the cosmological constant becomes appreciable) is indeed the size of the universe today — about 10^26 centimeters.
Which is correct size of universe? 10^26 or 10^29 since there is difference of factor of 1000 between two?
Could it be that after every 10^26cm ( length of scale), a new universe begins?
@Vinod Sehgal: Energy is not conserved in GR.
@Vinod Sehgal: Note that energy is not conserved in GR.
@Vinod Sehgal: Note that energy is not conserved in GR.
.
@Philip Helbig Is Law of conservation of energy not a fundamental law of Physics? where does energy goes?
Strange: In the RSS feed, I see 3 copies of my comment (due to some bug in the blog software, sometimes comments don’t show up—sometimes they didn’t get through, sometimes they did and appear later, but I have no way of knowing), but not here. I also see a reply to my comment in the RSS feed, but not here on the main page.
In brief, if energy is not conserved, it doesn’t make sense to ask where it goes, since the question assumes conservation.
Edward Harrison explains this (and essentially all the rest of classical cosmology) in his book Cosmology: The Science of the Universe. Do check it out.
OK, the previous comment appeared right away, along with the missing stuff. 🙁
Just type “energy conservation in GR” (without the quotes) into the Google search box and you will get lots of interesting reading, including a post from this very blog.
@Phillip Helbig After your comment regarding non-conservation of energy in GR, I googled on this topic. I came across an old blog by Sean caroll of 2010 in which he explains that due to dynamic nature of space (GR), energy is not conserved . I also came across an article by George Hoot which also speaks of non conservation of energy as per GR. With due regards to these stalwarts and also to Einstein, we can’t get lost of our wisdom, logic and common sense. Further, mathematics and its deduction are the language of Physics but per se they don’t reveal physical realty at ground level. Unless physical realty at ground level behind mathematical deductions does not become privy to our logical mental understanding, trust in pure mathematical deductions can lead to wrong direction .
For example, both observational cosmology and mathematical deductions establish that space is continuously expanding and that too at accelerated rates. With this also appears vacuum energy ( or dark energy). Now if I want to understand at logical
following issues at ground level :
I) from where does new space appears?
ii) from where does new vacuum energy appears?
iii) Is there any physicality of space? If yes, what is that physicality
iv) What is meant by curvature of space at physical ground level when GR does not say any thing about physicality of space?
Now when we want to understand above issues in terms of physics in logical level, stalwarts state that this as per GR or mathematical formulations tell this way. this is not correct approach. Any theory or any Scientist, however big/celebrity he/she may be can make mistakes
@ Philip Helbig For sake of argument, GR does take into account dark energy, therefore, GR might not be allowing conservation of energy but only baryonic mass and energy. But including dark energy, dark matter, total energy might be conserved. The way baryonic mass and energy are interchangeable, similarly there might also be some mechanism for interchange between dark stuff and baryonic stuff of universe. But the concept that some thing may disappear to no where or it may appear from no where, is illogical and against physical reality
@Vinod Sehgal: Please read the references I mentioned.
Typo check: In the paragraph starting “Two big problems” the 10^26 cm size you give is not the size of the Universe, since it is only 100 million light years. But you had earlier given 10^29 cm, which is correct. This is 100 billion light years, considerably larger than the age of the Universe, which leads to the horizon problem solved by inflation or something like it. With the cosmological constant known to 2% accuracy in the Planck 2015 results, the big question is: Why is the cosmological constant so small but not zero?
Vinod Sehgal: years ago I read Dr. Alan Guth’s popular-science book “The Inflationary Universe”, and his explanation made sense to me, although it may not to you. I just re-read Dr. Carroll’s 2010 post on the subject (energy conservation vs. GR) and he makes a brief mention of the view I associate with Dr. Guth at the end of his piece but does not prefer that explanation himself. The way I like to understand it is:
Energy comes from nothing as follows: 0 —> -E +E. That is, as space expands, the gravitational fields of matter extend into that space, creating negative energy, which is then balanced by a release of positive energy. We have known that a gravitational field in space can be considered to carry negative energy since Newton, who showed that a hollow sphere does not contain any interior gravitational field due to its own mass (gravitational forces from all parts of the hollow sphere cancel at any point inside the inner diameter of the hollow sphere). As Dr. Guth says in his book, suppose we have a hollow planet in the shape of a soccer ball (surface composed of hexagons and pentagons) and removed material around the edges of the surface plates. Gravitation force of the plates upon each other would pull them together at a smaller radius from the center, shrinking the planet, and reducing the interior volume of gravity-free space. At the same time, the shrinkage forces would be doing work, creating energy – for example, if zero-tension springs connected the plates to a central point, the springs would be compressed, storing some of the created energy. More volume of space containing the gravitational field of the planet (the difference between the original inside volume and the new, smaller inside volume) has produced more energy, so the energy of space containing gravitational forces can be thought of as negative.
That is probably a simplistic explanation which does not cover all cases, but I like it.
