Time-travel gives me a headache, I really wouldn't be thrilled at all the potential paradoxes that can happen with that.
Ok that concludes the short part of my post
The next part is massive so get comfortable.
Before any talk of theories, here's what I've observed:
1) Confirmation of what Cullen said: I've done enough attempts at pk to confirm in my mind that its real, which leads to the idea that psi can somehow interact with physical matter.
2) There hasn't been any kind of test that can lock down whether Psi is a particle, energy, etc. Its quite unknown what it is at all.
3) Psi is a finite quanity, after enough psychic activity an individual will expend their reserves and find it hard or impossible to do any further activity.
4) Psi seems to be linked to physical systems in either the way it is perceived by the body or in a more direct way. In other words when you expend yourself psionically you typically feel physically tired. On the opposite endpoint of things, an increased amount of availible psi typically leads to someone feeling more physically capable/awake/etc.
5) People can change their capacity or ability to produce psi through enough use of psychic activity, presumably in the same way someone can exercise to grow physically stronger.
6) The intial capacity and/or production ability of psi differs between person to person, which would imply that there is a level of genetic variance.
7) The factor in #6 along with an individual's natural proficiency with various psychic abilities seems to *NOT* be related to an individual's general mental ability. This is weakly supported because this seems to be the generally given answer and thus generally accepted idea. Personal example: I am incredibly intelligent (as given by school performance, math proficiency, etc), but I seemed to originate with a capacity/production ability of psi that was well below average.
8) While its link to physical systems cannot be completely determined (see #4), psi can be used to bring about a physical reaction in the body. First obvious case is bio-pk and biofeedback. A more obscure case I've observed is when the body is made to focus an incredible amount of psi it will react on a level that is involuntary to semi-involuntary. Depending on how high "incredible" is this reaction could be a sudden jitter, a spasm, or an full-blown fit.
9) The body's ability to produce psi can be overstrained if an individual attempts to use all of their availible reserves or in some rare cases continues to attempt psychic activity after those reserves are completely spent. In light cases of this the body appears to generate psi at a slower pace until reserves are rebuilt to some level of normalcy. In extreme cases permanent damage can be done and the body never fully recovers in some way.
10) Animals have been observed to have some psychic potential to varying degrees (there is research on this listed on Psionic Social Club -
www.psc-online.org/sections/view.php?id=8 ) At a cursory glance these appear to be mainly the more complex organisms: cats. birds, etc.
11) Use of psychic abilities depletes measurable levels of nutrients in the body, particularly potassium.
12) Various tests have shown that psi can go through solid objects and is largely indetectable by any known techonology we have.
These observations seem simple enough, but the rammifications of them combined are not. The baseline or original capacity of a human to use psi varies as much as a genetic trait like height does. If psi use and production was merely an extension of our brain's own structure and ability it would be more inclined to be effected by mental prowess, as mental prowess suggests a brain that is particularly capable of thinking and other higher level activities. Psi unfortunately does not seem to be directly related to mental prowess however; this suggests that there is some fairly complex physical system in place that governs psychic ability and the ability to produce psi.
However that brings up the immediate question of why we haven't been able to identify such a physical system. While we have nowhere near a full grip of the brain's structure, we have been able to map out some of the major areas of what governs what. The same goes with the body in general, we do not have a full understanding of the various cells and organs, but we have enough knowledge taht we've spotted the important stuff. The amount of psi a human can generate and manipulate is such that it seems unlikely that this physical system is something incredibly small that could have been missed. It is possible but not likely. Assuming that the unlikely case is not true and that the physical system has to be at least an "un-obscure" size, there is a problem as to where it is. As said before on at least a cursory level we know what does what in the body. We know what parts of the brain control certain motor functions just as we know where each major organ is and what it does. This only leaves two real possibilities:
1) Psi is created as a byproduct of an already identified physical gland, organ, or system.
2) An already identified physical gland, organ, or system does what we thought it does but somehow also has a second function in producing psi. This is the less likely case as again, it makes scientists and biologists have to be a lot less bright then they are "Opps! We didn't notice that gland appears to be doing something else." While in the brain that could be possible, it is less likely to be true.
