1

General Science / Re: What is Quantum Tunnelling and how does Quantum Tunnelling work?

« on: 01/02/2022 19:41:13 »

Hi again.

   So let's see if there are any questions left over from Aeris.

Let's say, hypothetically speaking, a macroscopic object like a table or a chair undergoes Quantum Tunneling and essentially teleports from one location to another while I'm still looking at it. What would that look like? would the object just pop right out of and then immediately back into existence in the blink of an eye?

    Let's just look at a microscopic objects for a moment (before we speculate and generalise to macroscopic objects).
We're going to consider the typical situation with a square barrier potential between two regions of exactly the same potential  (region I and region III).
    Here's the diagram again:


We're going to fire a particle toward the barrier (from region I) which has Energy, E < V₀  exactly as before and we've already discussed the wave function and shown animated diagrams of this earlier.

    Firstly remember that the wave function is not the particle,  there isn't anything with properties like a particle until you go looking for it (make an observation to locate the particle).   The wave function just indicates the probability of finding the particle at a particular place.
   If you go back through the earier discussions and animated diagram you'll notice that the wave function isn't always 0 inside the barrier.   There is some time when the particle could be found there.

   Now this is where various sources of information (not just PopSci) are going to mess things up or mis-represent what seems to be shown by the mathematics.
   The amount of time over which the particle could be found "in the barrier" is controversial.   Some sources are going to tell you that it "instantly appears" on the other side of the barrier or just that "it will never be found in the barrier" etc.   I don't wish to use too much bad language but this is clearly utter bolderdash.

   Just go back and look at the animated diagram carefully if you want to, instead of doing the mathematics.   There are times when the real and imaginary components of the wave function are non-zero at a fixed x position inside the barrier.  So the square of the modulus of the wave function is not 0 at that time, this is the probability of finding the particle at that given point x in space and given time t.  I'm labouring the point here but we just need to be clear that the probability of finding the particle at that position x in the barrier is not 0 for some of the time.  The probability of finding of the particle in the barrier does not drop to 0 until some finite non-zero time has elapsed after the incident wave packet hit the barrier.   You will find many articles, some textbooks and countless discussions on Quora and similar websites that discuss qunatum tunneling as if it's instant.   Some of them are quite interesting and authoritative and discuss problems like the apparent breech of the speed of light   (If the particle could move from one side of a barrier of thickness, d>0, to the other side instantly than that is faster than light speed travel).   They're all good in their own way except that the fundamental premise they were based on was bollderdash.

    Anyway, the mathematics never implied that tunneling would be instant.

    Here's one article (from Scientific American) that describes an attempt to actually measure how long it takes a particle to tunnel through a barrier:
https://www.scientificamerican.com/article/quantum-tunneling-is-not-instantaneous-physicists-show/
   The details aren't too important, we just need to note that there may actually be some way of observing or measuring tunneling time in practice and it does not seem to be instantaneous.   It can be that the particle spends some time in the barrier.

   Anyway, we can now try to generalise this to a macroscopic scale:  Basically, there's no reason to assume that the quantum tunneling of your chair from region I to region III would be "instant".   It's not going to go "poof" from here and just "poof" into existance over there.  It is very likely to spend some time "in the barrier" between the two places.   I'm not sure what this would "look like" but it could be a lot less impressive than teleporting.   Given a piece of space between the start and end point (i.e. a piece of space in the barrier), then the chair could be found there for a short amount of time during the tunneling.   I really don't know how to paraphrase this, applying QM to macroscopic objects is always just going to be speculation anyway.   It might look like the chair was just moving from the start position to the end position and occupies at least some but possibly all of the positions between those two points in passing.  A whole lot less impressive than teleportation, I'm sorry to dissapoint you.

Another long, post, sorry.    In summary the only important thing is that Quantum Tunneling isn't instant and may not look like teleportation.

Best Wishes.

LATE EDITING:   I probably should make it clear that the time it takes for a particle to tunnel through a barrier is controversial.   This was stated originally but it's worth stating again.  You should probably make your own investigations.  Personally, I'm sticking to what the Mathematics shows.

2

General Science / Re: What is Quantum Tunnelling and how does Quantum Tunnelling work?

« on: 01/02/2022 12:29:16 »

Hi.

If you state it as barrier potential, it's unclear what the dimension is.

    Sadly this terminology is used in the literature.  The "potential" is shown on the diagram in units of energy (for example Joules not Volts).  So it is the potential energy that the particle would have if it was physically located there.
      It's clear what you meant by the barrier energy but having just received the long post from Colin2B it would be wise to avoid saying anything that looks like E and carries the name "Energy" since that is usually reserved for the Energy of the particle.   The Energy of the particle is just called "the Energy", it almost always has the symbol E and it would be the total energy = potential energy + kinetic energy  under classical mechanics.

Best Wishes.

       

3

General Science / Re: What is Quantum Tunnelling and how does Quantum Tunnelling work?

« on: 31/01/2022 14:04:59 »

Hi.

If the barrier energy is increased to 40, will there be a portion of the wave packet passes through the barrier?

   Yes.    (In line with the previous post, it's the barriers potential you are talking about and not the energy of the particle).    The transmitted wave packet will have a smaller amplitude.

     http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/barr.html
Is actually a very useful link.   (It was found by Colin2B and used in his earlier post).   It offers an online calculator to determine transmission coefficients when a particle approaches a barrier of given height and width.
    The transmission coefficient  is approximately the ratio of (the square of) the amplitude of the transmitted wave to the (square of the) amplitude of the incident wave.   This decreases as the potential barrier height increases.

Best Wishes.

4

General Science / Re: What is Quantum Tunnelling and how does Quantum Tunnelling work?

« on: 31/01/2022 13:55:31 »

Hi again.

  This is going to get difficult for Aeris (or anyone else) to make sense of.   I'll spend a moment to try and pull the comments from Halc, Clin2B and myself together a bit.

Several of us picked this quote to represent something Aeris asked:

So it's kinda like the whole "Heat only moves from hot to cold" thing? The origin point of whatever is about to Quantum Tunnel needs to be in a state of higher energy than the end point? Is this right?

       However,  Halc  was always talking about the potential  when he first discussed the situation.    In classical mechanics (not qunatum mechanics) the potential energy is only one contribution to the total energy of the particle.
       Eternal Student was also careful to talk about the potential.
       Aeris was the only one to say "Energy" but most of us knew that they were talking only about the potential.
       Colin2B has spoken about the (total) Energy, E, of the particle.

Here's the overall summary:
   Halc suggested the tunneling would occurr from region I (where the particle started from) to region III (where the particle ends up) only if  the potential   in region I was higher than region III.
   Eternal Student (E.S. or "me") disagreed with that.
   E.S. also suggested that Halc's comment would be reasonable on a statistical basis  (so Halc doesn't have to feel too bad about suggesting it in the first place).
    Colin2B hasn't commented on that directly but once again has shown a diagram and hyperlink where the potentials in the two regions are exactly the same.

    Colin2B has commented that the (total) Energy, E, of the particle remains constant on both sides of the barrier.
    E.S. agrees with that and would actually strengthen it:   The Energy remains constant wherever the particle is found.   Even if you found it inside the barrier it would still hold.   

(This is going to take a moment to explain since a classical mechanics view of things would make it impossible for the potential V that the particle is experiencing at some place and time to be greater than the total energy of the system.  It would look like the kinetic energy had to be some negative value in order for the total Energy, E, to be less than V.  This might be a topic for later discussion since Aeris has already asked about conservation laws like the conservation of energy but for now I'm going to walk away and leave it there.   The Energy, E, remains constant).

Best Wishes.     

5

General Science / Re: What is Quantum Tunnelling and how does Quantum Tunnelling work?

