I also remember reading that there are 10^87 electrons in the universe so there should be a similar amount of protons (I dont know how they would come to this estimate, especially since there may be large parts of the universe we can't even see.)

10^87 is too many (this was perhaps an older estimate before Planck 2015 data).  It should be closer to 10^80.

The method for finding that value is to first note that the density of the universe is close to the critical density, which we know from measuring how the scale factor of the universe changed with time, and also by measuring the geometry (close to spatial flatness).  Then we invoke the fact that the universe is homogeneous on large scales.  So we can multiply that density by the volume of the observable universe to get the total mass.  Finally, multiply that result by the fraction of the density of the universe that is in the form of baryons.  Since most of the of the universe is hydrogen (which is just protons), we can get the number of protons that way.  The number of electrons will be close to equal to the number of protons since the universe is electrically neutral. 

(Aside:  To be more accurate we can also account for the neutrons in the heavier elements, but since those are a smaller fraction it matters little to the result, especially when also considering the other uncertainties in the numbers going into this derivation, especially the value of the Hubble constant.)

Let's try the calculation ourselves.

Using H = 68km/s/Mpc, we get the critical density of 8.7x10^-27 kg/m³.  Note the critical density depends on H squared, so uncertainties in the exact value of H matter a lot.

Using Lambda-CDM with H=68km/s, Ω_m = 0.31, and Ω_tot = 1, the comoving volume of the observable universe is about 12000Gpc³.  Again the value of H matters here. The comoving volume is bigger if the Hubble constant is smaller.  This is nice actually because it somewhat cancels the effect of uncertainty in H on the critical density.

Multiplying the density by that volume, we get a total mass of the observable universe to be about 3x10⁵⁴kg.

Now we must account for the fraction which is baryons.  Dark energy is 69% of the universe's mass/energy density, and dark matter is 26%.  Baryons are only 4.9%, plus or minus 0.1%!

Multiplying 3x10⁵⁴kg by 4.9%, and dividing by the mass of a proton, we get 9x10⁷⁹ protons in the universe.  Let's call it 10⁸⁰ as an order of magnitude estimate.

 I read about this years ago and wondered if any headway had been made in determining the lifetime of a proton and if we found out that it was finite, even if it was very long, how that would alter our cosmological theories.

Yes, there are various prediction that protons themselves are unstable and might decay.  But it has not yet been observed, and the fact that it hasn't been observed helps place a lower limit on how long the half-life of the proton must be.  It is something ridiculous, like 10³⁴ years!  We can do some math and calculate how big of a pool of water you would need to expect to have one proton in it decay per year, or whatever, for various estimates of the possible proton half-life.  It ends up being very big, but not completely impractical.  In fact there are a number of projects in the works to try to detect it, assuming it happens at all.  For example, the new Japanese detector Hyper-Kamiokande:

[youtube]JFOE3D2z7LM[/youtube]

If the universe was even slightly positively curved and you drew a triangle on a scale large enough to measure that curve, the angles would add up to slightly more than 180 degrees, just like if you drew such a large triangle on the surface of the earth?

That's exactly right.   And if it is instead negatively curved, then the angles will instead add up to less than 180 degrees.  That the sum of angles in a triangle exactly equals 180 is a special property of flat geometry.

Any thoughts on quark entanglement? Does anyone think we can use that in some way? 

Stellarator- for quantum computing maybe?  I think tunneling and teleportation can be used in the same way, we've been able to teleport large molecules from what I have read- though I dont understand why the source must be "destroyed"- can the source not be kept while a duplicate is generated?

Thanks, Wat, so the 10^80 figure applies to the observable universe only?  Thats a pretty neat way of figuring it out! I wonder what a proton would decay into?  A neutron decays into a proton plus an electron plus a neutrino if I remember correctly, and a proton should further decay into hmmm lol.  I find it fascinating that all these particles are made of quarks and the further away the quarks get the stronger the attractive force gets (its like a rubber band.)  And if there is an intermediate stage between neutron stars and black holes we might have quark stars!   There are even some possible candidate quark stars!   I wonder how low the scale can go, as quarks themselves might be made up of even smaller particles called preons (and there might even be preon stars)- though none of this has any solid evidence for it as far as any I can recall.

