# Aether & higgs field

1. Feb 14, 2009

### Haibara Ai

Can someone explain to me what Aether is? And what's the difference between the Higgs field and the aether?

thanks

2. Feb 15, 2009

### JustinLevy

When people started to learn that light acted like a wave, they reasoned that there was some medium which the light was a wave perturbation on. This was a fairly reasonable assumption at the time, as all known waves at the time occurred in some medium. They called this medium for electrodynamics the aether. As with sound in air or ocean waves on the water, the relevant speed is the speed with respect to the medium. So they thought that the speed of light (or maxwell's equations in general) were only true in one coordinate system ... the "aether frame" in which the aether is at reast. Experiment later showed that such an aether did not exist (or at the very least had no effect on experiment and therefore was not a subject for science). So the aether is now a defunct topic accept for certain gravity theories that try to add in a dynamic background field that breaks lorentz invariance... but these are not mainstream.

As described above, the aether is not related to the Higgs at all.
Furthermore the (standard model) Higgs field is completely relativistic, so does not provide any preferred frame / lorentz breaking effects either.

3. Feb 20, 2009

### Sideways

The difference between any field (including the Higgs Field; others would be the electromagnetic field, strong field, etc.) and the aether is that fields are Lorentz invariant, meaning they can accomodate special relativity theory. The "aether" is Galilean invariant, and can't accomodate relativity theory.

The "field" view has been successful in matching real data; the "aether" view has not.

To explain specifically what the "Higgs Field" is quite a deep subject, but basically, its presence is necessary (in some form) if the Standard Model electroweak unification theory is correct.
(Hope this helps...)

4. Feb 20, 2009

### robousy

...I would add that an aether in the 5th dimension would still preserve 4D lorentz invariance, and have some quite interesting effects.

For example, consider a scalar field coupled to an aether field $u^a$in the fifth dimension:

$$\mathcal{L}_{\phi}= \frac{1}{2} (\partial\phi)^2 -\frac{1}{2} m^2\phi^2-\frac{1}{2\mu^2_\phi}u^a u^b\partial_a\phi\partial_b\phi$$
where
$$u^a=(0,0,0,0,v)$$
Solving the higher dimensional Euler Lagrange equations
$$\partial_a \left(\frac{\partial \mathcal{L}}{\partial(\partial_a\phi)}\right)-\frac{\partial \mathcal{L}}{\partial \phi}=0$$
you can quickly obtain:
$$\partial_a\partial^a\phi-m^2\phi=\mu^{-2}_\phi\partial_a(u^au^b\partial_b\phi)$$
expressed in momentum space you get:
$$\phi \propto e^{ik_ax^a}=e^{ik_\mu x^\mu}e^{ik_5y}$$
For the term involving the VEV of the aether field you can quickly obtain:
$$\mu^{-2}_\phi\partial_a(u^au^b\partial_b\phi)&=&\mu^{-2}_\phi\partial_5(u^5u^5\partial_5\phi)$$
$$=\frac{v^2k_5^2}{\mu_\phi^2}\phi$$
If we now impose periodic boundary conditions on the wave vector in the fifth dimension
$$k_5=\frac{n\pi}{R}$$
you find
$$-k_\mu k^\mu=m^2+(1+\alpha_\phi^2)\left(\frac{n\pi}{R}\right)^2$$
The interpretation of this is that the mass spacing for the KK tower is enhanced. This is actually a pretty neat way to hide extra dimensions - eg, they could still be large, but the modified momentum dispersion relations simply mean that extremely high momentum would be required to observe them.

5. Feb 21, 2009

### Haibara Ai

Thanks a lot
:)

6. Feb 26, 2009

### distanceless

why does the term $$-\frac{1}{2\mu^2_\phi}u^a u^b\partial_a\phi\partial_b\phi$$ stand for the interaction between aether and scalar field?

thanks

7. Feb 28, 2009

### Naty1

Try Wikipedia for the Higgs Field:
http://en.wikipedia.org/wiki/Higgs_field

The Higgs boson is the particle manifestation (quanta) of the Higgs field like the photon is the particle manifestation of the electromagnetic field...If they ever get the large hadron collider running in Europe, it is hoped that will be able to confirm the existence of the HIGGS boson...