Since psi appears to be prevalent only in humans and more complex animals, it appears to be the case that it has something to do with the nervous system. In other words, its not likely to be generated in a gland in the middle of your foot.
Biology has defined a fair deal of knowledge on how cells and the body in general are supplied with energy and capable of functioning. Since this is the case, we can throw the theory that Psi is the body's main means of storing and transfering energy right out. The observations of psi's interaction with the body beg the question however of what role psi does have, and where it is. To some level the body can percieve and respond to psi, so it is not entirely unlinked to physical systems. Psi has been observed to be present in the body, but I'm not so sure that is in any way indicatory that it is "coarsing through our veins." More likely since psi can simply go through solid matter, it is produced by the body then kept around the body but a matter of concious or subconcious will (the latter more likely). This could also explain the presence of what scanners see as someone's "energy field." This is the first purposed theory so far that doesn't assume scientists are dumber than they probably are. Since we cannot directly detect or measure psi, a situation as this theory proposes could easily exist without being noticed in measurements.
That theory possibly answers where psi is or is stored. What it is, is harder to say. Since psi can be used to enhance physical ability or in extreme cases lead to muscles moving on a somewhat involunatary manner, psi must be at least convertable to a type of energy the physical body can more readily use. Some might say that this enhancement could be a kind of "self-tk" but his is unlikely as tk seems to be somewhat inefficient in moving objects under most people's ability with it. While the involuntary movements could be the body's reaction and not a direct influence, this is also unlikely. In one case in my experience where the former mentioned scenario (physical enhancement) was attempting to be brought on as the intended result, psi was observed to flood into the major muscle groups and concentrate there. Again while it cannot be conclusively said that this couldn't merely bring on a physical reaction, it seems more likely that the psi was directly being utilized for physical energy, as some of the more extreme cases (switching examples to the latter case of involunatry motion) have been too violent to have not been fueled by some physical energy. That is the motions were very energy consuming, which would lead to the idea that that energy would have to be rapidly provided from some source.
However, pk makes it obvious that psi must also be able to interact directly with inanimate objects to physical move them. This strains the before mentioned theory, as it is increasing the number of ways psi can convert itself or be converted. Since psi goes through solid objects and has proven very difficult to detect under a wide variety of instruments, it is unlikely that it is a physical particle and is more likely some form of energy. Physical particles can absorb energy and physically move as a result of that, but it is rare or even possibly unheard of for them to directly move something (this may get shot down by someone, I'm just thinking that shining a flashlight at a piece of paper doesn't cause it to move). So psi would have to be converted into a form that was somewhat physical so that it could directly interact with physical matter. The only possible way to explain that feels almost like a loophole in saying that maybe like light it is both a particle and energy at the same time, which is a paradox but at least in the case of light the only way the full range of its behavior can be explained.
That psi is a finite quality, the human body's capacity to produce it can be increased through regular use, and extreme overuse can cause either temporary or peramanent damage makes psi capacity seem like a muscle. This works great in analogies, but to exist in reality the physical system responsible for psi would have to have an incredible capacity for change. This is another support for psi being part of the brain, since the only parts of the body seen to be capable of "rewiring" themselves to the point of changing core functionality are the brain and *possibly* the more complex parts of the spinal column. Again the latter case is less likely as this behavior is seen much more in the brain.
The idea that psi is a finite quality itself is supported by the observation that use of psi depletes physical nutrients and blood sugar. If the elements of the body psi depletes as a result of its functioning are finite (which they are), psi itself must be finite. This also implies that whatever psi is the body must have to use physical resources to make it. That last point seems almost too obvious to mention, but the rammification is psi can't be too much of a strange or otherworldly particle since our mostly "normal" human bodies use normal components to make it.
I'm not sure at this point after typing for at least an hour whether I might have lost a point I was developing or intended to develop, so I apologize for any lose ends I may have left.
May I ask you move this to the Advanced forum? This is not an entry level discussion.
It makes me happy to have advanced discussions.....even when they do go over my head. I'm not much of a scientist or scientific/analytical mind. 
*sighs* 
Not by any means fully fleshed out here. That would be impossible.