I've always found triangles to be special (the least number of sides of any polygon)- on a flat surface you can use them to prove that the shortest path between two points is a straight line.  I remember figuring that out by myself in 7th grade and the teacher stared at me and wondered where I got that from lol.  On a curved surface of course, this wouldn't apply.  Though you could still use a triangle to prove what kind of curve would be the shortest path between two points.

though I dont understand why the source must be "destroyed"- can the source not be kept while a duplicate is generated?

No-cloning theorem.   This is something very fundamental to quantum mechanics, and it's easy to get lost in the weeds in terms of understanding rigorously why it must be true.  But there's a minutephysics video that does a pretty good job of explaining it more conceptually without too much of the math.


[youtube]owPC60Ue0BE[/youtube]

Thanks, Wat, so the 10^80 figure applies to the observable universe only?

That's right.  We don't know how much bigger the entire universe is compared to just the observable part (what lies within our particle horizon).  It could very well be infinite (if the density is equal or less than the critical value so that space is flat or negatively curved).  There might be an infinite number of protons/electrons/anything in the entire universe in that case.

If the universe is instead positively curved then the total volume must be finite.  If we know the radius of curvature then we could calculate the total volume, and then assuming homogeneity for the whole thing, the total number of particles.

I wonder what a proton would decay into?

In order to decay there must be a violation of conservation of baryon number.  Since protons are the lightest known baryons, and we have so far no evidence of such a violation, this implies they don't decay at all.  

If they do decay, then the decay still must conserve quantities like charge and spin.  One way to do so is for it to decay to a pion and positron (and then the pion decays further into two photons).  Those photons could then be detected to provide evidence of the proton decay, depending on their energy and the angle between them.  That's what they'll be looking for in the next generation of detectors.

Though you could still use a triangle to prove what kind of curve would be the shortest path between two points.

  My favorite inversion of this idea is to find the shortest path between two points in spacetime.  It ends up behaving quite the opposite of intuition.  For example, the distance traced through spacetime by a photon is zero.  And for any two events separated more in time than in space, the straight path between them ends up being the longest path.  Spacetime physics is very weird and very fun.

edit:  moved some spacetime / Hawking Radiation discussion to the astro Q&A

Oh I think part of my post got lost- wasn't anything all that significant I dont think, just the part about the pi meson being interesting because it's its own antiparticle and some more stuff about triangles that I cant remember right now lol.  I was going to post something about tetrahedrons and other platonic solids having interesting properties too, but that would be going just a little off topic lol.

No-cloning theorem.  This is something very fundamental to quantum mechanics, and it's easy to get lost in the weeds in terms of understanding rigorously why it must be true.

This is why I'll never step into a Star Trek-esque teleporter  . 

Thought you would find this interesting

https://www.nytimes.com/2017/02/20/scie ... ule=inline

Feb. 20, 2017

327
There is a crisis brewing in the cosmos, or perhaps in the community of cosmologists. The universe seems to be expanding too fast, some astronomers say.

Recent measurements of the distances and velocities of faraway galaxies don’t agree with a hard-won “standard model” of the cosmos that has prevailed for the past two decades.

The latest result shows a 9 percent discrepancy in the value of a long-sought number called the Hubble constant, which describes how fast the universe is expanding. But in a measure of how precise cosmologists think their science has become, this small mismatch has fostered a debate about just how well we know the cosmos.

“If it is real, we will learn new physics,” said Wendy Freedman of the University of Chicago, who has spent most of her career charting the size and growth of the universe.

Tension between different measured values of the Hubble constant goes back a long way.  Different researchers using different observational methods and analyses often came up with different answers, and in the old days cosmologists were split into two camps: one wanting to use H=50km/s/Mpc, and the other H=100km/s/Mpc.  A 100% difference!  A 9% discrepancy today sounds very good compared to that.

The measurements of H do get better over time.  From deciding whether to use H=50 or H=100, more recent observations have said "Nah, it's closer to the middle", and they've been converging toward about H=70.  With Planck, it's about H=68.  But different methods still lead to slightly different answers, and the error bars don't always overlap.

[center]A history of measurements of the Hubble Constant:[/center]
[center][/center]
[center][/center]

Most cosmologists deal with this discrepancy by publishing any results that depend on H in terms of a parameter, lower-case "h", which is in units of 100km/s/Mpc.  That way their findings can be checked or compared with any value of H we might come by.