« on: 30/01/2022 04:26:26 »

hundreds and hundreds of time in the Sun

This possibly refers to the reaction proton + proton = deuterium +  positron + neutrino (+ energy)
- At the extreme temperatures and density in the center of the Sun, protons run into each other at high speed all the time, but the positive charge of the protons keeps them apart. In empty space, the electrostatic force has infinite range, but in the dense proton/electron soup in the core of the Sun, it has an effective range of the distance to the nearest pair of electrons. This is a potential barrier to protons colliding.
- The strong nuclear force is attractive on very small distances, but repulsive at slightly longer distances (and falls to zero quickly). This is another barrier to two protons colliding.
- Very rarely (the rate-limiting step), one of the protons can decay in that short instant when they are in close proximity, and form deuterium, which is stable. This decay is governed by the weak nuclear force, which has an extremely short range. This is another barrier to the formation of Deuterium.

There is energy released in this process (seen as kinetic energy), so it obeys conservation of energy
- Momentum is balanced (in fact it was "missing" momentum that led to the discovery of the neutrino)
- Some of that energy is carried off to distant parts of the cosmos by the neutrino, the positron annihilates in a pair of gamma rays, while the kinetic energy of the deuterium creates heat, the lowest form of energy. So entropy increases.
https://en.wikipedia.org/wiki/Stellar_nucleosynthesis#Hydrogen_fusion

electronics...how radio waves work?

Most modern semiconductors are based on Field-Effect Transistors (FETs), which have an electrostatic barrier produced by the Gate terminal, blocking electrons or holes from traveling between Source and Drain terminals.
- However, a small number of electrons do tunnel through this electrostatic barrier.
- So by small changes in the Gate voltage, you can produce big changes in the current flowing between Source and Drain, producing power amplification.
- In your cellphone, many stages of amplification produce the transmitted signal, and also amplify and decode the received signals.
- In fact, this tunneling, or "leakage current" is a real barrier to progress in semiconductors, as increasing the density of chips requires making smaller FETs. Because they are physically smaller, tunneling becomes more likely, so they consume more power, even when they are supposed to be "OFF".
- So a small amount of tunneling allows transistors to work, but too much tunneling means that they no longer work.
https://en.wikipedia.org/wiki/Field-effect_transistor

The radio waves themselves don't have a barrier to overcome. The sea of electrons move freely with in the metal antenna; oscillating voltages from the transmitter circuitry push these electrons to & fro. This oscillating current and voltage creates disturbances in the electromagnetic field that propagate off "to infinity".

pencils

Pencils contain graphite (carbon) and wood (which also contains carbon).
- the wood contains a small fraction of carbon 14, which is (very slightly) radioactive, and decays with a half-life of 5,730 years
- It is energetically favourable for the C14 to decay, but the Strong Nuclear Force creates a potential barrier.
- Every second, some C14 atoms in the pencil wood will overcome this barrier, and decay
- All the C14 in the graphite decayed long ago.
- These are single-atom quantum tunneling, by distances around the size of a nucleus.
- So the whole pencil won't move
- And it especially won't move by any width that you are capable of observing.
https://en.wikipedia.org/wiki/Radiocarbon_dating

what exactly constitutes as a potential barrier?

It can be any force - examples above have been an electrostatic barrier, the strong nuclear force or weak nuclear force.

Gravity might provide a potential barrier in the vicinity of a black hole (eg Hawking radiation), but in our solar system, gravity potentials are so weak that we never see it as a barrier to be overcome - normal atomic vibrations occur up-and-down just as well as side-to-side.

As the energy of objects increases, they can overcome increasingly strong barriers:
- At room temperature, atoms in air can travel upwards at 1000km/h, allowing you to hear sounds below you. But near absolute zero, the atoms move much more slowly, and have more trouble overcoming the gravitational potential barrier.
- But SpaceX can overcome Earth's gravitational potential barrier - with immense effort. And New Horizons overcame the Sun's gravitational potential barrier.
- At room temperature, electrons in a FET can overcome a potential barrier amounting to Megavolts per meter (over a distance of nanometers). But if you try to operate them at too high a temperature, the thermal energy of the electrons is routinely enough to overcome the potential barrier, and you get more current, increasing the temperature further= thermal runaway.
- In the center of the Sun (or an atomic bomb), Protons can overcome the strong nuclear force.
- Atoms of Uranium routinely overcome the potential barrier of the Strong Nuclear force, and it fissions into smaller atoms.
- Neutrinos can (very rarely) overcome the (very short-range) potential barrier of the Weak Nuclear force, and interact with normal matter.

Oops! Overlap with 2 posts!

6

General Science / Re: What is Quantum Tunnelling and how does Quantum Tunnelling work?

« on: 30/01/2022 03:46:04 »

Hi.

Fascinating. I wonder though, what exactly constitutes as a potential barrier in this regard?

     Just about anything.    Quantum mechanics describes a situation where there is a wave function, usually written Ψ and a "potential" usually written V.   The potential is just a function of position and time.   If you like mathematics V = V(x,t).   That's all there is to it.   The potential is what will create your barrier.
   As Halc stated, the simplest systems to model involve something like a charged particle in an electric field, so V(x,t) is just the electrical potential at position x and time t.    However the potential can be anything you like,   it could be a hybrid of a potential due to the strong nuclear force plus some potential due to some electric field potential... whatever you're modelling at the time.   I've not seen gravitational potential being used but I don't see why it couldn't be.  The source of the potential hardly matters, it's just "the potential" which exists throughout space and time and the particle would experience this potential if it was there (and at that time).
      If we take your chair example and simplify the situation so that we are only asking the electrons in it to tunnell to somewhere else, then the empty space just to the left of the chair is "the barrier".   The chair has some electrons bound to its atoms.  Assuming the nucleii don't move, then we can find some approximation for the potential those electrons experience, most of it will be an elctrostatic potential.   The electrons have a certain energy and will usually be found in certain places where the potential is low, this will be around the atoms in the usual electron clouds.   (The exact solution is going to be impossible to calculate but very roughly we should get a solution like the sort of thing chemists draw for electron orbitals in molecules).   That potential has some value everywhere in space (and time) and indeed there is some small chance of finding a few electrons well away from their usual orbital cloud positions.     The usually empty space just to the left of the chair is a region of such high potential that a typical electron should rarely be found there.   Under classical (not qunatum) mechanics the electron should never be there because it would need an energy that is greater than it actually has (under classical mechanics the electron has effectively escaped from the atom which would demand that it has been given the full ionisation energy normally due for that atom and that electron starting from it's ususal orbital).   Anyway, the point is that the empty space just left of the chair is "the barrier", it's the region where the potential exceeds the energy, E, that is nominally available for the electron(s).
   
      Now, let's go back to considering a simpler system where there is only one particle and some potential V(x,t).   The system has a certain energy, E,  and in classical mechanics there would be no way that the particle you are modelling could be found or should exist in any place or time where the potential exceeds the Energy, E, that was available.   It simply does not have the energy to get there or exist there.   In Quantum mechanics things are a bit different:  The particle that is being modelled with the wave function, ψ(x,t),  can sometimes be found in a region where the potential exceeds the nominal amount of Energy, E, that was available.     Any region where the potential exceeds the energy, E, is called a "barrier".  In classical mechanics it would be very much a hard barrier, there's no way the particle can get beyond it or through it.   In Quantum mechanics a barrier has less effect on the wave function.   Instead of forcing the wave function all the way down to absolute 0 (which is saying "there's no chance of finding the particle here"),  the wave function will usually just fall off rapidly as you move into the barrier, typically you see an exponential fall off with distance and the wave function is often said to become "evanescent".
    An ideal or infinite barrier is one where the potential becomes infinite in value and it's a discontinuous jump (it's finite all the way for x < barrier location and then  precisely at x = barrier location  the potential jumps straight up to ∞ and stays there for x> barrier location).   There's probably no such barrier in the real world but it's a useful idea for the mathematics.   For an ideal or infinite barrier, the wave function is forced to absolute 0 value the moment you enter the barrier.  Only these ideal or infinite barriers act like true hard barriers in Quantum Mechanics.   Anyway, there's not thought to be any real life situation where a potential field shows behaviour like this, the potential may become very large and over a short amount of distance but it doesn't ever go vertical (making a discontinuous jump over 0 distance) and it never reaches an infinite value, just a large but finite value.   So... as far as quantum mechanics is concerned that's not a hard barrier, the particle can be found inisde that region (with a probability that falls off exponentialy as you progress further into the barrier).
    Quantum tunnelling is not just about finding a particle inside a region that should be a barrier.   Usually you have a situation where there are two regions of fairly low potential.   Two patches of space where the particle could easily exist since the system has Energy, E, greater than that potential.  If the barrier between these two regions is only finite (non ideal) then the evanescent wave function (recall that it's falling off exponentially with distance) will reach the other low potential region.  Once it get's there, it's fine it doesn't decay anymore.  The solution for the wave equation should give you perfectly satisfactory stationary states etc.    This is the sort of thing that happens when a particle is created in the first region and fired toward a barrier but there is a perfectly low enough potential region on the other side of the barrier.   What you get on the other side of the barrier is a perfectly stable wave function but just with much lower amplitude then the incident wave function that was sent into the barrier (most of the wave function is simply reflected back into the original patch - but some gets through).

