Cosmology - Cosmic Conundrum in Scientific American of February 2021

This document contains comments about the article Cosmic Conundrum by Clara Moskowitz In Scientific American of February 2021.
The strangely small value of the cosmological constant is one of the biggest unsolved mysteries in physics.
See also: ScientificAm_September_2004-A-Cosmic-Conundrum.htm



The article starts with the header:

In every bit of nothing, there is something.

What does the author means with nothing and with something?
From the physical point of view, when there is nothing there can not be something.
From the visible point of view, when we observe nothing there can be something physical, but invisible for the human eye.
If you zoom in on empty space and take out all the planets, stars and galaxies, you might expect a pure vacuum, but you'd be wrong.
The problem is you can not do this in reality, which means there is no way to decide that something is wrong.
Any way what is a pure vacuum?
In stead you would find a dynamic scene, with particles sparking to life and disappearing almost immediately.
What is the physical meaning of 'finding' something? Can you physical measure these particles?
Quantum mechanics, the theory governing the infinitesimal world, does not allow for nothingness.
The elementary particles, which are described by the standard model, are not governed by any theory. Governed, meaning in the sense of controlled. These particles can influence each other but their movement is not controlled. In general: the behaviour of the world at any scale, is not controlled by any law Specific not by quantum mechanics. See also: Reflection 1 - Laws and Mathematics
At any given moment in time and space, energy can never be perfectly zero - there is always some wiggle room.
The problem is, that we are discussing here the time before or after the Big Bang? To understand the sentence you must first have an idea what energy means. Secondly what zero energy means.
Out of that wiggle room "virtual" particles can arise - specifically a pair made of a particle and its antiparticle, which annihilate each other and are gone as quickly as they came.
If this is the case you cannot speak about a vacuum i.e. something that is empty and has zero energy. To create these virtual particles also some form of energy is required, for example in principle some sort of 'photons' can do this trick, implying that space is not empty.
The problem with vacuum energy is that there is not enough of it.
You can only discuss the concept vacuum energy when the concept is clear.
This raises the question: what exactly means that a vacuum has energy in the first place. How is it measured?
Friedmann equation

The birth of a problem

page 22

The Cosmological constant has a chequered history.
But in 1929 astronomer Edwin Hubble measured the speeds of many galaxies and found, to his surprise, that they all are moving away from us - in fact, the further away the galaxy, the faster it was going.
This raises an important question: Are all the astronomers, every where in the universe, observing the same?
What that means if they observe the same than we are moving away from them, like they are moving away from us.
This raises two questions: This question is important because when light (photons) travels towards us from a distance, the photons physical could become older. This can reflect a frequency change. It should be remembered that each photon is a package of energy.
His measurement showed that space is expanding everywhere and no matter where you look, it will seem as as all galaxies are receding because the distance between everything is constantly growing.
This is not correct. It seems as if all the galaxies are receding and as such that the distance between all galaxies is increasing.
It should be warned that interpretation of these measurements is not easy, because the further away the more you observe in the past. One type of explanation is that the 'total' universe is rotating. It is like a giant galaxy.
Faced, with this news, Einstein decided a couple of years later to remove the cosmological constant from his equations.
Did he really remove this constant, or did he set this constant (ie. lampda) to zero?
For a while the cosmological constant was a footnote of history, but it was quietly preparing for a comeback.
In the late 1990 two teams were competing to measure how much the expansion of the universe was slowing down as a result of gravity pulling matter inward.
What was the reason of this exercise? In real it is very difficult to measure both an expansion and a contraction.
In 1998 and 1999 they published their results based on measurements of supernovae, whose distances could be detemined very accurately.
THe next sentence implies that this is 'not' the case.
THe most distant of these supernovae turned out to be much dimmer and therefore farther away than expected.
In some sense this is not so strange, because the light of any object should become dimmer based on distance.
The expansion was not slowing down at all - it was speeding up.
Although the cosmological constant allowed scientists to balance Einstein field equations again, making them predict an accelerating univerese like the one astronomers had observed, the value of the constant didn't make sense.
The value of the cosmological constant, should be calculated such that the Einstein field equations matches observations. If the value does than the Einstein field equations describe the evolution of the universe as observed. It is important to remark that the solution calculated only mathes visible observations. What this means that in reality of the present, only what lies in our immediate neughbourhood can be observed. In the past only what lies at far distances.
It actually worsened a problem that had been bothering scientists for a while.
It is not only the cosmological constant but the Einststein field equations could also be part of the problem.
In the years that the constant lay on the cutting-room floor, physicists had linked this term from GR with the concept of vacuum enegy from quantum mechanics.
But the vacuum energy was supposed to be huge.
When this term is huge the question is if it physical trully represents a vacuum i.e. something where there is nothing.

