Beginner questions on elementary particles

[Helicobacter]

Why are all particles of a particular type of elementary particle all exactly the same?

What kind of a process causes a lot of identical elementary particles to appear?

How can a infinitely dense, hot, and small piece of space become a system with finite bounds (on energy, number of particles etc.)? There has to be something extra, otherwise why isn't there a universe with [current number of protons on this universe]+n, where n is an arbitrary number?

I'm not a physics person so I would appreciate plain language. Thanks!

 

[Simon Bridge]

Why are all particles of a particular type of elementary particle all exactly the same?

They are not... leptons can be electrons and mesons for eg.

But if you mean "why are all electrons exactly the same as each other" the answer is we don't know, they just are. There does not seem to be any reason for them to be different.

What kind of a process causes a lot of identical elementary particles to appear?

Quantum ones - usually they cause sets of different elementary particles to appear. They pop in and out all the time in the quantum foam.

How can a infinitely dense, hot, and small piece of space become a system with finite bounds

... it pretty much has to - that state is very unstable. You want to read some of Hawkin's lectures on cosmology. It's quantum again... and a very big question.

I'm not a physics person so I would appreciate plain language.

Sounds like you have been thinking about the problem of complexity (cosmological argument in theology) - recall that science seeks to explain natural phenomena in terms of nature.

This is a work in progress and not all the answers are available yet. So far it has been very successful and almost everything that was thought to only have a supernatural explanation has turned out to have a natural one as well.

If you want to understand stuff at the heart of physics you will have to learn mathematics ... math is the language of physics. If you don't learn the math you won't understand the laymans descriptions you get and they will always seem somehow wrong. All they can do is give you an impression... like reading poetry translated from another language: sometimes you get it sometimes you just have to learn the language.

 

[Helicobacter]

but if you have some piece of space with infinite energy, if you extend it more and more you have an infinite supply of energy to use in the extended space- you never run out of infinite energy...or not?

the highest math I've taken is calc III and linear algebra. what kind of math subject should i read up on to understand quantum mechanics better?

 

[Simon Bridge]

Who says an infinitely compressed space has infinite energy?

Of course, one of the problems with this sort of discussion is that it is not just space that was all compressed, but time as well. In the very early universe, the time axis was not even differentiated from space in most of the models. This creates a common-language problem - we don't have normal every-day words to deal with time as a direction or how space-time behaves. We are forced to use mathematical terms and practice.

To get a feel for the math, you want to do a quantum physics course - the math used for the descriptions you will get are a subset of what a math course will teach you, and physicists use math a bit differently to mathematicians.

There may be a cosmology course that will fit the bill. The concepts you are looking for are all about relativity and quantum field theory ... but you will start to make sense of things before you hit the fringes of what is known and where you get several models for everything.

Meantime -
http://www.hawking.org.uk/lectures.html
In particular:
http://www.hawking.org.uk/the-beginning-of-time.html

Hawking is quite clear and his public lectures will give you a taste of the ideas.

 

[Helicobacter]

Thanks for those links.

The reason I thought there was infinite energy is because I remember the terms "infinitely hot", "infinite heat" with the singularity.

 

[humanino]

leptons can be electrons and mesons for eg.

Leptons are never mesons. Mesons are quark-antiquark bound states (setting aside exotic possibilities) and thus are hadrons : they feel the strong force. Leptons do not feel the strong force directly. Leptons and hadrons are actually the two broadest classification for matter particles.

But if you mean "why are all electrons exactly the same as each other" the answer is we don't know, they just are. There does not seem to be any reason for them to be different.

This is not quite correct either. The fact that all electrons are the same is indeed a postulate in quantum mechanics. But it is not a postulate of quantum field theory, rather it is to be seen as a consequence of the axioms⁽¹⁾. The difference between quantum mechanics and quantum field theory is that the latter is the only known consistent way of combining quantum mechanics with special relativity⁽²⁾. All electrons arise as excitations of the same field.

The specific mathematics has to do with local fields and (anti)commutation rules, but there is a neat physical way of understanding why two electrons cannot have distinguishing intrinsic properties once special relativity is taken into account. Say you have two electrons in front of you. You cannot exclude that in the future, one of them will annihilate with a positron, and that this positron is the same as the one with which your other electron was created long ago in the past.