    Wiki has a few good diagrams and animations for this:




    The more general situation that is considered to be Quantum tunneling doesn't involve "firing" a localised quantum packet at a barrier.    Instead you just have a situation where there is a particle with energy, E, and you place no other restrictions on it (don't try to fire it at the barrier, just leave it to exist wherever it can and solve the wave equations to see what you get).   The potential will represent a situation where there are two patches of space with a reasonably low potential and some region between them which is the barrier.  This barrier can even be an ideal or infinte barrier.  Anyway, the solutions you get indicate that the wave function will be non-zero (just to clarify it has time dependance so it might be 0 some of the time at a given place but it's not 0 all the time in that place) in both regions of low potential.   This indicates that there is some chance of finding the particle in either region.   If the barrier was ideal (an infinite square wall barrier) then the chances of finding the particle anywhere between those two regions is always 0,  yet somehow the particle can be found in either of the two regions.   You could find it in the first region today but the second region tomorrow etc.  It's NEVER going to be found in between the two, just in one or the other.   In this respect if we try to explain this as if the wave was a physical particle then we can imagine that the particle tunnels between the two regions in some amazing way,  it seems capable of disappearing from one and re-appearing in the other.    (However, it's never actually going to do that while you are observing the particle, under observation it stays in region 1 or region 2, it isn't going to relocate until the system is left unobserved.  This is a seperate issue, I hardly know why I mentioned it except that everyone always wants to "see" the thing disappear and re-appear - but this thing is more like a magician doing something behind the curtain, you can't see it happening but when it's done the doves have moved from their original cage to other cage).

    That's about all I know about Quantum mechanics and tunnelling.  I can put some equations down but I don't think anyone will want to see that.  Anyway they're in books and they explain it better than I can.

    I can already see that Wikipedia has sections about types of behaviour that they consider to be "Qunatum tunnelling" that I know nothing about.

This is a long post,  I'm signing off for now.

Best Wishes.

7

General Science / Re: What is Quantum Tunnelling and how does Quantum Tunnelling work?

« on: 29/01/2022 17:19:32 »

Nice to see you again. I'm no expert, so forgive my naive and occasionally humorous answers.

1. So... according to various online sources, Quantum Tunneling can happen at any random time to any collection of particles across short or even huge distances. But like, if that's really the case, why doesn't happen more frequently in the macroscopic world?

The huge distances are improbable, so it is rarely measured when it happens. The short distances happen all the time. All electronics and even your thought processes depend on it.

Like, Quantum Tunneling apparently happens all the time, hundreds and hundreds of time in the Sun during it's nuclear fusion energy generating process, but what about the Sun is so particularly special that it happens THAT much?

It happens all the time everywhere. Perhaps there is a process in the sun that depends on it, so it gets good press there. But in happens in your pencil as well, which doesn't result in a noticeable difference so nobody writes articles about that.

Are quantum mechanical effects like Quantum Tunneling more likely to take place in high-energy environments like the Sun's core?

I don't think it is considered tunneling unless there is some potential barrier that ends up getting crossed. So maybe in the pencil, the same effects are going on (essentially teleporting), but sans barrier, it's just probabilistic brownian motion and not officially considered tunneling. In light of that, it is more likely to take place where such barriers of potential exist to cross. It doesn't seem to go to a place of higher potential, so your chair (below) isn't going to tunnel up onto the table like it does in the poltergeist movie.

2. Let's say, hypothetically speaking, a macroscopic object like a table or a chair undergoes Quantum Tunneling and essentially teleports from one location to another while I'm still looking at it. What would that look like?

Straight out of Douglas Adams books and his improbability drive. It would look exactly like it was teleported: now it's here, now it's there. The distance is insanely improbable even for a small particle. To have every particle in the chair do it that distance, and all at the exact same time is improbable to more zeroes that I can express.

would the object just pop right out of and then immediately back into existence in the blink of an eye? Would there be some flashy-looking sparkles or a poof of smoke like in movies and TV shows? Would there be some kind of distortion effect that would hurt my eyes?

If only the chair did it, there would be a pop when air filled the place where the chair used to be. I know, I actually did the experiment once, with an egg. One wonders what happens to the air and dust that was already at the new location for the chair.
As for the egg, I microwaved a boiled and peeled egg, set the plate on the table, went and got some other stuff, sat down, and touched the egg with a fork. It quantum tunneled away with that characteristic pop of the air filling the vacant space. Unfortunately it didn't all go the same direction. I found a good deal of it on the ceiling of the next room, but none at all on my plate.

doesn't the act of them tunneling from one region of space to another in an instant all on their own kind of break several conservation laws?

It seems to, yes. The chair moving say a cm to the left seems to violate the conservation of the center of gravity of a system with no force acting on it. This is true of even a single particle, so more is going on than just this simplistic view. Tunneling seems to occur always from a higher potential to a lower one, so there's already an external force of sorts making it want to go that way, held in check only by the barrier. So the chair maybe can teleport to downstairs despite the energy barrier (the floor) being in the way. But it isn't going to just move left a cm.

If a macroscopic object disappeared right in front of my eyes and then repapered 20 feet in the air, wouldn't that break the law of conservation of momentum?

Not if still stationary up there. You did break conservation of energy by doing that. My chair going downstairs also does. Where did its potential energy go when it did that? At least it didn't create new energy.

Is Quantum Tunneling NOT considered to be a Thermodynamic Process? If so, could it theoretically combat the evilness of entropy and save the Universe from heat death (given enough time of course)?

Nope. The entropy of the universe goes up oodles of orders of magnitude faster than tunneling events can undo it.

4. Like I said earlier, Quantum Tunneling apparently takes place all the time in the Sun's core during the conversion of Hydrogen to Helium

That's a complex process involving many steps. I'm quite aware of two ways to do it (proton-proton reactions and CNO catalyst reactions), but not aware of which of the steps in each method require tunneling.

HOW do we know this?

The quantum gearheads have figured it out. It's apparently impossible by normal means since insurmountable barriers (probably put up by the strong force) cannot be classically crossed.

8

Physics, Astronomy & Cosmology / Re: What do we know about Dark Energy?

« on: 11/01/2022 11:45:25 »

Hi Aeris and everyone.
    I needed a distraction so I had started writing something for this thread a few days ago but it has grown a bit too large.  Rather than just throwing it all away, I might as well just post what I've done.  It's long, so feel free to just ignore it.   I've not checked the spelling or grammar or tidied it up much, sorry

   I have a bit of time to look through this and add some comments, I hope you won't mind.

   Let's race through what we use as the basis for this sort of cosmology and see where "dark energy" and the expansion of space apppears and begs for some explanation.   This is General Relativity and especially the Friedmann equations as far as I'm concerned.