When Neutron stars collide, the gravity waves they create could help physicits studying the cosmological constant
The gravity waves the neutrom stars create, can not be the explanation or cause why the two Neutron stars collide.

The first to formally calculate the value of the cosmological constant based on quantum theory's predictions for the vacuum energy was physicist Yakov Zel'dovich, who found in 1967 that the energy should make the cosmological constant gigantic.
The whole problem is to what extend you can calculate the cosmological constant, as part of Einstein's Field equations, based on quantum mechanics. Part of the problem is that to what extend empty space is relevant for the evolution of the Universe.
Anyway, the most logical route to follow should be based on observations.
Thirty years later, when astronomers realized that the expansion of the cosmos was accelerating, the problem didn't go away.
The amount of acceleration, through shocking at the time, was still minuscule compared with what quantum theory said it should be.
Again the same question: How relevant is the quantum theory.
It became more difficult to understand why it might be just slightly more than nothing.
The problem is even more complicated. The evolution of the universe is described by physical phases. Allmost at the beginning we had the inflation theory, which showed a burst of gigantic growth in size. Next there was a period were the size increased at a fixed rate and now we observe an increasing rate, which implies acceleration. All these periods require a physical explanation.
"Its value is very weird" says Katherine Freese. "Even weider than zero"
That the acceleration is small is not so strange. . What is strange that there is only value relevant for the whole of the universe.
The cosmological constant is technically just a constant of nature, a number in an equation that can take on any value.
It is not that simple. The first question to answer is if the equation is the correct discrition to describe the evolution of the universe based on observations. This equation includes certain parameters which also have to be calculated to match observations.
Nothing about quantum field theory was falsified when its predictions didn't match astronomical measurements, and the theory is still as usefull as it ever was.
When you have a theory which predictions don't match observations you have a serious problem. At the same time you have to answer the question to what extend that theory is relevant to describe astronomical phenomena.

Theories Galore

page 23

Most proposed solutions to the cosmological constant problem fall into three categories:
At this point it is not clear why the cosmological constant is a problem and what the solutions try to solve.
Next in this sentence:
  • Change the general relativity equations that describe the expansion of the universe.
  • Modify the quantum field theory equations that predict the amount of vacuum energy
  • Throw something entirely new into the mix.
For each solution you have the same issue: What has the solution to do with the cosmological constant problem.
Tweaking GR could change the role the cosmological constant plays - or cut it altogether.
IMO this leads to a route which never ends, specific it is not clear what the purpose of this whole exercise is.
Another angle on updating GR is called sequestration, proposed by Padilla and his collegues.
IMO this also leads to a route which never ends, specific it is not clear what the purpose of this whole exercise is.
They modify Einstein's theory in a way that seals gravity off so it cannot feel the effects of vacuum energy.
This is a very strange proposal. Original 'everyone' agreed and understood that vacuum Energy is important to understand the evolution of the Univerese and all of a suden it is agreed that this is a mistake. Such a proposel, without any clear explanation, is bad the trust in science
If GR is not the problem, though, maybe quantum mechanics is.
IMO this also leads to a route which never ends, specific it is not clear what the purpose of this whole exercise is.
Maybe both GR and quantum mechanics are the problem. Maybe it is even possible that the problem cannot be solved by mathematics. See also: Reflection 1 - Laws and Mathematics and beyond.
But the resolution might require more than just mathematical finagling the traditional equations.
Also this is a dangerous route.
One recent unorthodox idea is aproposal by Steve Carlip of University of California, Davis, that spacetime is fundamentally made of "foam".
Spacetime is not a concept that describes something that exists. Space, either either empty or not is something that exists. At the same time completely empty space, within the boundaries of all of space created after the BigBang is also non existing.
In this picture, the curvature of space would constantly fluctuate on extermely small scales, well beyond anything we could hope to measure.
"The curvature of space" can not be measured which makes all of this tricky.

page 24

Three Pieces of the Puzzle.

The cosmological constant problem is a major mystery in physics. The value of the constant, part of Einstein's GR equations, seems to be much smaller than theories predict it should be.
Which 'theories' are meant? The sentence is not clear.
At the heart of this puzzle are three intertwined concepts - vacuum energy (the energy of empty space), dark energy (the cause of the accelerating universe) and the constant itself.
The problem is none of these terms are physical clear.
Starting point of the evolution of the universe is, that at any instant, the total universe is expanding in size. The consequence is that the energy density is decreasing, but it does not mean that the energy density is everywhere the same. When we assume that vacuum energy is involved than it should be physical clear what it means.

