heisenberg uncertainty principle - What is meant by "Nothing" in Physics/Quantum Physics?

I am not a phycisist, so please forgive my ignorance. This is related to my posts and this.
I am trying to understand what is meant by the term "Nothing" in physics or Quantum Field Theory (QFT) since it seems to me that this term is not used in the way we understand it in everyday language.

So QFT seems to suggest (in a nutshell) that "things pop out of nothing".
But from wiki I see the following quote:

"According to quantum theory, the vacuum contains neither matter nor energy, but it does contain fluctuations, transitions between something and nothing in which potential existence can be transformed into real existence by the addition of energy.(Energy and matter are equivalent, since all matter ultimately consists of packets of energy.) Thus, the vacuum's totally empty space is actually a seething turmoil of creation and annihilation, which to the ordinary world appears calm because the scale of fluctuations in the vacuum is tiny and the fluctuations tend to cancel each other out.

So what is "Nothing" in QFT? If this quote is correct, I can interpret it only as follows:
The "Nothing" is not in the way used in everyday speech but is composed of "transitions" i.e. something that is "about to become"
Is this correct? If yes, why is this defined as "Nothing"? Something that is "about to become" is not nothing but there is something prerequisite.
In very lame terms: Einstein was born a non-physicist but became a physicist, so if this is a correct analogy, then there

1. there is something underlying that was non-something that became something


2. A non-something came into something because something else (not nothing) permitted it to become. E.g. Einstein's talent (or Mozart's) would have been lost had he been born in Africa or in a country with no educational facilities. So he would not become a physicist (but the required talent would be present but not come into reality)

Could someone please help me understand this (perhaps trivial to you) concept?

Answer

In Physics "nothing" is generally taken to be the lowest energy state of a theory. We wouldn't normally use the word "nothing" but instead describe the lowest energy state as the "vacuum". I can't think of an intuitive way to describe the QM vacuum because all the obvious analogies have "something" instead of nothing "nothing", so I'll do my best but you may still find the idea hard to grasp. That's not just you - everybody finds it hard to grasp.

Start with the classical description of an electric field (Maxwell's equations). It's not too hard to image an electric field as a field filling space. You can even feel the field: for example if you put your hand near an old style TV screen you can feel the static electricity. You can imagine turning down the electric field until it disappears completely, in which case you are left with the vacuum i.e. nothing.

Now imagine the same field, but this time we're using the quantum description of the field (Quantum Electrodynamics instead of Maxell's equations). At the classical level the field is approximately the same as the description Maxwell's equations give, but now we have fluctuations in the field due to the energy-time uncertainty principle. Just as before, imagine turning down the electric field until it disappears. Unlike the classical description, the (average) electric field may disappear but the fluctuations do not. This means the quantum vacuum is different from the classical vacuum because it contains the fluctuations even after you've turned the field down to zero.

The key point is that when I say "turn the field down" I mean reduce the energy to the lowest it will go i.e. you can't make the energy of the electric field any lower. By definition this is what we call the "vacuum" even though it isn't empty (i.e. it contains the fluctuations). It isn't possible to make the vacuum any emptier because the fluctuations are always present and you can't remove them.

astrophysics - How do neutron stars burn? Is it decay or fusion or something else?

• What makes a neutron star burn, and what kind of fusion/decay is happening there?


• What is supposed to happen with a neutron star in the long run? What if it cools, then what do the degenerated matter looks like after it cools? Will the gravitational equilibrium be ruined after some burn time? How does it explode if it can explode at all?

Answer

With normal stars, the "burning", that is to say the fusion reaction, produces a pressure that counteracts the pull of gravity to keep the star from collapsing. But with neutron stars, the protons and electrons in the star have combined into neutrons*.

The Pauli exclusion principle causes the neutrons to resist further compression. That is, the neutrons, being identical fermions, can't all be put in the same state. So to get them closer and closer together you have to go into higher and higher energy states. Thus, there is an energy cost in compressing the star, and this results in a sort of pressure called "degeneracy pressure".

It is this pressure that stabilizes the neutron star against collapse (assuming it doesn't have enough mass to overcome this pressure and become a black hole). So they don't need to "burn" to maintain their stability, and so far as I know, they don't. At least not in the sense of a normal star where you have atomic nuclei fusing.

• Note: Neutrons aren't made of protons and elections, but this transformation can happen by means of the weak nuclear force. Normally neutrons aren't stable outside of the atomic nucleus -- instead the transformation would go the other way and a free neutron would decay into a proton and electron (there's also an anti-electron neutrino produced). But under the intense gravitational pressure in a collapsed star, the neutrons are stable, which allows us to end up with neutron stars.

