I have a graph of $1/$current against resistance, which is a straight line of positive gradient. I know that the gradient represents $1/V$ but I can't work out how the equation $1/I= r/E + R/E$ relates to $y=mx+c$. Could somebody please tell me what each part of $y=mx+c$ represents in relation to $1/I= r/E + R/E$?
Rearranged equation for Emf= IR + Ir
I cannot seem to find any peer-reviewed (or other) reference to an integer-spin Stern-Gerlach experiment. It shouldn't be too hard to do: just find you friendly neighbourhood Deuterium ion and shoot it through a Stern-Gerlach magnet.
Can one devise a photonic Stern-Gerlach experiment, i.e. spatial seperation of polarization states? One should also see only two states in this case, because the spin-0 photon state is "reserved" for EM-interactions (this might be too simple a statement, but this is how I understand it currently).
EDIT it seems some of you are misunderstanding the question: I am inquiring about a Stern-Gerlach-like experiment, where spin states have been split, and by extension the perpendicular nature of non-commuting measurements. So only the concept of the S-G experiment as extensively described in introductory QM textbooks such as Sakurai.
Answer
You can absolutely do a corresponding experiment with light. In fact, it's the easiest way by far. Instead of a magnetic field, you would use a polarizing beam splitter to separate the two states, which as the name suggests is a cube that reflects light of one polarization and passes light of the other polarization. To do a Stern-Gerlach like experiment all one needs is a polarized photon source, a few of these cubes and a few half waveplates to change photon polarization, and then some photon detector looking at outputs.
This wouldn't normally be called a Stern-Gerlach experiment, which is specific to using a magnetic field to separate particles with magnetic moments, but the mathematics describing it is the same, as is the basic lesson that angular momentum is quantized and measurements in different directions don't commute.
As for atoms, a quick search found a Stern-Gerlach like experiment with not just single atoms, but a BEC: http://www.uibk.ac.at/exphys/ultracold/projects/rubidium/rb87bec/ I can't immediately find a single-atom experiment with Rubidium, but I bet it's out there if you look around.
Answer
You're of course right. Experimentally established, known laws of physics - especially the equivalence principle - are enough to be certain that antimatter has the same gravitational properties - including universal attraction - as ordinary matter.
http://motls.blogspot.com/2010/09/can-antimatters-gravity-be-repulsive.html
The justification of further experiments by "tests of antimatter's gravity" is partly based on ignorance and partly on deliberate deception to get funding.
I read an article about possibility of existence of multiverse and came up with a conflicting view with one of the sentences written in the article which goes as follows:
"If space-time goes on forever, then it must start repeating at some point, because there are a finite number of ways particles can be arranged in space and time."
What does this mean? What does it mean to say when it hints that it must start repeating at some point? Also, where are these multiverses enclosed within? If they are expanding at such a rate, is the container in which they are enclosed also expanding?
Answer
If the universe is infinite there is obviously an infinite number of ways of arranging the matter within it, so there is no requirement for the universe to repeat at large scales. What the article is suggesting is more subtle than this.
Suppose we take a finite volume. This could be as small as you, or as large as the observable universe, but in both cases there is a finite number of ways of arranging the matter in a finite volume. The reason there is only a finite number of ways is that we assume separations smaller than the Planck length can't be distinguished. So our finite volume is made up of a large but finite number of Planck volumes, and there is only a finite way of arranging the matter between this finite number of Planck volumes. Depending on how you do the calculation the number of ways of arranging the matter in the observable universe is around $2^{10^{118}}$.
So if you assume the universe is completely random then the probability of a randomly selected volume the size of the observable universe looking just like ours is 1 in $2^{10^{118}}$. This is obviously very unlikely, but in an infinite universe there are an infinite number of observable universe sized volumes, so somewhere there will be an exact replica of our observable universe. In fact there will be an infinite number of such exact replicas.
None of this has anything to do mith multiple universes. The argument above is just that there must be repeating regions within our universe.
We know that The net electric field due to two equal and oppsite charges is 0.
But let us consider a charge +Q in an isolated system. An electric field E will be emitted by it.
Similarly, a -Q charge will absorb an electric field E.
When both are in the same system then the magnitude field emitted by +Q and -Q should be added.
So can it be said that an electric field 2E is between +Q and -Q.
If an electric field E is generated by +Q towards -Q
And an electric field E is generated by -Q towards itself.
If both are in same direction, shouldn't both be aded to give 2E between them.
Of course the net will remain 0.
Answer
The net electric field due to two equal and oppsite charges is 0.