   Space is too complicated to construct the actual stress-energy-momentum tensor that should be used in the Einstein Field Equations.  There are too many planets, bits of gas and assorted stuff all over the place.  We find new meteors in or near our solar system all the time and looking ouside of our solar system we find new stars with our telescopes every week.   The recent Hubble "deep field" photographs demonstrate that what may appear to be fairly empty space at first glance is likely to be full of stars and indeed whole galaxies.   
   So let's assert that there is no hope of constructing the actual stress-energy tensor we would really want.  Some sources will mention that we couldn't realistically solve the Einstein Field Equations with such a complicated stress-energy tensor anyway - this is true but almost irrelevant.  It's not a question of how much computing power could be brought to bear on the problem.  We just DO NOT HAVE the information we need - we would need to know the location of everything in the universe.
    So, what we do is simplify the situation.  There is an assumption that the universe is isotropic and homogeneous.   The commonly used models treat space as if it is filled by something that is referred to as a "cosmological fluid".   What is a cosmological fluid?   See textbooks for a full answer.  I've got to rush over things here:  A cosmological fluid is directly comparable to an ideal fluid in other areas of physics.  Our comsological fluid has many components, each component would behave like a fluid in it's own right.  The cosmological fluid is the fluid you get when you mix all those components up perfectly ("stir well") to create a homogenised fluid.  The use of the term "fluid" isn't suggesting that there is some liquid thing in space, just that the stress-energy tensor we need for GR is equivalent to the stress-energy tensor produced by an ideal fluid. 

   - - - - - -
First stop, or pause for thought
    What if modeling the contents of space as if it is a cosmological fluid is NOT reasonable.   Specifically, we know that space is not isotropic and homogeneous at small scales.   What if this makes an important difference to the final results you extract from General Relativity and the Einstein Field Equations (EFE)?   Let's phrase this another way:  We cannot use the correct stress-energy tensor in the EFE, so instead we use something that is like an idealised average and assumed to remain quite unform across the universe.   We simply hope that the results we obtain will apply to the universe in some average sense, or over large enough scales.
    This might sound like a small issue, if you input an average value n times then you get an output which should be much the same as if you had really inputted n different individual values.  This works well where the function performed on the input is "linear", but it falls apart if the function is non-linear.  The sort of calculations and manipulations perfomed in GR are sometimes non-linear.
  - - - - -
 
    Anyway, what do we get from the Einstein Field Equations with this assumption?  We get the Friedmann equations.
Here's the first Friedmann equation:

     = 

[This form of the Friedmann equation is from page 338, An introduction to Spacetime and Geometry, Sean Carroll]

where H = The Hubble "constant"   (but it's important to note that H= H(t) will vary with time).
   G = usual Gravitational constant.
   ρ_i  =  energy density of the   i th  component of the cosmological fluid.   There is just one value of the index i which represents a "fictitious" energy density contribution from the curvature of space.  To say that another way, there is a term  ρ_c  which is NOT the energy density of a component of the cosmological fluid, it is just here to replace the need to add a term dependant on k into the equation.   (Just for the sake of completion, ρ_c = where k = curvature.   So that, ρ_c, the energy density due to curvature is positive if k is negative and vice versa).


   What do we see from this equation?
  H is real valued,  so  H² is certainly non-negative. 
  Therefore, it is not possible for all of the energy densitiy components  ρ_i  to be negative.
   We can apply the model for arbitrary cosmological fluids, for example, where there is JUST matter and no other fluid components.  There could always be a fictitious energy density for the curvature of space, which is a shame - but we can at least reduce the right hand side of the equation to a sum of just two components.  At least one of these must be non-negative by the earlier reasoning.
    So if the energy density contribution from curvature is negative then the energy density of any (proper) component in the cosmological fluid must be positive.  Editing:   This post is too long, I can't go through all the arguments that suggest energy densities should be positive (they are only suggestions anyway).
    We could just make the reasonable assumption that the energy density contribution of any real component of the contents of space must be positive.  I mean, this is quite reasonable, if there is something there then it should have some mass (which is equivalent to energy density) or else be something with a positive energy like a photon.   However, the full situation is potentially more complicated and I would refer anyone to chapter 4, section 6   of the aforementioned book (Spacetime and Geom, Carroll)  where the various Energy conditions that might constrain the stress-energy tensor are discussed.  Without further discussion, we will be assuming the Weak Energy Condition (WEC), so that all energy densities of any component of our cosmological fluid will be non-negative.

   OK, We need to take the idea that  ρ_i  ≥ 0  for every real component of the cosmological fluid and go forward to look at the second  Friedmann equation:
   
       = 

  Where ρ_i = energy density of i th component  (as before) ;
P_i = Pressure of the i th component.
and  a = a(t) is the scale factor.

   In this equation we don't have to include the index, i, that represented a component from the curvature of space.  We can if you want but the (fictitious) pressure from the curvature component would be precisely negative one-third of it's fictitous energy density, so the whole term  ρ + 3P   becomes 0 and including another 0 in the sum is just needless work.

   Now we are assuming that every ρ_i  ≥ 0.     So if the pressure, P_i , from each component of the cosmological fluid was also positive,    then the entire right hand side of the equation is negative.   Since the scale factor, a, is always non-negative,  we see that    would always be negative.

   This quantity is one parameter that can be used to describe the acceleration of expansion of space.   There is another parameter    which can also be used to examine and describe the acceleration of expansion.  They are not the same and there can be situations where    > 0   but  <0   (for example consider a(t) = t²).  This, I think, is where most of the discrepency between Halc and Origin has come from in one of the earlier posts.
    I'm going to follow the convention from the textbook previously mentioned:

   In practice, "accelerating" usually refers to a situation where >0,  even if  < 0.

[page 339,  Spacetime and Geometry, Sean Carroll]

   Anyway, what we conclude is that if every component of the cosmological fluid had the properties you would imagine for a fluid - specifically that they have positive energy density and positive pressure - then it is inescapable that the acceleration of the expansion of space would be negative  ( <0).  To paraphrase this, the expansion would NOT be accelerating it would be slowing down.

   This is not what we have actually observed.  In our real universe it seems that > 0  at the current time  ("the expansion of space is accelerating").  Let's do exactly what some physicist(s) had to do:  Look at the Friedmann equations again and recognise that what we need is a component of the cosmological fluid that is most unusual.  It would have properties that are unlike any real fluid you might find in your house.  We need a component with negative energy density  OR ELSE  a negative pressure   (or both would be just fine).  This really strange component of the contents of space is what you might like to call "dark energy".

1.   Could it be something with a negative energy density?  Well, maybe.  This would violate the Weak Energy Condition (WEC) but maybe that was just too restrictive and far too optimistic anyway.  We could replace this with another condition like the Null Energy Condition (NEC) which effectively allows a cosmological fluid component to have negative energy density provded the pressure of the fluid is positive and compensates sufficiently.  What does this mean?  Let's be honest, it's not worth discussing here.  See page 175 of Spacetime and Geometry, Sean Carroll if you're intersted.  It's not the choice that most physicists have made and seems less promising as an explanation of what dark energy is.

2.    Could it be something with a negative pressure?  Again maybe.  This is the choice more physicists will make.  It is possible to imagine that there is a component of the contents of space that we will call "vacuum energy".  Vacuum energy can be modeled with the stress energy tensor of a fluid with parameter ω = -1.   All this means is that it's a fluid (as far as the stress energy tensor is concerned) and its pressure is precisely the negative of its energy density.

3.   Just for the sake of completion we could mention that if we were to assume the Strong Energy Condition (SEC) must apply to components of the cosmological fluid, then it is inescapable that ρ + 3P ≥ 0 for every component and then    is always negative.   Hence, the acceleration of expansion is quite bad news for the SEC:   At least one component of the cosmological fluid must have properties that violate the Strong Energy Condition.

  Are we all done? Almost,  we need to just take a quick glance at the Einstein Field Equation (EFE).  Here it is:

G_μν  =  k .  T_μν        (where k = a constant)

  The left hand side involves the geometry, especially the curvature, of space.  The right hand side involves the contents of space.  In particular, the right hand side involves the energy and momentum of the contents of space.  It's an equation, so if you change one side then the other side must change and vice versa - change the other side and the first side has to change.  There is a well known saying that I will paraphrase here:   The left hand side tells matter how it should move.   The right hand side tells space how it should curve. 

    At the moment, with the EFE in the form shown above,    vacuum energy is included in the over-all stress-energy tensor of the universe  T_μν  but we can break this tensor apart into two pieces, one part from the vacuum energy and the other part being... well everything else that isn't vacuum energy  (so that will be the other cosomological fluid components we had in our cosmological model).
   We get this:
G_μν  =  k .  T'_μν    -   Λ.  g_μν         (where  k and Λ = some constants).  Note that T'_μν does have a dash ' in it but it's not printing clearly -  it's not quite the same as  T_μν we have subtracted the vacuum energy component out of it.
 