Edit: This is of course a very approximate picture. The link posted by Thomas Thernel has much more detail. One good point to emphasize is that, as you might expect, the density is greater at the center of a neutron star than at its outskirts, so the star won't really be all neutrons... you'll have more neutrons closer to the center, and more ordinary atomic nuclei further out. Apparently some interesting sorts of structures can form from the remaining nuclei, even at the point where it's 90-95% neutrons.

logical deduction - 6 prisoners, 2 colors, one mute

Just like the classic 4 prisoners hats riddle, here we have 6 prisoners buried to their necks in the ground. They can only look straight ahead so that A only sees B, C, D, E while B sees C, D, E, and so on and F is completely hidden from view. The warden gives them each hats and tells them that there are 3 red hats and 3 white hats. The warden also tells them that he has cut out one prisoner's tongue (in this case C) so that he cannot speak at all (the mute knows that he is mute). All prisoners are executed if they make any noise other than to clearly announce their own hat color. If a prisoner answers correctly, all prisoners will be set free. If incorrectly they will all be executed.

One prisoner will be able to say his own hat color with certainty. Which one?

---

To clear up some confusion:
1) No prisoner knows who the mute is except the mute himself.
2) The picture is how the story actually went down.

3) The lateral thinking tag was added just because the solution takes some time-dimensional thinking.

Answer

It will be

B.

Both A and B can see, what C sees, and that's why they both know that

C knows his hat colour: If C had a white hat, then both A and B would be able to trivially announce their hats. Neither did, and they cannot both be mute, so C must know that his hat isn't white. Because C isn't announcing his colour, both A and B know that C must be the mute.

From there, the problem reverts to the earlier one:

B knows that A isn't the mute (because C is), and also that A isn't seeing three white hats (because A has't announced his hat), so B can decuce that his hat is red.

quantum field theory - On scheme dependence in QFT renormalization

I searched for the answer to my question quite a while and it seems nobody ever asked similar questions or it is written explicitly in any textbooks. The question is,

1. If physical parameters of any theory change with energy scale at which the theory tried to describe, then why are those physical parameters listed on the cover page of any physics textbook (say, on the cover of many modern physics textbooks the electric charge $e = -1.602 \times 10^{-19}\;\mathrm{C}$, electron mass = ..., and so on are listed) are not associated with any energy scale at which the experiments are conducted to measure them? Is it because these parameters are quite insensitive to the energy scale under which the parameters are measured? but then how insensitive?

Below is what I know and my basic understanding of my problem. I just learned that parameters in a QFT change with the energy scale at which the theory tried to describe. I have also seen some path integrals associated with some kinds of Feynman diagrams diverge, that is, the embarassing perturbative expansion where each term diverges.

The initial renormalization idea is that parameters are not physical. They are just parameters to describe the physics of interest. So, there can be a gap between physical parameters like physical mass and electric charge and bare parameters. (Well, I think this idea is really...lame honestly speaking, how can you just change your face and turn around to say those parameters are not parameters you thought just because your way to calculating things does not give you a consistent answer?)

Well, so one simply cheats by separating the bare parameters into a physical, finite piece which is what we want and a divergent piece which is unphysical. For example, m_b = m_phy + m_div, where m_b is bare mass and m_phy is physical mass which is finite and m_div is infinity. This is sort of absorbing path integral infinity into the counter term part m_div.

This comes to my second question (though I think this one will be answered if I keep learning renormalization of QFT):

2. How do we deal with the arbitrariness of writing (infinity) = (finite) + (infinity)?

I have read the regularization part of QFT textbook and OK with the calculation to separate the divergent part of a path integral, i.e. introducing some cutoff or arbitrary energy scale and to write the divergent path integral as some pole (which is the divergent part) plus the finite part which usually depends on the arbitrary energy scale if using dimensional regularization. However, as expected, the finite part depends on some arbitrary new parameters you introduced to "regularize" the divergent path integral. Then, how can we start to do prediction? how do we get rid of this arbitrariness? What comes to my mind is to conduct a few experiments and fit the finite part (which contains arbitrary energy scale) with the experimental values you measured. After this is done, one can start to predict in other experiment.

A classical explanation of the changing electric charge under different scale is the screening effect caused by vacuum polarization. I think this argument is OK as I accept vacuum fluctuations. However, if this is true, why did no one ever told us that?