This is only true if the two charges are located in the exact same location. For example, a block of copper sitting on your lab bench contains an equal amount of electrons and protons, occupying the same volume of space, so the block of copper produces no net external electric field.
But if you separate the two charges from each other, they will produce a non-zero electric field everywhere in space. (This field will get very weak, but still non-zero, at locations much further from the charges than the distance between the charges)
It's actually easier to produce "zero net field" using two equal and same-signed charges.
For example, if I have two point charges with charge $+Q$ at locations $+x$ and $-x$ on the x-axis, then they will produce zero net field at the origin, since the field from one charge will be pointing right and the field from the other will be pointing left.
So can it be said that an electric field 2E is between +Q and -Q.
If an electric field E is generated by +Q towards -Q
And an electric field E is generated by -Q towards itself.
If both are in same direction, shouldn't both be aded to give 2E between them.
Exactly.
Of course the net will remain 0.
I'm not quite sure what you mean by this.
It is true in the sense of Gauss's Law. If you construct a closed surface around the two charges then the net electric flux through the surface will be 0.
But that's not the same as saying the "net field" is 0.
The net field is measured at a point in space, and is non-zero everywhere in your system. The net flux is measured over a surface, and can be zero if you construct the surface to contain the two charges.
To get to the point - what's the defining differences between them? Alas, my current understanding of a spinor is limited. All I know is that they are used to describe fermions (?), but I'm not sure why?
Although I should probably grasp the above first, what is the difference between Dirac, Weyl and Majorana spinors? I know that there are similarities (as in overlaps) and that the Dirac spinor is a solution to the Dirac equation etc. But what's their mathematical differences, their purpose and their importance?
(It might be good to note that I'm coming from a string theory perspective. Plus I've exhausted Wikipedia here.)
Answer
Recall a Dirac spinor which obeys the Dirac Lagrangian
$$\mathcal{L} = \bar{\psi}(i\gamma^{\mu}\partial_\mu -m)\psi.$$
The Dirac spinor is a four-component spinor, but may be decomposed into a pair of two-component spinors, i.e. we propose
$$\psi = \left( \begin{array}{c} u_+\\ u_-\end{array}\right),$$
and the Dirac Lagrangian becomes,
$$\mathcal{L} = iu_{-}^{\dagger}\sigma^{\mu}\partial_{\mu}u_{-} + iu_{+}^{\dagger}\bar{\sigma}^{\mu}\partial_{\mu}u_{+} -m(u^{\dagger}_{+}u_{-} + u_{-}^{\dagger}u_{+})$$
where $\sigma^{\mu} = (\mathbb{1},\sigma^{i})$ and $\bar{\sigma}^{\mu} = (\mathbb{1},-\sigma^{i})$ where $\sigma^{i}$ are the Pauli matrices and $i=1,..,3.$ The two-component spinors $u_{+}$ and $u_{-}$ are called Weyl or chiral spinors. In the limit $m\to 0$, a fermion can be described by a single Weyl spinor, satisfying e.g.
$$i\bar{\sigma}^{\mu}\partial_{\mu}u_{+}=0.$$
Majorana fermions are similar to Weyl fermions; they also have two-components. But they must satisfy a reality condition and they must be invariant under charge conjugation. When you expand a Majorana fermion, the Fourier coefficients (or operators upon canonical quantization) are real. In other words, a Majorana fermion $\psi_{M}$ may be written in terms of Weyl spinors as,
$$\psi_M = \left( \begin{array}{c} u_+\\ -i \sigma^2u^\ast_+\end{array}\right).$$
Majorana spinors are used frequently in supersymmetric theories. In the Wess-Zumino model - the simplest SUSY model - a supermultiplet is constructed from a complex scalar, auxiliary pseudo-scalar field, and Majorana spinor precisely because it has two degrees of freedom unlike a Dirac spinor. The action of the theory is simply,
$$S \sim - \int d^4x \left( \frac{1}{2}\partial^\mu \phi^{\ast}\partial_\mu \phi + i \psi^{\dagger}\bar{\sigma}^\mu \partial_\mu \psi + |F|^2 \right)$$
where $F$ is the auxiliary field, whose equations of motion set $F=0$ but is necessary on grounds of consistency due to the degrees of freedom off-shell and on-shell.
I was thinking that maybe photons loss energy naturally when they travel great distances.
Or maybe the mass of all matter is increasing over time and therefore photons emitted in the past are necessarily less energetic.
Or is the expansion of space backed up by so much other evidences that trying to find another explanation is completely foolish?