  Anyway, being an equation, we can take the  last term over to the other side as usual.   We  get this:
G_μν  + Λ g_μν   =  k .  T'_μν        (where k and Λ = some constants)
   Now that form of the EFE shown just above is known as the EFE with a cosmological constant, Λ.   It describes how space curves in response to some stress-energy  given by the tensor  T'    under the assumption that there should be a cosmological constant Λ.    Equally the equation tells us how the contents described by the tensor T' must move in response to spatial curvature given by the left hand side  (under the assumption that there is a cosmological constant Λ).
    There is very subtle shift here but it all happens just because something was put on one side of the equation and not the other side.  I'm going to phrase it another way:   With a cosmological constant, there is a change in the rules of movement for the contents of space.   However, the contents of space is given by the tensor T' which does not need to include any component so strange as vacuum energy (we subtracted that bit out).
     Without a cosmological constant the rules of movement are different (arguably simpler)  BUT  there must be a strange component in the contents space that behaves like vacuum energy.

Finally we're ready to answer a question from Aeris directly:

Has anyone ever considered the possibility that Dark Energy may not exist at all and that the space can just expand without any outside force dark energy acting on it?

   Yes, very much so.   With a cosmological constant in the Einstein Field Equations, the rules of movement for the contents of space are just different and space can expand and indeed accelerate even if all it has in it is just the more conventional contents (not dark energy) that we're all happy with.

Is that all there is to it then?  There isn't any dark energy, it's just that we should have a cosmological constant in the EFE,  i.e.  just accept that General Relativity needed a slight adjustment?
    Most of what we attribute to dark energy can be explained by a non-zero cosmological constant but not necessarily all of it.    The terms "vacuum energy" and "dark energy" are sometimes used interchangeably but there should really be a fine distinction between the two.  Vacuum energy is presumed to be a constant and uniform characteristic (or component) of any volume of space, so it's energy density never changes.  No matter where or when you sample 1 cubic metre of space there should be the same amount of vacuum energy in it.   Dark energy may be something that does have a little variation through space (and possibly time). 
     Here's one example:  Refer to page 360 of Spacetime and Geometry, Sean Carroll  -  where it is suggested that the comsological constant may not quite as  "constant" as we might have hoped.  This means it would be more like a parameter or quantity associated with something specific to that piece of space (let's call it the "dark energy" in that bit of space).   So dark energy mimics the behaviour of vacuum energy as far as General Relativity is concerned but the amount of dark energy might vary slightly across the universe and through time.
    The spatial variation in dark energy should be small (according to Carroll) otherwise the effects of a high concentration in one area of space would have been noticed similar to the way dark matter was detected.

--- This is too long,  I'm stopping now.  Bye and best wishes  ----

9

General Science / Re: Matter is Apparently Made of Fields, But How the Heck does that Work?!

« on: 16/11/2021 00:07:45 »

Soooo... fields, as I've described them in my question don't actually exist and are just an easy way to describe how something in the physical world works and behaves?

They don’t exist in the way you think about them, but what they measure and model are real enough.
Temperature exists, wind exists, the effect of what we call a magnetic field exists.
The last one is a really good example. We define a magnetic field by the force and direction of that force (vector) on a test magnet at a particular point. The force on the magnet is very real, it’s effect is one we can feel. The field is how we describe it.
This field does exist in all space, because in theory the field from one fridge magnet goes out to infinity, although it would be so small as to be impossible to measure it even at a few meters. So now you need to ask a question, does the field cause the magnet or does the magnet cause the field. Field theory doesn’t care, it just describes and predicts the behaviour of things affected by the magnetic field - there you see, our limited language forces us to attribute action to the field 
Not everything is cut and dried, as @Halc says current view is that particle & antiparticle are described by the same field, but we might find something in the future that changes that.

10

General Science / Re: Matter is Apparently Made of Fields, But How the Heck does that Work?!

« on: 15/11/2021 19:10:15 »

Ok so, around two-ish months ago, I was told by a Cosmologist that what we perceive as matter doesn't actually exist and that the alleged particles that we think it's comprised of are actually "Excitations of fields intrinsic to the universe."

It means that fundamentally, matter isn't the stuff with classic properties that we might find intuitive.
Note that matter is made of 'excitations', not made of 'fields' which the title suggests.

Where are these fields even located anyway?

Colin2B gives a good reply to this reference to fields as existing objects, which doesn't work.

Did these fields always exist

A field doesn't seem meaningful outside the context of what is our spacetime. As to 'always', um... there is not a time in which say one could not meaningfully express a measurement of a particular field. This is debatable. Just after the big bang (well under one second), the 'fundamental forces' had not yet separated into those that we know today, and thus their fields may not have been meaningfully distinct at the time.

Are there fields for antiparticles as well as regular particles?

I'm not sure of this. I had understood that a particle and its antiparticle are different excitations of the same field, but it could also be that they're separate fields with symmetric properties.

Does Dark Matter get its own field as well?

Jury out. There's no viable theory of the nature of dark matter at this point. It seems to affect spacetime, which involves gravitations fields, but it seems to not involve other known fields nor even new ones since except gravitationally, it seems not to interact with itself in any way.

What about Atoms and Molecules? Where do they fit in all of this?

Same as people. They're complex things composed of simpler things. They ride the line of classic physics.

Seriously, I cannot stress how much this single statement destroyed everything I thought I previously knew about matter and the sub-atomic world.

Why? What did you 'know' before? The nice classic model of atoms made of nice colored balls with orbiting electrons? That went out the window quite some time ago.
Even the model above (excitations in fields) is more classic than is suspected. It suggests that the field is always in some objective state, however much known or not. This is probably not the case, but some suggest that it is, preferring to abandon rules like cause preceding effect, which I personally find distasteful.

Soooo... fields, as I've described them in my question don't actually exist and are just an easy way to describe how something in the physical world works and behaves?

We measure their values, so that's existence in my book. I suppose it depends on your definition of 'exists'. A field usually cannot be measured directly. Only excitations (differences in the fields at different events) can be meausred. For instance, I cannot measure the gravitational potential of Earth at sea level, but I can measure the change in that potential between sea level and 100 meters up.

11

Physics, Astronomy & Cosmology / Re: The Physics of Neutron Stars

« on: 11/11/2021 20:56:26 »

Oh. So... it's NOT made only out of Neutrons? That's... honestly really lame, ngl.

Apparently the protons (or more accurately, positively charged 'quark soup' as evan points out) and electrons can't get to each other, preventing further reactions that would make more neutrons. Still, how do the protons end up in the middle instead of mixed through the neutrons like they are in a large nucleus? Under such conditions, they are perhaps more dense, allowing more mass to pack into less space, and hence the neutrons buoy up forming the 'insulating' layer outside. I can't say for sure.

Does Dark Matter even react with ANY of the four forces?

Just gravity, and if you don't count that as a 'force', then there's only three forces and dark matter doesn't interact via any of them. But dark matter still causes gravitational time dilation if you concentrate it somewhere, so that's a gravitational effect.
Dark matter shoots straight through a neutron star and back out, but if it comes within the photon-sphere of a black hole, it's not ever coming out, and it adds to the mass of the black hole.

I've been led to believe that all of the Sun's energy came from the nuclear fusion processes happening in its core where Hydrogen atoms are fused together into Helium.

That's a very short description, but hydrogen is made of just a proton, and the neutrons need to come from somewhere, so the process has to involve the creation of them if it is to make helium, which is two of each. That's why our attempts to fuse hydrogen on Earth first has to find the rare isotope of hydrogen ²H with the neutron already present. ¹H (a lone proton) just doesn't fuse to anything.

Not too long ago I was told that the Sun also produced Antimatter.

Yes, as part of the neutron-creation process. Two protons collide and one emits a neutrino and a positron, leaving a neutron behind. Charge/lepton-number is nicely preserved. Everybody goes home happy.

Is there anything ELSE that the Sun does that I don't know about?