If you did create both electrons separately, you had to produce at least two positrons to do so (or something even more complicated involving neutrinos), the argument becomes longer, but essentially remains the same. So, neglect this complication for the moment, imagine that you did not create those electrons yourself.

So let us say that long ago in the past, one of your electrons was created like so :
http://upload.wikimedia.org/wikipedia/commons/a/ab/Feynman_diagram_for_Pair_Production.svg
The positron goes on to live his own life, you come along and compare the electron on the right with another and the claim is that they cannot be different. This claim stems from the fact that the other electron could in the future annihilate with the same positron in the image above, in a reverse diagram. Essentially, when you stick special relativity into quantum mechanics, quantum numbers flow along world-lines in spacetime, and we can interpret opposite quantum numbers for antiparticles as flow from the future (the arrow on the positron line is to the past, this is an arrow for quantum number conserved along the world-line, although the positron momentum does flow to the future : the positron traveling to the future is indistinguishable from an electron traveling to the past).

This business is not just neat, it means that we derive precise relations between electron-positron annihilation into two photons and electron-photon (Compton) scattering for instance. Those are called crossing relations.

(1) As always in physics, there is of course no axiomatic derivation of reality. The indistinguishability of electrons was known before quantum field theory, and while unexplained it was taken into account in the formulation of the theory. What I am trying to convey here is a common point of view that, when quantum mechanics and special relativity are put together, antiparticles and the indistinguishability of excitations of the same field become a necessity.

(2) Attempted generalization of quantum field theory of point particles, such as string theory, share the same properties w.r.t. crossing and the relation between fields and their particle-antiparticle excitations. In fact, string theory is even more radical in this respect, since according to it everything would be excitation of the same unique field.

 

[Simon Bridge]

The reason I thought there was infinite energy is because I remember the terms "infinitely hot", "infinite heat" with the singularity.

Wikipedia has a pretty standard description - it says: According to the Big Bang model, the Universe expanded from an extremely dense and hot state and continues to expand today.
... notice "extremely hot" not "infinitely" hot.

However the same articles points out: Extrapolation of the expansion of the Universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past.
... possibly this is the sort of thing you were thinking of?
Notice how specific it is - it does not say the Universe was like that but that GR is like that.

The singularity is regarded as a break-down of GR and current models attempt to get rid of it. Our concepts of energy and time and so on don't count for much before the Planck epoch. However, I think I can give you an idea, by analogy, how this would work:

An ideal monatomic gas with a finite temperature and internal energy is observed to be expanding adiabatically ... from two states of the system, we can extrapolate backwards to a very hot dense state at some time ... as the volume approaches zero, the internal energy and the temperature diverge (approach infinity).

Of course, a real gas is not infinitely compressible.

In the early universe you have a lot of matter very close together, this gives us some pretty extreme space-time, which may result in some kind of minimum compressed state. But in this case, it is all of space-time that is compressed - those Hawking lectures in the links discuss some of the ideas.

 

[Simon Bridge]

Leptons are never mesons.

Yeah I stuffed up - my bad.

I blame the "mu meson" counting experiment those guys did on Mt Washington.
We understand that muons are not mesons ... muons are quite closely related to electrons, so perhaps I should have said that some leptons are neutrinos. That should cover the point I was trying for.

As for Field Theory - well, I saw all that (what you said) looming and chickened out.
These descriptions can get bogged down when people start asking why the other positron cannot annihilate with our electron... maybe it's not different in that way? And questioning the why's of the axioms and so on and so on.

Right at the start I was concerned that OP was thinking in terms of the cosmological argument and looking for analytic explanations. So I went the path of exposure to ideas. Even so, I'm glad someone has had a go.

I remember Feynman relating a speculation he had as a student, I think it was in the QED or the Character of Physical Law lectures, that a positron was an electron traveling backwards in time. That all electrons are the same because they are, in fact, the same electron. We see lots of them due to the electron zig-zagging back and forth in time. This gave rise to the notation in Feynman diagrams - where the arrow on an antiparticle points backwards in time.