What does a 9% change in the present value of the Hubble Constant imply about the universe, if it turns out to be correct?  Let's see what happens if we increase H by 9% (e.g. from 67.8 to 73.9 km/s/Mpc), but keep everything else the same.  What this ends up doing is reduce the current age of the universe by about 8%:

[center][/center]
[center]Increasing the Hubble Constant by 9%, from H=67.8 to 73.9 km/s/Mpc[/center]

To understand the younger age, note that the Hubble Constant generally decreases with time (even if the expansion is speeding up), which I explain here.  So the universe must be younger for it to have dropped to this higher Hubble Constant today, for the same amount of matter and radiation and so forth.  

Alternatively, increasing H by 9% can work with keeping the age of the universe the same, if the amounts of dark matter and dark energy are different.  Here I run the model with 27% less matter (meaning 27% less to the sum of regular matter and dark matter together), and 6% more dark energy.  This change serves to also keep the total density of the universe the same (close to the critical density), so that the geometry is still spatially flat.

[center][/center]
[center]Same Age of Universe: Ω_m = 0.225, Ω_Λ = 0.775[/center]
[center](vs. Ω_m = 0.309, Ω_Λ = 0.691)[/center]


This of course would be a pretty drastic change to the amount of matter in the universe compared to what observations suggest.  Planck 2015 data, and other measurements, show the total amount of matter to be pretty close to 0.30, meaning 30% of the critical density.  Of this 30%, only 5% is accounted for as normal matter, and 25% is dark.  And the error bars on these are only of the order of 1%.  So reducing the total matter to just 0.22 is an extreme change, and probably not the correct answer.  It will be interesting to see what does end up being the correct answer, and if the higher value of Hubble Constant stands up to more data and scrutiny.


Also, a fun and relevant fact.  With the recent LIGO gravitational wave detection from the merging neutron stars (which told us how far away the event occurred), combined with the optical observation (which told us how much the signal from it was redshifted by the expansion of the universe), it was possible to measure the value of the Hubble Constant in a brand new way!  Unfortunately, from that one observation the error bars turn out to be too large (H₀ = 70km/s/Mpc, plus or minus about 10), so it does not help resolve these discrepancies.  But with more observations of events like that, it easily could!

Another example of how different researchers making measurements of the same thing do not always get answers that agree within error: the early measurements of the charge of the electron:    (image pilfered from a post on stackexchange)

[center][/center]


[left]The best description of science is not that it gets the right answer.  It approaches the right answer, or (hopefully), gets less wrong over time. [/left]

Well stated Wat, this puts a new twist on the Heisenberg Uncertainty Principle

9% doesn't sound very big compared to the 50 to 100 gap the two camps were in before!

Of all things I am uncertain, except that I must be uncertain by at least half of the reduced Planck constant.

Added:
I removed a post containing a bunch of links.  Please, on this forum, do not just make links to suggested reading with very little else for context and call it a post.  I view this almost as spam.  Make an effort instead to write your own content to get a discussion going, and use links as references or supplemental material.  Thanks!

Of all things I am uncertain, except that I must be uncertain by at least half of the reduced Planck constant.

Added:
I removed a post containing a bunch of links.  Please, on this forum, do not just make links to suggested reading with very little else for context and call it a post.  I view this almost as spam.  Make an effort instead to write your own content to get a discussion going, and use links as references or supplemental material.  Thanks!

I had read all the articles and I was going to post a descriptive term for each link but I was late getting out the door this morning lol, I was going to come home tonight and edit it to include more descriptive information, some of the articles were mindblowing, like two mathematicians who have disproven the Cosmic Censorship Theorem, which is amazing.  I saved everything so I will repost with the descriptors in a few.

https://www.quantamagazine.org/the-mult ... -20141103/

The multiverse measurability problem

https://www.quantamagazine.org/multiver ... -20141110/

Multiverse how to find proof from colliding universes


https://www.quantamagazine.org/newfound ... -20171023/

how a wormhole could allow information to escape black holes

https://www.quantamagazine.org/wormhole ... -20150424/

mentions EP=EPR and the possible duality between microwormholes and quantum entanglement and how the Heisenberg Uncertainty Principle breaks down under certain special circumstances!