We all could spend a lifetime and still not know all about the sun, or about any other subject for that matter.

I didn't mean ignore as in get rid of. I meant ignore as in you, the person touching it, weren't affected by the things whatsoever (basically Superman).

Hard to say. What are you touching? The outermost layers? That's like touching Earth by colliding with one upper-most atmosphere atom. You'd not notice.
With a neutron star, it would be fatal to a human to even get close to it, like in low orbit or something. So you'd need to be superman just to be there, let alone actually contact anything.

So I said it was 'hard'. You'd not be able to move the surface, except to make waves of some sort in the atmosphere.

Engineer was the wrong word. I meant extracting pieces of a Neutron Star with a giant megastructure of sorts and then building materials and objects from that. Would that be slightly more plausible?

You'd have to use something like EM force to do it, and it obviously is being dwarfed by the other forces, so no way to touch it with any tool without the tool just becoming part of it.
If you had a piece of it, it wouldn't be stable for even an instant, and would probably act like a bomb or something. It needs the pressure to be stable.

12

Physics, Astronomy & Cosmology / Re: The Physics of Neutron Stars

« on: 11/11/2021 20:37:41 »

Question 1. Are Neutron Stars really made up of ONLY Neutrons

As mentioned above, there is a thin outer shell of plasma (iron nuclei and electrons), at extremely high temperature (eg 600,000C).
What is in the middle is less clear - we can't easily bang neutrons together at high velocity and see what happens.
Some people think that at extreme pressures, there may be a further phase change, and the individual neutrons might break down into a denser "quark soup" - a so-called quark star.

The NICER experiment on the ISS is trying to confirm this theory (or not) by measuring the radius and mass of neutron stars; from this they can see if the density exceeds the maximum packing density of neutrons, implying that quark stars might exist.
 See: https://en.wikipedia.org/wiki/Neutron_Star_Interior_Composition_Explorer

Question 3: would be logical to assume that (neutron stars) too don't interact with light .. and would therefore be invisible as well

The extreme temperature of the outer shell of a neutron star produces "black body radiation" extending well into the X-Ray region of the spectrum, and down into the infra-red (the intense radio pulses of certain neutron stars "pulsars" possibly come from other mechanisms to do with the intense magnetic field).
"Hot Spots" on the surface act as a lighthouse, spinning around so we see them flashing in our direction.

Question 5. What would a Neutron Star feel like to touch?

You can't touch it.
The intense gravitational field would rip your fingertips off your fingers, rip your fingers off your hands, and rip your arms off your body (spaghettified).
And all this before you came even close to the neutron star.

extracting pieces of a Neutron Star with a giant megastructure

You are describing mining a neutron star.

Let's think of the reverse - how a neutron star is formed.
Something 1 to 1.5 times mass of the Sun (say 1 million km across) compresses down into a neutron star perhaps 20km in diameter, 50,000 times less.
As soon as you extract a piece of neutron star, it would be relieved of the intense gravity holding it together, and all the neutrons would rapidly decay (about half every 12 minutes), forming a hot, intensely radioactive plasma that takes up 10¹⁴ times more volume - the ultimate neutron bomb.

This is added to the problems of the spaghettification of your equipment, the fact that it would be crushed into a mere smear on the surface (even mountains are thought to be less than 1mm high) and the fact that no solid matter can exist at the 600,000C surface temperature of a neutron star.

brain-scratching

If you want to read a science fiction novel that weaves an alien plot around the known (or inferred) physics of the surface of neutron stars, Read "Dragon's Egg" by Robert Forward.
https://en.wikipedia.org/wiki/Dragon%27s_Egg 

13

Physics, Astronomy & Cosmology / Re: The Physics of Neutron Stars

« on: 11/11/2021 18:03:31 »

Question 2. Assuming Neutron Stars really are made up of only Neutrons, what exactly holds them together and keeps them stable? I mean, it can't be the Electromagnetic force if it's made up of only Neutrons, right?

Gravity holds them together. They're stable because there's nothing else they can be. It would require energy to say decay them into a proton/electron since there's no room for that pair. So it's stable.

It's not just a solid ball of neutrons. The inner crust is made of essentially superfluid neutrons. The outer crust has ions and electrons. The outer core has protons of all things, implying a massive charge imbalance between the inside and outside.  See wiki page showing pictures of the how the more current models lay it out.

Question 3. The reason why we're not able to see Dark Matter with our eyes or our various forms of technology is because it doesn't interact with the Electromagnetic force and therefore doesn't emit, reflect or even absorb light. If Neutron Stars had a similar thing going on, it would be logical to assume that they too don't interact with light in any way shape or form and would therefore be invisible as well.[/quote]Of course they interact with the various forces. Something needs to keep it from collapsing, which is mostly the strong force. Dark matter doesn't interact with the strong force, and would pass right through a neutron star and out the other side. Light does not do this, so a neutron star doesn't behave at all like dark matter. They emit/reflect light just fine, so you can see them.

Question 4. According to a YouTube video I found online, Neutron Stars form when the pressure of a collapsing star gets so great, that Protons and Electrons fuse together into Neutrons. Assuming this information is correct, how the hell does this not violate conservation of Baryon and Lepton number?

This goes on all the time in our sun, creating neutrons at the rate of tons per second, and no violation occurs. It does involve creation of a neutrino which probably exits the star. See proton-proton reaction.

Question 5. What would a Neutron Star feel like to touch? Obviously we would have to ignore the existence of the insane thermal radiation, blinding light, super strong gravitational field and super strong magnetic field

That eliminates pretty much all of what it would be like. It's just a hard rock with all that taken away, despite it being liquid on the surface.

but would the star itself feel like normal, gaseous plasma stars, or something else entirely?

There is an atmosphere if that's what you're asking. The hard part is below that. Our sun is pretty much all plasma

If it really is made up of only Neutrons, would you just fall right through it

Of course not. The other forces would prevent you from penetrating, else it would fall into itself.

the lack of the Electromagnetic force simulating the sensation of touch (this is after all, the force that allows things to touch each other in the first place).

That's because EM stops you before your atoms get close enough to the door knob to allow other forces to come into play.

Questions 6. How feasible on a scale of 1 to 10 would it be to engineer everyday objects and materials out of the same stuff Neutron Stars are made of?

Would think not at all. It isn't stable without the pressure, and there's no EM way to generate that sort of pressure.

No idea about strangelets.

14

General Science / Re: Even More Questions that Antimatter to Me

« on: 06/11/2021 23:51:58 »

Hi again,

Ah, I see. So even if we found a way to magically remove the virtual particles popping in and out of existence all of the time, we would still have underlying, universal fields in space representing each of the four fundamental forces that hold all of existence together, thus preventing it from ever being truly empty. That also means that photons (and all forms of electromagnetic radiation) can exist independently of matter. Sweet!

    Yes, that's the right idea.
    Sadly, there's some junk or technical details that get in the way.  We couldn't remove all the virtual particles, they are a consequence of the field existing and quantum uncertainty.  So the only way to remove the virtual particles would be to remove the field.   Also, it's not certain that the four fundamental forces as we know them would exist in exactly the same way during the early universe.  The electromagnetic force seems to unify with the weak force to become the electro-weak force, for example.  So some of the fundamental forces are "missing" or blended into one.    However, you do seem to be expressing the general idea correctly.   Don't forget that matter particles like leptons and quarks should also be represented by their own fields (these particles are just excitations in their own underlying field, which just like other fields also exist throughout all of space).  So all we're really saying is that a photon field could have excitations in it (photons can exist) without any requirement for the matter fields to have some excitation (no matter particles have to exist).

it seems highly unlikely that, if I ever did take up a career in the world of science and physics, you'd be one of the people I'd teach.

    In a few years, if I can still work a computer, I will be needing help and some tolerance from people like yourself.

Best Wishes.

15

General Science / Re: Even More Questions that Antimatter to Me

« on: 06/11/2021 21:58:14 »

Hi.

Happy birthday to your dad.

Sooooo... the asymmetry that allowed regular matter to triumph over antimatter was brought about by the early universe being in a state of insanely high energy? It's that simple?

