# How can the properties of the same element differ

1. Dec 22, 2009

### neelakash

Hi friends,
Can you help me to seeing the meaning of the following pat from Gottfried's book on qm?to illustrate the failure of classical physics before the invention of quantum physics,he says---

"classical physics cannot explain why the properties of a sample of an element are identical to that of any other sample of the same element irrespective of their prior chemical or physical history-whether one sample has been extracted from one compound and another from a different compound by totally different methods...

I cannot see what is the point of the authir.Dalton told in 1808 that the same element has identical atoms...so...if we are sure we have the same element from two or more different sources it should be obvious they would have the ientical proprties...Isn't it?

2. Dec 22, 2009

### Bob S

3. Dec 22, 2009

### alxm

It's just a badly written bit of text. The discovery (among physicists) of the discrete nature of matter and the discrete nature of energy spectra did overlap in time around 1900. But I think the two questions shouldn't be conflated, especially considering that chemists had universally accepted the 'atomic hypothesis' since at least the Karlsruhe congress.

4. Dec 22, 2009

### peteratcam

You shouldn't read too much into it.

Nevertheless, there is a quite deep point here (which might not be the one the author was getting at): it should be considered a mystery as to why the protons we find on earth are identical in every way to the ones (for example) which arrive in cosmic rays which originate a long time ago in a galaxy far, far away. This mystery is only resolved in a quantum field theory understanding of the particles which make up the universe.

5. Dec 22, 2009

### Avodyne

The point is that in classical physics and in nonrelativistic quantum mechanics, you are free to postulate that two different particles (say, two electrons) are identical (same mass, charge, magnetic moment, etc), but nothing in the mathematical formalism forces this on you. In relativistic quantum field theory, on the other hand, you have a finite number of fields, and for each field there is a particular type of particle. The theory predicts that all electrons are excitations of the electron field, and that all electrons are identical. And that integer-spin particles obey Bose statistics, and odd-half-integer spin particles obey Fermi statistics.

6. Dec 23, 2009

### neelakash

I think,in simplest terms,the question means why different samples of the same element have the same properties...[we are assuming a single allotropic form].

@Avodyne

Can you please be a little more clear?

7. Dec 23, 2009

### Avodyne

In classical mechanics or nonrelativistic quantum mechanics, if you want to talk about $N$ electrons, you write down a hamiltonian that depends on $N$ coordinates and $N$ momenta $(x_i,p_i)$, $i=1,\ldots,N$. (For simplicity I am ignoring spin.) If the particles are "identical", then the hamiltonian should be completely symmetric on the any exchange $(x_i,p_i)\leftrightarrow(x_j,p_j)$. You can, of course, choose a hamiltonian with this property, but there is nothing that forces you to do so; you can choose a hamiltonian without this property.

In quantum field theory, on the other hand, to describe any number of (say) electrons, the basic object is a quantum field $\psi(x,t)$, and there is a hamiltonian built out of this field. All electrons are then automatically identical. If you want a particle that is not an electron (like, say, a proton), you need to introduce a second quantum field. Then all particles described by that field will be identical.
Thus the observed fact that there are a finite number of particle types, but an apparently arbitrarily large number of particles of each type, all identical, has a simple explanation in quantum field theory, but no explanation at all (except as an additional postulate) in classical mechanics and nonrelativistic quantum mechanics.

Last edited: Dec 24, 2009
8. Dec 25, 2009

### neelakash

I am looking at what you have written a liitle later...After talking to few people I got the following idea:

The idea is of a classical atom.Since, the atoms were to have internal structure (evident from excitation spectrum experiments),people thought of them to have some internal structure.Samples of the same element from different sources were thought to contain the same atom with different internal structures corresponding to parent history.

[input from one person from another website] Classically, we might have thought, as some Greek scholars did, that atoms were like little balls. And furthermore, these little balls could be decorated with all kinds of little widgets and spikes and grooves and so on which distinguish one element from another. For example, let's imagine oxygen has 2 widgets, 2 spikes, and 0 grooves, while nitrogen has 2 widgets, 1 spike, and 1 groove.

All atoms of a given element are the same in so far as they have the same number of widgets, spikes, and grooves. However, we might imagine that each feature has some internal degrees of freedom. For example, maybe widgets can be "on" or "off", or maybe spikes can rotate around some axis. This would mean that oxygen has internal structure which could potentially depend on its history. For example, maybe oxygen atoms coming from an oven have their widgets randomly distributed between "on" and "off", but oxygen atoms in water always have their widgets in the "off" position. If the state of a widget doesn't change in time as an atom sits by itself, then each atom would have some "long term" memory of its previous experiences.

Since,in those days,the idea of chemistry was not well developed,people used to think that the sample I have in hand contains that decorated form of the particular atom corresponding to the history of the parent compound.Testing the compound was thought to give properties manifesting the history of the parent location.It was a surprise of the classical theory of the atom that all these properties turned out to be the same.