For me, the theosophical notion of multiple planes of existence is fascinating and thought provoking, but also very challenging to the rational mind. Perhaps "rational" is not the right term. It may be better to say that the notion of other planes of reality is challenging to a modern mentality overawed by the success and prestige of science. Accordingly, if the planes of theosophy are scientifically plausible, then the modern mentality is comfortable with them. However, if science deems them implausible, it is difficult to resist doubts about them. Thus, I initially greeted the postulations of contemporary physics of other dimensions with a sigh of relief. I thought that these other dimensions must correspond to the planes of Blavatsky, et. al.
The Theosophist David Pratt, however, has thrown cold water on this initial impression:
"Theosophy postulates endless interpenetrating worlds or planes composed of different grades of energy-substance, with only our own immediate world being within our range of perception. But other planes are not extra ‘dimensions’; on the contrary, objects and entities on any plane are extended in three dimensions – no more and no less." (davidpratt.info/farce.htm) [Emphasis added]
Okay. But certainly, there are other senses of "dimension" in play; perhaps these other senses correlate to the planes described by occultists. Again, Pratt writes:
"…It is very fashionable nowadays for physicists to speculate about additional dimensions. M-theory, for example, postulates 7 extra spatial dimensions, which are said to be curled up so small (10-33 cm) that they are undetectable. But these are just mathematical abstractions for which there is not a shred of evidence. They certainly do not resemble the other planes of energy-substance spoken of in the occult tradition. These planes, which are beyond our range of perception, interpenetrate our own physical world, and are said to be inhabited by a variety of entities… [Emphasis added]
"In its broadest sense, a 'dimension' is any measurable quantity. Examples are length, breadth, and height, which are commonly referred to as the three 'spatial' dimensions. Other dimensions are temperature, mass, charge, time, etc. If entities are said to be living in other 'dimensions', an obvious question is: how many spatial dimensions do these other 'dimensions' have? Some researchers actually speak of a three-dimensional parallel universe existing in a superior 'dimension'. This clearly shows that the word 'dimension' is being used in different senses. It is therefore better to speak of other (invisible) worlds, realms, planes, etc. than of other dimensions. Moreover, common sense dictates that no entities or objects, on any plane, can have fewer than three spatial dimensions; nor is there any reason to suppose that they can have more than three." (davidpratt.info/ufo1.htm ) [Emphasis added]
Now we seem to be onto something. When scientists postulate dimensions in the sense of parallel universes, these might approximate to the planes of theosophy. Yet there are further aspects of the latter planes that do not quite mesh with the dimensions/planes of the physicists.
The traditional theosophical conception of the universe is hierarchical. As I understand it, the astral plane is higher, in the sense of more real, than the gross physical plane. Similarly, the causal plane is higher than the astral plane. I do not believe contemporary scientific speculation conceives of any of the parallel worlds as "more real" or closer to an absolute reality than another. It would seem that there could be numerous parallel worlds (in the physicists' sense) coexisting on the same hierarchical plane (in the theosophists' sense). If this is so, even as we welcome the parallel dimensions of contemporary scientific speculation, we may have to look elsewhere for further grounding of the theosophical idea of hierarchical planes.
As I suggested above, "scientific" and "rational" do not necessarily coincide. There are other ways of thinking about reality in a rational way other than that of empirical science. What I am suggesting is that while we may wait on science to justify certain ideas or hypotheses, it is not irrational to accept a hypothesis in the meantime, at least tentatively, if its plausibility can be established in some other way.
One analogue to the theosophical system of planes is to be found in Plato. (Heck, this may be where many of these ideas originated.) Plato's schema of the Divided Line can be viewed as indicating different planes of reality, conceived of from a purely philosophical point of view:
I do not want to rehearse the various arguments in favor of or against a Platonic model of reality at the present time. All I am suggesting is that to appreciate the system of planes as a whole, it may be necessary, for the time being, to think of philosophical, rather than empirical-scientific, reasons for positing them. Hopefully, science will eventually corroborate these ideas; but one can rationally accede to their plausibility even without scientific justification. Moreover, one can accede to their plausibility without going so far as to commit to a full-fledged belief in them.
Another analogue that helps me to consider the system of planes as possibly real is the Vedantic dichotomy between the Absolute on the one hand and the realm of Maya on the other. This is an idealistic conception of reality in that it makes Consciousness fundamental. Although this may seem to fly in the face of experience, it really does not inasmuch as the Consciousness in question is not that of any finite individual or group of finite individuals. The stability and regularity we find in the world MIGHT be grounded in an Infinite Consciousness. Arguably, such a conjecture cannot be empirically disproven since no empirical evidence would count against it. Likewise, there is no ordinary means of verifying it either. Supposedly, it becomes self-evident once one evolves to a sufficient level of consciousness.
Well, either you find this perspective appealing or you do not. Let's say you provisionally accept it. Then the astral and causal planes would be the aspects of reality that are intermediate between our plane and the Absolute Reality. On this view, there is no reason to object to the possibility of parallel worlds within a given plane if they could be confirmed by science. More importantly, if one looks at reality from this point of view, the existence of other planes does not seem strange or unlikely. In contrast to the ordinary physicalistic conception than is forced to strain itself to accommodate a hierarchical reality, the Vedantic-Idealistic (or, alternatively the Platonic-Idealistic) conception STARTS OFF with a stratified reality. The theosophical planes come along for the ride as the specific strata within this world-view.
Obviously, this doesn't prove anything. But it seems to open up a way of making the notion of alternate planes tolerable to the rational mind.