@ Jim V Thanks for your quite elaborate response regarding origin of energy. But a further examination will make it obvious that there are many flaws in the arguments
I) Ist in reality at ground physical level, there should nothing as positive or negative energy. Any energy should be some physical reality devoid of any positive or negative elements embedded in it. Positive or negative are only mathematical notations to indicate opposite effects of particular energy.
ii “That is, as space expands, the gravitational fields of matter extend into that space, creating negative energy”
Above statement by you is the crux of whole issue which I want to dissect further to highlight many unresolved issues which are impediments iA clear understanding.
a) You started with as “space expands”. What is meant by expansion of space? What is the Physics of space expansion? From where and how additional space emerges out and appears in space? If space is not a physical reality, what sense it implies by its expansion? From where vacuum energy (dark energy) emerges out? Are vacuum energy ( dark energy) synonymous or different.
In this respect, there are host of issues regarding space about which we don’t have clear understanding. But we trust space expansion since theories and stalwarts tell it so. Kindly note that I am not refuting space expansion but unless above issues regarding space are clear, I take it with a punch of salt or as matter of deep faith ( Not logical understanding) like a religious faith since theories and stalwarts tell like this way. But in scientific understanding, there should be logic at every step and your inner self should become privy to that logic
II) Secondly, you stated that gravitational field extents into space creating negative energy
As per GR and as you have stated, gravitational field comes into effect by the distortion of space by matter. It implies distortion ( or curvature) or gravitation should come into effect by the mutual interaction of matter and space. This means both space and matter should be possessing some physicality and there should be some coupling between these two. Secondly, there should be some energy content in either matter or space or both which on mutual interaction between two gets translated into gravitational force ( whether negative or positive immaterial) Now gray areas in this description are
a) Though we have developed quite good understanding of physicality of space but regarding space we don’t even know whether it has some physicality or not let alone knowledge about its physicality. It has become fashionable to use the word “fabric of space time” without knowing about what fabric
b) We don’t have any understanding of the interacting force or coupling between matter and space but still we trust that space is distorted
c) Except mathematical formulations, we don’t know about the physicality of distortion of space.
d) we don’t from which source of energy( whether matter or space or both) gets translated into gravitational energy in space. Forget negative or positive. Both are physical realities
e) Description of gravitation by GR as distortion of space time had appeared when nothing was known about dark energy or dark matter. Now in any description of gravitation, role of dark energy or dark matter needs to be incorporated. After all, need for dark matter had arisen to account for gravitational effect whether high rotation of galaxies or clusters or gravitational lensing
One thing. No physical reality can disappear into “no where’ ( conservation of energy as per GR) OR no physical reality can appear from “no where” ( Quantum principle of zero energy _ Lawrence Crauss). A physical reality shall appear or disappear from/to into some other physical reality
If I continue further with such gray issues it may become quite elaborative which is not possible in these comments column
” With the cosmological constant known to 2% accuracy in the Planck 2015 results, the big question is: Why is the cosmological constant so small but not zero?”
Do you think that this is really a problem? What do you think about the explanation by Bianchi and Rovelli in http://arxiv.org/abs/1002.3966?
People keep trotting out these problems. When someone claims that they have been solved and/or are misunderstood and cites a paper in a leading journal and/or by a well respected scientist as evidence, this is almost always met with silence. If Bianchi and Rovelli are wrong, please say so and/or write a paper pointing out their mistake. Otherwise, how is science to progress?
The idea “that something can’t come from nothing” is a principle of logic (if that is what you are implying) has never seemed to sound to me. In my view, either it can (in which case space can expand and virtual particles can exist briefly, and so on), or it can’t (in which case we have no explanation for Hubble’s Constant, the Casmir Effect, and so on). Logic only tells us how to get from assumptions to conclusions, not what the assumptions should be.
@ Jim V When I mentioned that there is nothing per se in negative or positive energy, I just wanted to highlight that positive and negative pertains to opposing effects by such energies in a common system resulting in zero effect. Now this null result by opposing energies should not be interpreted as that the origin of such energies is from “Nothing”. Yes, as you have also mentioned in your previous post emergence of any existential entity from “nothing” is illogical and in none of branch of knowledge, Science even more, faulty or wrong logic is acceptable
Casimir effect and popping out of virtual pair of particles demonstrate that empty space( vacuum) have been interpreted erroneously as “nothing” and that there is “something” in vacuum state also
In my many previous posts, I wanted to highlight the attention of commentators on following confounding big issues
I) Is distortion of space by Mass ( GR) is tangible physical realty or mere some mathematical construct. If it is physical realty, a series of subsequent issues viz physicality of space, nature of interacting force between matter and space, particles/components of matter creating distortion and nature of distortion are implied
ii) I am not refuting expansion of space since so many astronomers have interpreted red shift in light from remote galaxies as expansion of space. But if we do accept this, series of subsequent issues are implied viz source from where expanded space appears, source from where vacuum energy (dark energy) or cosmological constant appears associated with additional space appears, destination where loss of energy of light ( due to red shift) disappears excluding due to dust.
I shall welcome if you can address above issues in straight manner
vinodsehgal1955@gmail.com
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