Friday, August 19, 2005

It's a dimension thing...

Many have heard of 'string theory,' which then turned into 'superstring theory' after supersymmetry was added, and now that has changed names and is called 'M theory.' Whichever name you know it by, it is weird, wild stuff for the imagination. These are theories that are trying to identify the connection between te forces of nature - electromagnetism, the strong and weak nuclear forces (strong binds quarks together and holds the nucleus together, weak is responsible for radoactivity), and gravity. Tying in gravity is the hard part, it turns out. In order to do it, many theorists believe there must be extra dimensions besides the four-dimensional world Einstein taught us about. I won't go into all that here since there are many sites dedicated to it already (click here for an outstanding one!), but if interested check out this description from my old Fermilab experiment about how experimental tests are being conducted that search for extra dimensions.


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vonny said...

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Erica said...

I don't really understand how unification of the forces works... that website you linked to your entry said that gravity can only be unified with the rest of the forces at really high energies, but if the forces really are unified, doesn't that mean that they should be unified at ALL energies? For example, I know the relativistic transformations between electric and magnetic fields only become relevant at high speeds, but they still work for all speeds. It seems like forces aren't really unified if the unification only works on a particular energy scale.

I don't understand that Kaluza Klein thing either. How is it that we're supposed to be able to see the momentum of gravitons if the gravitons are in another dimension? In 3D, we wouldn't be able to tell if a baseball or whatever was moving or not if we could only see stuff in a plane and the baseball was moving perpendicular to that plane.

Lastly, one of the things they talk about in that website is collisions where particles escape our brane, but how do you tell the difference between a collision where energy is missing because something left the brane and a collision where energy is missing because something undetectable (i.e. neutrinos) came ot of it?

...sorry this is so long. I tend to get a little carried away with physics websites.

vonny said...


As usual, your questions are the right ones to ask!

Unification is an interesting concept. The easiest to consider is E&M. In static cases electric and magnetic fields are separate, distinct fields and create their own forces. Electrostatic fields do not couple to magnetic fields, and vice versa. However, if you add energy (in a sense, raise the temperature) in the form of kinetic energy, all of the sudden you have electromagnetic induction. We say they are unified in the sense taht in Maxwell's equations, to give an accurate description of the behaviors of E and B fields, they need to be included in teh same equations (Ampere's law and Faraday's law). The description is only complete if E and B are coupled together in the same equations. This is what we mean by unification, that they are two forms of the same thing, and the 'same thing' depends on energy/temperature.

So we now have electromagnetism. Keep raisng the temperature. Just like for something like water, there are phase transitions. This is another concept that is included in unification theories. Liquid water looks and behaves a lot different than ice, as does steam as you get hotter, but fundamentally they are all just H2O. At a high enough temperature, we can no longer tell the difference between the electromagnetic force and weak nuclear force. Mathematically, in the Standard Model, photons and Z bosons are described by a field equation that includes both the electromagnetic scalar potential (the A you may have seen in electromagnetic theroy) and the weak feld. There is a superposition of the two fields that describes photons and Z bosons! In other words, you need both fields to describe each force, just like Maxwell's equation. In more complicated ways, the strong force is superposed with the electroweak force. This is why we need particle accelerators to investigate unification...nothing else gets us to the energies/temps where all this happens.

Gravity presumably gets involved at much higher temperatures than we are able to create now. Gravity must have come into its own shortly after the big bang. This is why we cannot say anything about it experimentally yet.

As for Kaluza-Klein theories, they were te first to introduce extra dimensions beyond our 4-D relativistic universe. Adding other dimensions works because if you allow a graviton to move freely among all these extra dimensions, the coupling with our macrocosmic 4-D spacetime is very weak, accounting for the incredible weakness of gravity. What's more, in M-theory where you have multidimensional strings as the basic constituent of everything, you get away from point masses and no longer have infinities appear in the equations (like for a black hole singularity, where Newtonian and Einsteinan gravity both divide by zero radius, and the equations blow up). This is one of the attractive features (pun intended!) of all these weird extra-dimension theories. A possibility you have in experiments looking for gravitons is that there is missing momentum. This is what we look for to account for neutrinos, for example. Now, you are correct, there is a missing momentum from a neutrino, or from a graviton? This is the hard part, and where the real work comes in to do a few things - understand background rates, understand experimental and systematic uncertainties, and use theoretical simulations (such as Monte Carlo simulations) to help guide you in your search. It is tough and sophisticated analysis, but in the end one can get an acceptable answer if the data sample is large enough for good statistical analysis.

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