Vacuum Energy

The energy in empty space, made of virtual particles - pairs of particles and antiparticles that constantly appear and disappear.
The amount of Vacuum Energy can be small

The Cosmological Constant

A term, represented by the Greek letter Lambda, that Einstein included in his general relativity equations that describe how matter and energy bend spacetime.
The issue is much more what exactly means: the bending of space time. How is this measured.

The Einsteins Field equations

This equation consists of 6 terms.
  • Gij the term which describes the curvature of space time.
  • gij the term which describes the structure of space time.
  • Lamda the cosmological constant is a term that can describe a repulsive force throughout space.
  • G the gravitational constant
  • Tij the term which describes the energy and momentum of matter and radiation.
  • c is the speed of light.
Specific the details of the terms Gij, gij and Tij are very important to understant the structure of the universe.
'Nothing' is mentioned of what is observed. What makes all of this complicated and almost unsolvable that all observations are a function of x,y,z and t, with t in the the range between 0 and 13.7 billion years and with r in the range of 0 and 45 billion light years.

Dark Energy

The force causing the expansion of the universe to accelerate.
"Its a kind of whild idea," Carlip says."It is a desparate measure, but so is every other attempt to deal with the cosmological constant, and these are desparate times."
If you are not sure than don't propose it
Sorkin, who says Carlip's spacetime foam is "going in the right direction" also has his own entry in the field.
All these proposals make a very bad impression on science
According to this model, spacetime is fundamentally discrete - meaning that instead of being smooth, continuous expanse, it is broken up into tiny chunks, individual units of space and time that represent the building blocks of the universe just as are the building blocks of matter.
Spacetime does not exist as such it cannot be broken op in individual units. Space can be divided into individual units of space, but time cannot.
If this is the case, calculating the cosmological constant involves dividing by the number of spacetime units in the universe, leading to a value much closer to what astronomers observe.
And what do astronomers observe? Not mentioning this makes this whole theory tricky.
One of the most prominent - and by some, most hated - solution to the cosmological problem is called the antropic principle.
When you mention the antropic principle all of science disappears into quicksand.
Other physicists, though, consider this philosphy a cop-out. "Its giving up on the problem" Sorkin Says.
He is completely correct. But still: Exactly what is the problem. The cosmological problem, seul, cannot be the problem. It is much larger. It are the equations which harbor this constant.
"At this point it becomes a matter of taste" Carlip says "Probably the answer is something that nobody's thought of."
Maybe the answer lies in the direction to recognize that humans have a limited capability to understand the reality. Behind that limit there is human uncertainty. For example to explain what happened before the Big Bang is such a limit. Even the time very close to the Big Bang is 'filled' with uncertainties.

Constancy or Quitessence

page 25

The Cosmological Constant remains the best explanation for dark energy - the mysterious force causing the expansion of space to accelerate.
It is very tricky to mention concepts like the acceleration of space. Only objects can have a speed.
But what if dark energy is n't actually related to the cosmological constant or vacuum enegy at all?
To answer that question you must have a clear definition what each one physical means. When the cosmological constant is linked to an equation you must first clearly explain what each term in the equation means.
What if the universe's vacuum energy is somehow perfectly canceled out and the cosmological constant is zero?
What that means is that both vacuum energy and the cosmological don't exist. Ofcourse that is a simple solution, but IMO not very scientifically.
In that case, dark energy might be the work of something called quintessence.
This sentence is not clear.
Quintessence would be some form of energy throughout space with negative pressure.
What is the definition of negative pressure?
In contrast to the cosmological constant, quitessence could change over in time
This seams to indicate that the two concepts 'cosmological constant' and 'vacuum energy' are replaced by quitessence.
To test whether dark energy is caused by quintessence or the cosmological constant, scientists must determine whether the strength of dark energy has changed over time.
It will be interesting to know how the strength of dark energy is measured.
No indications of inconstant constants have yet emerged.
Still the real issue is insofar the constants involved, are actual measured or calculated, to arrive to this conclusion.

