Matter-antimatter asymmetry - a simple explanation?

[JoaLi]

TL;DR Summary

Can the resulting excess of matter over antimatter just be the result of a statistical process with average and standard deviation so that it would be normal and not an exception to expect a deviation? Taking as model system the Hawking radiation where 2 particles from vacuum fluctuation get separated from each other at the event horizon. Whereas this separation is a random event to decide if the particle to escape is matter or antimatter. So could it have been at the beginning of our universe?

Dear collegues,

I would like to share and discuss a simple explanation to the matter-antimatter asymmetry. Maybe this explanation is too simple, but your feedback is appreciated.

I would like to start with what inspired me to this idea. The Hawking radiation. You know the event horizon of a black hole. The Hawking radiation comes from particles that are created by vacuum fluctuations and then separated by the event horizon so that they cannot recombine to nothing. As this vacuum fluctuation generates pairs of matter and antimatter, there will always be a separation between them. However, as this process can be considered statistically, there will be produced an equal amount of matter and antimatter on each side of the event horizon given the law of big numbers in statistics, so that average value is expected to be zero.

Really? We can translate this experiment into the situation of flipping a coin, the coin can show either side - let it call here matter or antimatter - after each throw. If we do this experiment 10 times, we may expect on average 5 times side A and 5 times side B. However, in reality there not just is the average, but also the “standard deviation”. This means, doing a real coin flipping experiment, e.g. 10 times, we may end up with an asymmetry, e.g. 6:4 or 7:3. In fact, it is more likely that we will come up with a deviation from 1:1 than with exactly 1:1.

The interesting question is, will this deviation shrink, expand or stay, if we significantly increase the number of throws – e.g. from 10 to 1EX with this the number of pair building events at creation of the universe (so maybe a really large number)?

The formula to determine the standard deviation of such “Bernoulli Experiment” is known:

d = SQRT( n *p * (1 – p) )
= SQRT (n) * SQRT (p) * SQRT (1-p)

With n the number of throws of the coin, p the likelihood for either outcome – here ½ obviously.

Given p=1/2 as a constant, one can simplify the formula to:

d = SQRT(n) * const.
= SQRT(n) * 1/2

So this answers the question, if the standard deviation will shrink, expand or stay when doing this Bernoulli Experiment for a very large number of times: It is expanding by the square root of the number of tries.

So if at the beginning matter was created at a separating layer like an event horizon, it would be normal to expect an asymmetrical amount of matter (and antimatter) formed on either side of that separator. It is no special rules or laws of nature, that we might not yet know that somehow violate symmetry, but simple statistics on randomness and with randomness as a constitutive driving force of quantum mechanics. We see quantum mechanics behaving randomly all the time, so why not also for this case at the beginning?

 

[PeroK]

The statistical explanation is a fairly obvious one, but it begs the question about the nature of the process. This idea is discussed on the CERN webpage:

https://home.cern/science/physics/matter-antimatter-asymmetry-problem

 

[JoaLi]

Thank you for the link. On the site of CERN they mention the example of the coin experiment to expect a 50:50 outcome, but then speculate about a special, yet unknown mechanism ("magic marble") that influences some coins to always fall on either side, e.g. side A. I think this is still a different premise compared to what I mention above.

On the CERN site they write: "A coin has a 50-50 chance of landing on its head or its tail, so if enough coins are spun in exactly the same way, half should land on heads and the other half on tails. In the same way, half of the oscillating particles in the early universe should have decayed as matter and the other half as antimatter."

What I try to say above is that this premise is wrong: If you do a series of coin flips, you do NOT end up "half land on heads and the other half on tails". You do have a standard deviation based on a binomial distribution on this to what you end up. As I said, if you try yourself throwing a coin 10 times, you probably do NOT end up 5 head : 5 tails. You may end up 6:4 or 3:7. If you increase to 100, the standard deviation will be even greater. The standard deviation is increasing, not shrinking with the number of throws! This makes it more and more unlikely to exactly match 1:1 the more particles you create / aka coins you throw.

This is as you do this series of coin flips just once! Of course, if you do several such experiments, the "virtual average" over all of them is 50:50. But the Universe has been created just once, so it is like just 1 series of coin flips and not the average over ALL series of coin flips that are possible.

In the concept that I mention above, there is nothing influencing to prefer side A over B and not B over A, etc. The deviation is just statistically. All you need is a separator like an event horizon. So there would be a mirror universe with a complementary excess of antimatter. Why there is an excess of matter in our universe is just the result of a series of bernoulli experiments to randomly end up somewhere on the binomial distribution of results. Next time a universe will be created, the ratio may be different and antimatter may prevail in "our" universe to a different ratio, but very likely to any number different from 50:50.

 

[PeroK]

On the CERN site they write: "A coin has a 50-50 chance of landing on its head or its tail, so if enough coins are spun in exactly the same way, half should land on heads and the other half on tails. In the same way, half of the oscillating particles in the early universe should have decayed as matter and the other half as antimatter."

What I try to say above is that this premise is wrong:

Yes, you're correct. It is wrong.

If you do a series of coin flips, you do NOT end up "half land on heads and the other half on tails". You do have a standard deviation based on a binomial distribution on this to what you end up. As I said, if you try yourself throwing a coin 10 times, you probably do NOT end up 5 head : 5 tails. You may end up 6:4 or 3:7. If you increase to 100, the standard deviation will be even greater.

This is basic probability theory that whoever wrote that CERN page either didn't know or forgot about!

