What Is A Dimension?

 

In sci-fi movies there is often talk of “going to another dimension” as if there is some kind of barrier in between dimensions that can be crossed only if the circumstances are very special – usually the filmmakers are wise enough not to specify what these very special circumstances are. I will show in this blogpost that “Travelling to another dimension” is not only physically impossible; the phrase makes no sense from a logical point of view either.

            In the exact sciences, when we want to describe a physical situation we need a number of variables to do so. For example, if we wish to describe the fall of a stone then we need a minimum of three numbers to pinpoint the location of the stone in space (the space coordinates), and one number to locate the stone in time (the time coordinate). With the aid of these four numbers we can describe all possible developments of the situation. Viceversa, all possible states the stone can be in can be described in terms of these four numbers. The same goes for all material things that science is about: not only stones, but also houses and – in the case of sci-fi movies, spaceships – are described with the help of this minimal number of variables. Because those variables are needed to measure [1] they are called dimensions (from the Latin dimensio – a measuring). In our example of the falling stone every point in space and time is necessarily characterised by all dimensions because every dimension is by definition one of the minimal number of variables needed to describe a physical state (intuitively put:  a dimension must be everywhere [You can’t have a stone with length and height but without breadth]).

         flat,1000x1000,075,f

Someone might argue that the number of dimensions we believe to exist changes as science progresses. In certain extensions of Einstein’s relativity theory (such as the Kaluza–Klein theory) there exists a fifth spatial dimension; and in string theory – the theory that has been a promising candidate for the unification of relativity and quantum theory for at least 50 years – there are perhaps as many as 11 spatial dimensions.

That’s right: whereas it’s logically impossible to travel to alternate dimensions; it’s not logically impossible to discover alternate dimensions. The following example will show that.

Consider a bunch of very smart ants on a soccer ball. Suppose that these ants cannot look up due to some inheritable neck disease. Now if one of those ants were to come up with an antidote to this disease the ants would suddenly be able to look up and discover a third dimension. What they discover is not a third dimension into which they can now travel but rather that they have been living in three dimensions all the time (even before the antidote was discovered).

ants_moebius

[1] It is an unanswered question in the philosophy of science whether these numbers are merely needed to measure or whether they are the ‘realm’ in which is measured. Perhaps the latter choice is the more intuitive, but that choice incorporates the metaphysical claim that space is more than what is measured by a yardstick – a claim that Einstein was unwilling to make.

About fbenedictus

Philosopher of physics at Utrecht University, managing editor for Foundations of Physics and international paraclimbing athlete
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One Response to What Is A Dimension?

  1. Marco van Hulten says:

    whereas it’s logically impossible to travel to alternate dimensions; it’s not logically impossible to discover alternate dimensions
    Let’s assume string theory is correct (or is empirically adequate, whatever), then we do travel through alternate dimensions all the time, but we just don’t notice it. As it is physically occurring, it most certainly must be logically possible! Furthermore, the ants in your example are maybe physically bound to the object they live on, but there is again no logical impossibility here.

    Concerning the much-used phrase “travelling to another dimension”, I am rather annoyed by the to: this suggests that this other dimension would be something that lies out of our realm, like a parallel universe, which is actually often what the stories are about. However, one would travel through, or maybe into, another dimension, not to(wards). That is the part that makes not much sense to me, not that it wouldn’t be logically impossible.

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