wormhole, entanglement and the firewall paradox (also includes EP=EPR and quantum foam space-time substructure.)

https://www.quantamagazine.org/stephen- ... -20180314/

Stephen Hawkings and the black hole paradox

https://www.quantamagazine.org/mathemat ... -20180517/

mathematicians disprove conjecture made to save black holes (disproving cosmic censorship conjecture and showing the stability of the Cauchy horizon!)

https://www.quantamagazine.org/why-blac ... -20181206/

why black hole interiors grow forever

https://www.quantamagazine.org/complica ... s-20130524

complications in physics lend support to multiverse hypothesis

https://www.quantamagazine.org/frauchig ... -20181203/

paradox clarifies where our views of reality go wrong

https://www.quantamagazine.org/martin-r ... -20181205/

Martin Rees on the future of science and humanity

https://www.quantamagazine.org/edward-w ... -20171128/

Ed Witten (founder of M theory!) ponders the nature of reality


https://www.quantamagazine.org/albert-e ... -20181114/

Einstein, holograms and quantum gravity (and more on microwormholes foaming the fabric of space-time)

https://www.quantamagazine.org/frontier ... -20150803/

Frontiers of physics

https://www.quantamagazine.org/string-t ... -20150218/

String theory as the only theory that works in a toy model of another universe


https://www.quantamagazine.org/the-univ ... -20180823/

Pattern of the universe also popping up in math, physics and biology!

https://www.quantamagazine.org/20130524 ... unnatural/

Is Nature Unnatural?  Why our universe never should have been (strengthens the case for a multiverse)

https://www.quantamagazine.org/new-proo ... -20181107/

Infinite curves come in two types

    Multiverses?   ¯\_(ツ)_/¯

Okay, I'll bite. I'm not entirely sure if this has been asked before on the forum, Wats, but what might be some theoretical methods for detecting other multiverses? Or: if they are completely undetectable by us currently (as I suspect is the case), could some arrangement of universal conditions make it possible to for us to observe what is literally outside all we know, and all that ever was, from our particular vantage?

what might be some theoretical methods for detecting other multiverses?

I think it depends on the type of multiverse being considered.  If we imagine a set of universes that are physically separate and in no way interact with each other, then they cannot be detected in principle, so they are completely unfalsifiable.  Personally I find these the least interesting of the multiverse ideas, because we cannot know.

For an example, imagine measuring the location of a particle.  Outside of the measurement, quantum mechanics describes the particle's location by a "wave function".  A measurement could find it anywhere in the space of that wave, with the wave function describing the probability of finding it there.  Once you make the measurement and find where the particle is, the wave function "collapses" to that location:

[youtube]p7bzE1E5PMY[/youtube]

It is a mystery as to how nature "decides" where the wave function should collapse to -- where the particle will be found -- and this led to many different interpretations of quantum mechanics.

One interpretation says that the wave function isn't simply collapsing to the measured value.  Maybe it is actually collapsing to every value, and every value is found in a different universe!  This is the "many worlds" interpretation of quantum mechanics.  It predicts that measurements of quantum systems proliferate an infinite number of alternate universes.  A wild idea.  As far as I know, this interpretation is unfalsifiable.  There's no obvious way to tell that this is what's happening, or if there's just this universe and what we measure is all there is to know about the system.  


For an example of a multiverse idea that could be testable, imagine that our universe lives within some higher dimensional space.  Maybe that higher dimensional space is also populated with other universes, and occasionally they collide with each other.  This would be a Brane Cosmology.  It could be testable by searching for evidence of previous collisions between our universe and others.  Once in a while, a research group does claim to find such a thing, although no such findings have so far been found compelling or stood up to scrutiny by the broad community of cosmologists.

The gravitational wave detection of the merging neutron stars also acted as a test of this idea (that our universe lives in a higher dimensional space).  If it does, then some of the gravitational wave energy will "leak" out into those other dimensions as it travels.  So the gravitational wave intensity will drop more rapidly with distance.  What we observe is consistent with no leak at all, and no extra dimensions to the space.  When you stop to think about it, this is an amazing statement.  We can actually test for the existence of higher dimensions.  PBS Space-Time has a great episode about it.

[youtube]3HYw6vPR9qU[/youtube]

There are many other ways to hypothesize the existence of other universes, and for each of them it is an important question of if and how it could be testable.