SpaceTime Ripples and Neutron Stars

Upcoming experiments and astronomical observations may offer a way to discriminate between the proliferation of theories weeding out some and, just maybe, offering support for others.
This is all speculation.
Gravitational wave observatories such as LIGO in the US and Virgo in Europe are now regularly spotting waves produced by by cosmic cataclysms and these waves may prove useful in probing the nature of vacuum energy.
Gravitational waves are a by product of the movement of masses (all moving masses produce a variable gravitational field) and maybe have nothing in common with the concept of vacuum energy.
Some attempts to solve the cosmological constant problem rely on changes to general relativity that would cause gravity to travel slightly slower than the speed of light.
The movement of the objects in the universe rely on the strength of the masses involved and on the speed of gravity. This movement does not depend on the speed of light.. As such Einstein's Field equations should not include the parameter c but the parameter g i.e. the speed of gravity.
Newton assumes that the speed of light is infite and acts instantaneous. That is wrong The speed of light is important to perform vissible observations but not as part of how matter influences matter as a function of distance.
The fact that gravitational waves seem to arrive simultaneously with light from the same events has quashed that idea , rulling out a few theories already.
The original idea was that the speed of gravity was much larger than the speed of light. This idea was more or less inline with the idea of Isaac Newton, because he assumed that the speed of gravity was infinite. The fact that they are equal, invalidates Newton's idea.
Einstein's idea was that the speed of gravity and the speed of light are the same. The fact that they arrive simultaneous confirms his concept.
Gravitational waves are also revealing strange activity inside neutron stars.
Gravitational waves are a function of source that produces the waves. That means they are different depending about the number of objects involved and the shape of these objects. To assume that their shapes are also a function of the internal activities involved is difficult to demonstrate. IMO the only possible activities that could have some impact are internal (mass) density fluctuaties
Gravitational-wave observations might be sentive to the gravitational effects of extra vacuum energy here, potentially revealing secrets about the nature of vacuum energy.
All of this is highly speculative.
Lab setups that probe the universe at the smallest possible distances could be sensitive to some of the alterations of general relativity that physicists are proposing.
An example is the work of the Eöt-Wash group at the University of Washington, where scientists are using an extremely sensitive balance experiment to conduct precision tests of gravity.
Okay. More technical detail is required.
So far gravity has followed Newton's and Einstein's Laws to the letter in their tests and no hidden dimensions have been seen, but the scientists keep adjusting their balance to probe smaller and smaller separations.
Newton laws acts instantaneous and Einstein's Law not. To detect differences between these two require large distances and that is very difficult to perform here on earth.
Even if the group never detects deviations that affect vacuum energy, that would not be conclusive: it is possible that such changes occur at a distance beyond our reach.
Strange scientific conclusion.
Maybe one day some of them will have observational predictions that can be tested, but at this point we're not there.
That is different than claiming that they can be tested in a lab.
Or maybe scientists will discover a simpler fix.
The simplest fix is that the evolution of universe can not be described by mathematical equations. The problem is that the predictions can not be tested based on observations, because these same observations are also used to calculate the parameters or constants of these equations. (You need two sets of observations of the universe amply spaced in time.).
The 'same' problem exists also if you want to describe the evolution of the solar system. To do that you have to calculate the parameters involved. This are the masses of the sun and the planets involved and require observations in the past. To demonstrate that your model (Newton's Law) is 'correct' you need observations in the future. For the solar system this is 'easy'. For the whole of the universe actual impossible.

Reflection 1 - Laws and Mathematics

Laws nor Mathematics in anyway influence, control or govern the evolution or any process in the universe. The Universe is not empty, but contains matter and objects. The structure, the shape , how it is build and its chemical makeup changes in due course. All these changes are not controlled in some way, but are a reaction of how the objects influence each other.
Considering the planets in our solar system. Observing the state today it seems a stable configuration, but that was not always the situation. Millions of years ago, there were no nine planets, but many many more. They were then much smaller and the trajectories were not 'circles' but elliptic and more choatic. In the millions years in between these proto planets collided, fused and slowly formed the planets as existing today. Of course you can claim that in theory you can calculate what happened when two biljard balls collide on a flat surface. At the same time to predict the outcome of any fusion reaction is impossible. However when you perform the same reaction 1000 times you get a clear picture what you can expect.
This unprectability is the ony 'law' that is valid to describe the evolution of the creation of the stability of the present day planets.

Reflection 2 - What came first: Einsteins equations or the physical universe.

IMO the answer is simple: The physical universe and the evolution of the universe came first. Einsteins equations came second.
The evolution of the universe is in some sense a boiling pot of soup, of something, like the internal part of our Sun. At the beginning it was something extremely hot, or better very energetic. Slowly this whole boiling pot of soup expanded in size, cooled down and became less energetic.
The point is that this whole process is not controlled by any law. What is at stake are chemical reactions, which changed as a function of the changing conditions, influenced by each other, in the total universe relevant for that moment.
What we humans do is to try to unravel, as detailed as possible, what the details are of the processes that can be distinquished and if certain processes are identical we call these descriptions laws.

Einsteins equations are supposed to describe the evolution of the Universe.

Reflection 3 - Steve Carlip

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