   I don't KNOW that for certain.  No one does at this time.   However, it seems likely.
You're partially ignoring the state of the Inflaton field and the Higgs field.   Specifically inflation (if it occured, which most physicists think it did) had only recently stopped in the early universe when matter synthesis was happening.   So the energy in the inflaton field had fallen but possibly not as low as it is now.  I'm not aware of any experiments that claim to influence the inflaton field.  Simply getting to high energies (like high velocity particles that might locally re-create conditions of high temperature and pressure) may not be enough to set the inflaton field back up to to the state it was in.

Also theoretically speaking, if we COULD find a way to replicate this process, how much matter could we create before we unintentionally spawn a black hole?

   I don't do these experiments, they are a bit beyond the tools I have in the kitchen.    There was some media hype a little while back about the possibility of accidentally creating a micro-black hole at CERN.   Of course the media didn't really say that it COULD create be a MICRO black hole   only that CERN could create a Black Hole.
    Here's some relevant web-pages:
https://scoolmedia.com/en/cern-creates-a-black-hole-that-they-can-not-control/
   Here's one quote I quite like......
...Scientists did succeed in making a black hole and
they could not control it. The microscopic black hole dropped right through the particle
accelerators containment fields, gravity pulled the hole towards the center of the Earth where
the hole now is growing bigger by absorbing the atoms surrounding it. It is growing slowly now
but with every minute passed it is getting larger and larger at an ever increasing pace. A few
days are left until the hole will grow big enough and two jets from two opposite sides of the
Earth will blow up and prove us that there is a giant black hole eating our world from the inside
out.

    This is the somewhat more credible version.   It's not that different, I suppose....
https://science.nasa.gov/science-news/science-at-nasa/2008/10oct_lhc
The world did not end. Switching on the world's largest and most powerful particle accelerator near Geneva, Switzerland, did not trigger the creation of a microscopic black hole. And that black hole did not start rapidly sucking in surrounding matter faster and faster until it devoured the Earth, as sensationalist news reports had suggested it might.

Anyway....  the important thing to note is that creating a microscopic black hole isn't as dramatic as creating a science fiction sized black hole.   Hawking radiation increases in rate as the size of black hole decreases,  so microscopic black holes should last only a fraction of second and they are only harmful in the sense of creating huge tidal forces in a region that is extremely close to them.    If a black hole formed that had the mass parameter of a particle,   then it creates no more gravitational pull on you (at a distance of say 5 metres) then the original particle had.   Let's phrase that another way,  we all experience some gravity on the surface of earth.   However we could replace all of that matter with a tiny black hole right where the centre of the earth was.  If that black hole has the same mass parameter (e.g. if it was made from the stuff the earth was made from but just compressed into a small size).   Then provided you find a way to stay a distance away from the black hole that is equal to the radius of the earth you wouldn't notice any difference in the force of gravity.
    Anyway,   CERN were hoping to observe interesting things that might even include a micro black hole   BUT  to the best of my knowledge, they haven't.

    So, I don't really know how to answer your question:  We could spawn lots of black holes but it doesn't necessarily need to be too much of problem.   We are getting close to the sorts of energy densities that should create a micro black hole.  The main problem is likely to be that the black holes would rip the particles created in the close region into .... only speculation knows.... and/or merge with them to make a larger hole for a brief moment.   So it could be more of a production problem rather than anything else:   Do you recall A level organic chemistry where the yield of the product you wanted to create is lower than you hoped for?  Usually because the conditions were wrong - like it was too hot and some other products were formed and/or some of the desired product was accidentally decomposed.   Anyway, a blackhole could be a bit like this - something ruining your yield of desired product.

Best Wishes.

16

General Science / Re: Even More Questions that Antimatter to Me

« on: 05/11/2021 22:43:38 »

Hi again.

do you think you could tell me what exactly those conditions were by any chance? Could you at least tell me what we think those conditions were?

    Around the time of the big bang we expect the temperature, pressure and energy density to be extraordinarily high.  Physicist's often lump all of these descriptions and properties together and just say they are high energy conditions.  There may be other conditions like the inflaton field having only just switched off and/or the Higgs field having only just switched on (i.e. fields that we don't seem to be able to influence at the moment).
    There doesn't seem to be the technology available to recreate and also safely contain these extremes conditions and there are some theoretical limits anyway:  Since energy density and pressure are both sources of gravitation we could easily create a black hole by accident  (which would obviously tend to conceal what had actually happened during the experiment).   We are talking about establishing conditions that are within a hairs breadth of causing a singularity.   After all, baryogenesis and leptogenesis were thought to have occurred only a few moments after a singularity.
    At these sorts of energies it's thought that most of physics would be quite different.   Most of the theories we have are thought to be only low-energy approximations to the underlying principles.

If matter didn't exist yet at this point in time, that means that electromagnetic fields didn't exist either.

    That's not necessary.   The electromagnetic field exists and permeates all of space,  independently of whether there is matter there or not.   For example, an electric field exists even across a vaccum and any charged particle you had on the one side of that vaccum would still feel a force from a source on the other side of that vaccum.   EM radiation can certainly exist in and travel through a vaccum (infact it only has the speed c when it is doing this).
  (Technically the electromagnetic field is terminology associated with a classical field theory of electromagnetism and at these sorts of energies and relativistic conditions we should probably be using a quantised version but the principle would be the same.  Matter is not required).

Best Wishes.

I'm having a fun time talking about this stuff with you guys you're really helping me out.

   Great.  You're going to be helping me out in a few years and probably not just with some physics.

Best Wishes.

17

General Science / Re: Even More Questions that Antimatter to Me

« on: 05/11/2021 13:31:20 »

Hi again.

2. What are you referring to when you say when you say general theory?

   I was being quite vague.   Most theories concerning the standard model of particle of physics (so that'll be Quantum Field theory mainly) state that the baryon number and lepton number is always conserved in any interaction.     (See, https://en.wikipedia.org/wiki/Baryon_number,  for example).
     The synthesis of matter from photons seems to do this by always creating matter and anti-matter pairs, whenever the process has been observed in experiments.
   

3. When you say lepton number and baryon number must be conserved, what exactly do you mean by that.

   For a system the Baryon number, B, is a quantum number defined by
B =
    Where n₁ = the number of quarks in the system    and  n₂ = the number of anti-quarks in the system.

Similarly Lepton number is   L = N₁  -  N₂   where  N₁   and  N₂ are the numbers of Leptons and anti-Leptons  respectively.

    Along with  statements like this:
In particle physics, lepton number (historically also called lepton charge)[1] is a conserved quantum number representing the difference between the number of leptons and the number of antileptons in an elementary particle reaction.[2] Lepton number is an additive quantum number, so its sum is preserved in interactions     - Taken from https://en.wikipedia.org/wiki/Lepton_number.

Examples include radioactive decay by  Beta^-  emission.
   n    →     p+  +  e^-   + 

Initially (on the left hand side) we had a neutron,      B = 1  and no leptons   L =0.
After the interaction we have a proton   B =1   and an electron (L=+1) but also an  electron anti-neutrino  (L = -1)  giving a total  L = 1 - 1 = 0  = exactly the same as we started with.

Is it like conservation of charge where the net amount of leptons and baryons in the entire universe is zero?

   Yes.  See above.   Technically, the conservation of lepton and baryon number only implies that whatever these numbers were to start with, they never change after any interaction.   So  they would be exactly 0 all the time    if and only if   they were 0 initially.   However if there were some leptons and baryons around just after the big bang then that is the total number that will be conserved from then on.    (We think that there was only radiation around just after the big bang and leptogensis and baryogensis happened shortly afterwards).   

Are our current models of the universe dependent on those qualities being conserved, or will something terrible happen to the universe if they aren't conserved?

   Conservation of these quantum numbers helps to explain why we don't observe some interactions. 

Lepton number was introduced in 1953 to explain the absence of reactions such as
    ν    + n   →    p  +    e−   - Taken from Wiki.