All you need is a separator like an event horizon.

That's a big if. Where is this event horizon?

I'll look for a better reference. I must admit I'm a bit shocked by that CERN page.

 

[PeroK]

I couldn't find a good reference. The problem is that matter and antimatter are always created in precisely equal amounts. So, yes, if you could make half the resulting particles disappear, then you would have a statistical imbalance. But, simply postulating an event horizon to magic away half the particles isn't an answer.

I think what the CERN page was trying to say was that after creation if particles could transition from matter to antimatter, then this would be a possible explanation. Likewise it's not enough to wave your hands and say particle oscillations. To have a candidate theory, you would have to have a theoretical model of these oscillations and then test that model in the lab.

 

[Vanadium 50]

So, yes, if you could make half the resulting particles disappear, then you would have a statistical imbalance. But, simply postulating an event horizon to magic away half the particles isn't an answer.

It also doesn't work quantitatively. The matter in the universe is about 2.2% of the total energy. That works out so long as the total energy of the universe is around the same as 2000 protons.

Since it's vastly more, this theory is immediately falsified.

 

[phinds]

aking as model system the Hawking radiation where 2 particles from vacuum fluctuation get separated from each other at the event horizon.

Just FYI, the particle-pair description of Hawking radiation is NOT an actual description. It is a heuristic developed by Hawking himself to, as he put it, approximately explain in English that which can only be explained accurately with math.

As it is expressed here:
https://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html

In fact this argument also does not correspond in any clear way to the actual computation.

And to quote Hawking himself:
https://www.brainmaster.com/software/pubs/physics/Hawking Particle Creation.pdf

It should be emphasized that these pictures of the mechanism responsible for the thermal emission and area decrease are heuristic only and should not be taken too literally.

 

[Drakkith]

If you increase to 100, the standard deviation will be even greater. The standard deviation is increasing, not shrinking with the number of throws! This makes it more and more unlikely to exactly match 1:1 the more particles you create / aka coins you throw.

Certainly. The standard deviation increases, but the relative standard deviation (the value of standard deviation when compared with the mean value) decreases, generally approaching closer and closer to 50% as the number of coin tosses increases. And it's the relative standard deviation we're interested in, not the standard deviation. See below.

This is as you do this series of coin flips just once! Of course, if you do several such experiments, the "virtual average" over all of them is 50:50. But the Universe has been created just once, so it is like just 1 series of coin flips and not the average over ALL series of coin flips that are possible.

From a purely statistical point of view, it is overwhelmingly unlikely that a single creation event would generate anything but a nearly perfect 50% ratio in antimatter to matter. If we assume that there is about 10^80 particles in the observable universe, then the standard deviation is something like 10^40. That would make the expected ratio deviate from 50% by about 10^-38% I think? Hope that's all correct. I never worked with statistics.

The deviation is just statistically. All you need is a separator like an event horizon. So there would be a mirror universe with a complementary excess of antimatter.

Even assuming there was an event horizon to separate particles, you still need a mechanism to preferentially choose one type of particle over another to fall in vs escape.

 

[Vanadium 50]

Hope that's all correct. I never worked with statistics.

That's essentially my calculation, from the other direction. It;s correct, so long as we don't worry about factors of 1.35 and the like. The important thing is that there is 10,000,000,000,000,000,000,000,000,000,000,000,000 times as much matter in the universe than the OP's model would predict.

 

[JoaLi]

Thank you all for the good discussion. To summarize my understanding of your comments:

If the total energy in the universe would be about 2000 photons, then the standard deviation to expect would be about sqrt(2000) = 44.72 . That is about 2.2% of 2000, too, which is the observed ratio of matter to total energy. In such universe my model could be a likely explanation.

If the number of photons in the universe is something like 4E84, then the square root would be 2E42. This is far less than 2.2%, unfortunately.

Somehow, there is more matter than expected by my model. However, if you run the creation experiment once, to come close to standard deviation may be likely to expect, but any other deviation is not impossible, but included by the model. Of course, matching the standard deviation with the known values for total energy (=photons in the universe) in relation to the number of particles in the universe, would be an intuitive hint in favour of the theory. Yet any other result is not impossible. If you do 10 coin flips, it could be 9:1 and thus far away from the standard deviation, but still consistent with the theory. I understand that such reasoning is low satisfactory. It would go more the direction of the anthropic principle assuming there have been created numerous universes and most of them failed to yield the development of intelligent beings like us, but this one with so odd constants and pimped ratio of antimatter:matter worked...

At least one more robust answer to this comment:
"Even assuming there was an event horizon to separate particles, you still need a mechanism to preferentially choose one type of particle over another to fall in vs escape."

Actually not, because the standard deviation includes positive or negative deviation from the mean just by chance, just as your coin flip series could be 6:4 or 4:6. The one preferring matter, the other antimatter in your universe. Still without any specific mechanism except just randomness.

 

[PeterDonis]

if at the beginning matter was created at a separating layer like an event horizon

It wasn't. So your speculation won't work.

 

[PeterDonis]

If the total energy in the universe would be about 2000 photons

Protons. Not photons.

Somehow, there is more matter than expected by my model.

Not just "more". About 37 orders of magnitude more, as @Vanadium 50 said in post #9. You're not going to fix that by mucking about with standard deviations and random variation. Models that are off by that much are called "falsified" for a reason.

 

[PeterDonis]

Since the OP is personal speculation, which is not really on topic here anyway, and since there are at least two fatal flaws in the OP's model as pointed out above, this thread is closed.