Expansion of universe

QuestionEdit

Thanks, Phillip, for that detailed answer! I will peruse it in depth, when I get more time, later today. Until then, what about the possibility of the expansion of molecules - the 'space' between atoms? Is it possible that molecules are expanding? Thanks, Bruce

AnswerEdit

Hello again,

No, there is no chance molecules are expanding either. Again, if it were the case, then molecular spectroscopy - especially as applied to emission and other nebulae in space, would reveal it. But there are no abnormal signals, and the molecular spectra haven't altered - which would imply that the constants governing them haven't either.

For example, a typical diatomic molecule may execute vibration about an equilibrium point, and for which small vibrations of the molecule will occur at a frequency:

f_c = (1/2pi) [C/m]^1/2

where C is the "force constant": C = [d/dr{dP(r)/dr}]_r=r_o

where r_o is the equilibrium position.

Note the change of P(r) - the potential energy of the molecule, is with respect to r - the RADIUS of the molecule.

It may be shown that the energies associated with such an oscillating molecule will assume values of energy:

E_f = (f + 1/2)h-bar [C/m]^1/2

of

E_f = (f + 1/2) hf_c

where h is again Planck's constant. and f_c is as defined earlier.

Now, what if we were to allow the radius of the molecule to expand, meaning (r - r_o) would get ever larger and the vibrations about the equilibrium position (r_o) would take longer and longer?

I think you can see that the potential energy "well" (which sustains the molecule as a unit) would soon be breached and the atoms comprising it would be detached. There is only so much energy that can support it.

If one were to command extra energy to sustain the diatomic unit (prevent the breach from occurring) then the energy E_f would have to increase correspondingly - meaning h would have to alter (get much larger).

But, when we observe vibrational spectra of molecules, we continue to observe defined and quantized levels viz.

---E3 = 7hf_c/ 2 ---f = 3

---E2 = 5hf_c/ 2 ---f = 2

---E1 = 3hf_c/ 2 ---f = 1

---E_o = hf_c/2 -----f = 0 (zero point energy)

These levels observed in molecular (vibrational) spectra clearly show the (energy) spacings are normal and conform to the energies and frequencies computed for the already existing and defined values of r_o, (r - r_o) for given molecules.

Thus, the results of the spectral analysis-features show NO constant expansion of the molecule itself!

To put it another way, we don't detect or observe the radical change in the vibrational spectra that would support any such "molecular expansion" analogous to a cosmic expansion.

QuestionEdit

QUESTION: Hi Phillip, thank you for volunteering your time to answer these questions. My question is this: Assuming that the distance from the center of any 2 objects O is 1X, and the radius of objects O is 0.1X, and that time T has passed, should not the relationship between the objects and the space in between then remain the same? That is, space is always 0.8X?

If so, how could the universe appear to be expanding?

ANSWER: Hello,

Based on your example, it is impossible for the distance ("0.8X") between two objects to remain the same since it would violate Hubble's law, which has been repeatedly validated. Hubble's law states that any the farther an extragalactic object is from us the faster it is receding, i.e. the greater the recessional velocity. Objects at the same distance from us, meanwhile, recede from us at the same speed. Not the key word here is 'recede'. If your assumption was correct, however, and "space" is always of fixed distance, there couldn't be any recession. All objects would remain at fixed distances from us.

One more thing, the radius of an object has nothing to do with its expansion, no matter what its distance is. (Again, all aspects of expansion here are presumed to pertain to extragalactic objects with respect to us, NOT objects within our own Milky Way, OR even merely in our own Local Group of galaxies)

---------- FOLLOW-UP ----------

QUESTION: Phillip, Sorry to be confusing. I understand the concept is that space is expanding. My question relates specifically to that concept. Perhaps another way of asking it is this: If 'space' is expanding, would not the 'space' taken up by atoms themselves (not merely the space between atoms) expand at the same rate? Thus, assume: ---you and I are standing 10 feet apart today ---you and I are 1 foot radius ---we continued to live for x billion years (or you could insert galaxy a and galaxy b here)

the current 'space' theory is that space is expanding, thus items is space should recede from each other. However, if 'space' is expanding, should not the 'size' of each galaxy expand also?

Hope that's more clear.... Bruce

AnswerEdit

Hello,

Okay, I think your question emerges as clearer now. The answer, of course, is that no - atoms themselves do not expand. The Hubble law applies strictly to the *space between objects* not to the objects themselves - though I admit that's an interesting take that might be extrapolated from the principle of velocity recession.

Atoms, fyi, are governed by the laws of quantum mechanics and the Schrodinger wave equation, especially for the hydrogen atom as it applies to most atoms in the universe. (And in fact, most atoms (95%) are ionized so are electrically conducting plasmas - so lack outermost electrons.)

What about the hydrogen atoms that do have electrons?

Their properties and especially the energy levels derived therefrom (say the energy levels associated with a primarily hydrogen fusion star) lead to the prediction of the key lines of emission for the hydrogen spectrum. When we examine the results of solving the pertinent equation for the 1-electron atom, we find an energy expression of the form:

E_n = (Quantity)/ n^2

Where the bracketed quantity is a constant depending on the value of the atomic radius r, the left hand side shows E_n or some energy E referenced to a level (principal quantum number) n.

What this model shows is the quantization of atomic energy, energy released by an atom comes in quanta - not continuously. That is, when we observe an atom - say like hydrogen- we should find "lines" of discrete energy emission corresponding to these energies.

Now if "quantity" - contingent on the value of atomic radius, r, were to change it would mean other key constants (e.g. e, h) associated with it would have to as well! This we do not observe.

Let me break it down further and hope you can follow: We know the value of the energy E_1 associated with the hydrogen atom in its ground state, from spectroscopy is:

E_1= (Quantity)/ (1)^2

The radius (part of "quantity" above) is (again, assuming n= 1):

r = (h-bar)^2/ {m e^2 Z) where h-bar = (h/2 pi)^2 (Planck's constant of action divided by 2 pi), and m = 9.1 *10^-31 kg is the electron mass, and e is the electronic charge (e = 1.6 x 10^-16 C)

Since for hydrogen, Z = 1 so:

r_1 = h-bar)^2/ {m e^2)

When computed we obtain, r_1 (radius of the hydrogen atom associated with the ground state) as 0.529 A (Angstrom)

since 1 A (by def.) = 10^-8 cm = 10^-10 m then 0.529 A = 5.3 x 10^-9 cm = 5.3 x 10^-11 m

Now, if r were to "expand" what would have happen in order to preseve the value of E_1?

Well, then e, the electronic charge would have to change as well, and also h, the Planck constant. If we exclude any possibility that e can change and constrain it to strictly remain at the specified value, then Planck's constant would have to be significantly larger.

Let's say then as our galaxy recedes (space expands) 200x relative to another distant galaxy, we demand r_1 to also expand 200x. Then what value must h have to support it? Calculations show it would have to be h ~ 9.2 x 10^-33 J*s.

However, the most careful measurements (as published in the Table of Fundamental Constants in the Physicists' Desk Reference) show that h = 6.62 x 10^-34 J*s.

Thus, there is NO change.

Hence, there could not have been any "expansion" of the value of r_1. If there is no expansion associated with the radius for the hydrogen ground state we may be sure there is none for any other atom's ground state or higher energy state.

Hope this makes sense.