   However, I'm not sure that it actually arises as a necessary condition from some piece of mathematics that describes the quantum mechanics.  It just seems to be an assumption in the standard model of physics and it is is empirically or experimentally supported (but I don't know for certain).
   Certainly there are some theories that suggest Lepton number and Baryon number do not need to be conserved.
   See:    "Violations of Lepton number conservation laws"   https://en.wikipedia.org/wiki/Lepton_number#Violations_of_the_lepton_number_conservation_laws   
  and also,    "Physics beyond the standard model"      https://en.wikipedia.org/wiki/Physics_beyond_the_Standard_Model

Will something terrible happen to our universe if they aren't conserved?  Well, the universe will presumably carry on doing what it's been doing regardless of whether we understand it or not.   We (human beings) will drop the assumption that Lepton number and Baryon number is necessarily conserved but I don't think it will shake the usefullness of the standard model of particle physics too much.  Under typical situations the standard model does seem to be a useful approximation or model even if there are some unusual situations (perhaps in the time close to the big bang) where it's not so good.
    As people have already mentioned, we do believe that there is more matter in our observable universe than anti-matter and so we are all expecting that there is at least some mechanism whereby lepton and baryon numbers are not conserved.

Considering there's practically no antimatter in the entire universe, that seems quite unlikely to be the case, so what exactly is wrong with the idea of a process that results in the formation of only regular matter and no antimatter?

   Many physicists do expect that there is (or was) such a process, or alternatively some process whereby anti-matter decays (presumably back into photons) faster or more preferentially than ordinary matter would undergo the same process.   It may have required conditions that were only around just after the big bang, so it may not be repeatable now.

Best Wishes.

18

General Science / Re: Even More Questions that Antimatter to Me

« on: 05/11/2021 02:39:01 »

Hi again.
 

1. We can already create pairs of particles using this process, but can we potentially go a little further and create full-on atoms and molecules? Maybe some hydrogen gas or some water or something?

   You've had a good answer from Halc concerning creation of anti-matter atoms.
I'm suspicious you wanted an answer about creating ordinary matter atoms and/or entire molecules.  I'm also suspicious you have an eye on the science ficition ideas of creating matter in something like a start trek transporter or whatever the thing is they make stuff in...  a replicator I think - where Captain Picard gets his cup of Earl Grey.
    Well,  making an entire atom all in one go,  or straight from a photon is asking a lot but I suppose it's not impossible.   The energy of the photon(s) has to match or exceed the total rest mass of the particles you are hoping to create.  So for an entire  atom of hydrogen  plus  its partner  anti-hydrogen  that  works out at a photon with an energy of  1.88 GeV or more.   I haven't done that calculation... just found it on a web-page but it looks about right.   The protons and anti-protons are much more massive than an electron and positron which you could create with just 1.022 MeV.     Or to say it another way, the protons need  about 1800 times more energy in the gamma ray because they are about 1800 times more massive than an electron.    I really don't know if we have equipment to create gamma rays with that frequency, its pretty serious cosmic ray stuff.
     Anyway supposing you can get the photons (you know.... on the Google shopping channel it's amazing what you can get these days), you could try and fire those at some dense nuceli and hope for some of them to change into hydrogen plus anti-hydrogen.   Now these photons are so energetic that their penetration and absorption characteristics are quite different to the soft gamma rays that produced position-electron pairs.  These hard gamma rays will frequently just go through a gold target as if it wasn't there.   You'd hope to fire millions of these gamma rays at a gold target and only get a few to interact.   There's also very little you can do to stop other particles being created.  It's not certain that a proton and an electron would appear, you might just get a proton (and it's anti-proton) and the remaining energy of the photon might just give those protons more kinetic energy than usual.   To say that another way, it's not certain that all the energy of the incident photon would be changed into rest mass, some of it might be converted into kinetic energy for a smaller particle.   Anyway... the whole process has become extremely random.   If you get anything at all it'll be a shower of assorted stuff, some of which would have very high velocities and you'd probably never be able to capture it - but maybe a small portion of that stuff would actually be an entire atom of hydrogen (and anti-hydrogen or bits of anti-hydrogen that have fallen apart).
    CERN do not make their anti-hydrogen this way.  It's far more efficient to make the smaller components like positrons and anti-protons and then they almost self-assemble themselves into anti-hydrogen.  They don't even try to make the anti-protons straight from photons but instead they bombard a metal target with ordinary protons and collect some anti-protons that are produced from that.  Even the positrons aren't synthesised from photons, instead these apparently come from a radioactive sodium source that just emits positrons as part of it natural decay process.   All they do at CERN is collect these components, slow them down and allow them to come into contact inside a trap and then just wait for self-assembly into anti-atoms.    (Information source:  https://newscenter.lbl.gov/2010/11/17/antimatter-atoms/).
   In principle if you have a pair of anti-hydrogen atoms close together (and cold, i.e. at low velocities) chemistry should take over and they should self-assemble into a complete molecule of  anti-Hydrogen gas  ( I think the molecular formula has a bar over the H    like   this      ).
    Anyway, just focusing on the oridnary matter and not the anti-matter.  It would be more efficient to just try and sythesise the protons and electrons (probably in seperate places) and then push those protons through a cloud of electrons.  Since they have opposite charges they will attract and self-assemble into atoms of hydrogen at-least a fair portion of the time.  We already know that chemisry can take over form here and two atoms of Hydogen in close proximity will self-assemble into a molecule of Hydrogen gas (provided they are cold, i.e. have fairly low velocities).
    It's a bit messy and extremely random with high energy gamma rays and high velocity particle fragments flying off all over the place, plus it's a bit of hybrid between sythesising some elementary particles and then just sitting back and waiting for ordinary physics and chemistry to build a molecule for you.   However, with a few years of refinement it might look a little bit more like the replicator where Captain Picard gets his cup of Earl Grey tea.

Best Wishes.

19

General Science / Re: Even More Questions that Antimatter to Me

« on: 04/11/2021 22:28:45 »

It's important to remember that the "laws" of physics are descriptive, not prescriptive. They are how we observe the universe to work, not how some authority has ordained that it must work. So it's entirely possible that the creation of the observable universe did not follow some or indeed any of the laws we see in action every day, and even possible that we may occasionally observe some residue of the prior universe that seems to breach those laws.

20

General Science / Re: Even More Questions that Antimatter to Me

« on: 04/11/2021 16:22:40 »

Hi again.

I never said what else was involved and I don't think it matters, the point was that photons can be directly converted into a electron and a positron. 

    Yes, exactly -  and this relates to one of Aeris' questions in the most recent post....

C) Is there any evidence for particle synthesis and is it a process that we could theoretically recreate on Earth (be it now or in the distant future)?

1.   We can make positrons and electrons from gamma rays.  Just fire them toward some dense nuclei (like a lump of gold).   It's random but you get a fair chance for particle and anti-particle pair production if the nuclei have a high atomic number (like Gold) and also the gamma rays are of a frequency corresponding to an energy significantly above 1.022 MeV.

2.   There are also some reports where particle and anti-particle pairs have been created just by the collision of two photons  (i.e. without the need for a dense nucleus in the vicinity).   (see https://en.wikipedia.org/wiki/Matter_creation  but note that there are few credible sources and references on that article and I haven't read any of those myself).  It seems that this should happen and it is what we think must have happened in the early universe (since there wouldn't have been any dense nuclei around to get involved with matter creation until after there were already some nuclei).

3.   It is possible to create all fundamental particles in the standard model, including quarks, leptons and bosons using photons of varying energies above some minimum threshold, whether directly (by pair production), or by decay of the intermediate particle (such as a W− boson decaying to form an electron and an electron-antineutrino).  - quote from Wiki.   This is mainly a statement of theoretical possibility and I'm quite certain that we have NOT actually seen a great many heavy particles being created from photons in any experiments:   In no small part this is because the energies of the photons required are huge.  To create baryons like a proton and an anti-proton we should require photons in the hard gamma ray range,  > 1.88 GeV,  or  3 orders of magnitude higher than the experiments we have done to create electrons and positirons. 
    - - - - - -

It should be noted that in all of these particle synthesis reactions, we do seem to create everything in matter and anti-matter pairs.  This, along with the general theory suggests that quantities like "lepton number" and "baryon number" must be conserved.

Best Wishes.