"Be careful, the values of the physical parameters showing on the cover page of your modern physics textbook actually change if you conducted the experiment at a different energy scale!"

Answer

If you look at the PDG, equation ($10.7d$), you'll see that they define the electromagnetic constant $\alpha$ at a precise scale (the mass of the muon in this case). Later on they also give the value at different scales and it is indeed different. When quoting a value, if it is unclear from the context, one must always specify the scale.

They also explicitly say what is the energy scale of the "textbook" value of the electric charge

[...], with $\alpha^{-1} \sim 137$ appropriate at very low energy, i.e. close to the Thomson limit

If you keep scrolling to, for example, Table $\mathbf{10.2}$ you'll see some names under the voice "Scheme." These are shorthands for different prescriptions to separate the "bare" contribution into "renormalized" + "$\infty$". Again, unless clear from the context one must always specify what scheme has been used when quoting a Lagrangian parameter.

For instance the $\overline{\mathrm{MS}}$ stands for "modified minimal subtraction scheme." In there divergences appear as poles in a regulator $\varepsilon$ as $\varepsilon\to0$ and they are subtracted together with a constant $\gamma_E - \log (4\pi)$ chosen simply to make the expressions nicer in the end.

Some Rebus puzzles

So a rebus puzzle is basically where you have to work out the 'hidden' meaning. For example

would be

TH under STORM (because the TH is under the STORM) or Thunderstorm

So I've made 6 puzzles for you to enjoy :) Good luck!

---

Part II and III

Answer

From left to right, first row then second row:

Fishin(g) for compliments
Third time lucky
Four leaf clover (credit @silenus)
There is no I in TEAM
An inside job
i <3 u

quantum field theory - How is a blackbody spectrum formed in the Sun?

Sunlight can be treated as BB radiation. Why is it a continuous spectrum while the sun contains only a few elements and the radiation from the jumps between atomic levels are discrete? How does the photon gas achieve thermal equilibrium while they do not interact with themselves?

relativity - How are propositions concerning spacetime curvature constructed explicitly in terms of coincidences?

Is Einstein's insight [1] that

All our well-substantiated space-time propositions amount to the determination of space-time coincidences [such as] encounters between two or more [...] material points.

and [2] his (so recognized)

[...] view, according to which the physically real consists exclusively in that which can be constructed on the basis of spacetime coincidences, spacetime points, for example, being regarded as intersections of world lines

applicable to propositions concerning spacetime curvature ?

How, for instance, is the proposition

"spacetime containing the worldline of material point A is curved"

constructed and expressed explicitly on the basis of spacetime coincidences (in which the "material point" identified as A or suitable other "material points" took part) ?

---

Edit in response to the answers and comments presently provided (Sept. 12th, 2013):

• Trying to put my question more formally,

given that there is the set $S$ of any and all distinct "spacetimes" imaginable,
and that there is the function (or proposition)
$\kappa : S \rightarrow \{ true, false, undetermined \}$
which for any spacetime under consideration represents whether it is "curved", or "not curved", or not an eigenstate of "possessing any curvature" at all,

and further given a set of sufficiently many distinct names $W := \{ A, B, M, M', ... \}$,
and that there is the function
$coinc : S \rightarrow \text{ powerset}[ \text{ powerset}[ \, W \, ] \, ]$

which for any spacetime under consideration represents the set of (distinguishable) coincidences of (different, and distinctly named) "worldlines",

I'd like to know the explicit expression of the function (or proposition) $f : \text{ powerset}[ \text{ powerset}[ \, W \, ] \, ] \rightarrow \{ true, false, undetermined \}$,
for which
$\forall s \in S: f( coinc( s ) ) = \kappa( s )$.

Looking at the above quotes it may be expected that $f$ has been worked out and written down long ago already; therefore, please write it down in an answer here, or point me to the corresponding reference. However, here are

• Considerations which answers would be acceptable otherwise:

either a proof that such a requested function $f$ doesn't exist at all; presumably by exhibiting two distinct spacetimes $s_a$ and $s_b$ for which $coinc( s_a ) = coinc( s_b )$ but $\kappa( s_a ) \ne \kappa( s_b )$. (But recall the hole argument discussion relating to the difficulty of distinguishing spacetimes at all.)

Finally, if such a requested function $f$ can neither be explicitly stated, nor refuted, then

define the notion "geodesic" (which has already been used/presumed in answers below) or at least the notion "null geodesic" explicitly in terms of $coinc( s )$.