# Boxing Pythagoras

## WLC on the Speed of Light

I’ve been listening to a series from William Lane Craig’s Defenders podcast entitled “An Excursus on Natural Theology,” over at the Reasonable Faith website, of late. Needless to say, I have a lot I would like to say about almost the entirety of the series. However, today, I’m going to focus on a minor point which Dr. Craig makes in Part 6 of the series. Now, to be completely fair, this point is only tangential Dr. Craig’s overarching claims. By no means am I attempting to imply that the problems with this one issue somehow refute his whole Excursus– I’ll be dedicating a whole new series of posts to that, in the future. However, I chose to focus on this very minor point made by Dr. Craig for another reason entirely.

Once again, William Lane Craig has demonstrated himself to be rather ignorant in regards to the science which he attempts to discuss.

Dr. Craig is responding to a question in which he is asked to clarify what is meant by “metaphysical necessity.” He replies that there are different kinds of possibility or necessity, and one such is physical possibility or necessity. He then makes this statement (emphases in the original audio):

It’s physically impossible to accelerate an object through the speed of light, and make it go faster than light. That’s physically impossible. It’s against the laws of nature. But there’s no logical impossibility with that. There could have been a universe with different laws of nature, where you could accelerate something through the speed of light.

Apparently, Dr. Craig is entirely unaware that the only reason scientists believe it to be physically impossible to accelerate through the speed of light is because doing so would result in a logical impossibility.

Allow me to explain. This universal speed limit is derived from some of the formulae associated with Special Relativity. Particularly, it is found in the formulae for Time Dilation. As I’ve mentioned elsewhere on this blog, Relativity Theory bears implications on how time is measured by different observers in different frames of reference. The exact same event can be measured by one observer as taking less time than it did as measured by another observer. It is not that one of these observers is correct while the other is incorrect– both are equally correct in their claim. Time is not a single, monolithic flow. It is different for different observers.

It is possible, however, to predict the different rates at which time is measured in these different frames of reference. This comparison is known as Time Dilation, and it helps us to transform measurements made in one inertial frame into equivalent measurements from another inertial frame. The important part, for our discussion, is called the Lorentz factor and it is represented by the equation $\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$. In this equation, v is the velocity of the observer relative to the desired inertial frame, while c is the speed of light.

So, if you are at rest relative to the desired inertial frame, is 0, and thus the Lorentz factor is just 1, because $\gamma = \frac{1}{\sqrt{1-\frac{0}{c^2}}}=\frac{1}{\sqrt{1}}=1$. If, however, you were traveling at a bit under 87% of the speed of light (say, exactly $\frac{\sqrt{3}}{2}c$) in comparison to the desired frame, then the Lorentz factor is 2, because:

$\gamma = \frac{1}{\sqrt{1-\frac{(\frac{\sqrt{3}}{2}c)^2}{c^2}}}=\frac{1}{\sqrt{1-\frac{\frac{3}{4}c^2}{c^2}}}=\frac{1}{\sqrt{1-\frac{3}{4}}}=\frac {1}{\sqrt{\frac{1}{4}}}=\frac{1}{\frac{1}{2}}=2$

That is to say, Time passes twice as quickly for someone traveling roughly 87% of the speed of light as it does for someone at rest relative to the traveler.

Now, what happens to the Lorentz factor when our traveler is moving at the speed of light as compared to the desired frame? Well, it’s fairly simple to plug those numbers into our equation, in order to get:

$\gamma = \frac{1}{\sqrt{1-\frac{c^2}{c^2}}}=\frac{1}{\sqrt{1-1}}=\frac{1}{\sqrt{0}}=\frac{1}{0}$

Those of you who remember your grade school arithmetic might recognize a problem, here. Traveling at the speed of light requires us to divide by zero. Dividing by zero is an undefined operation– it is logically impossible to divide any number by zero. This is why the speed of light acts as a universal speed limit on modern physical models: it introduces a logical impossibility.

While this may seem esoteric and pedantic, at first, please note that William Lane Craig has spent a very large part of his career discussing the nature of Time, and specifically dealing with the implications of Relativity on the perception of time. The Lorentz factor and its implications are not an obscure bit of Relativity Theory, only known to expert physicists. It’s common to pretty much every introductory course on Special Relativity. It is not at all unreasonable to expect that William Lane Craig should be familiar with this very basic bit of knowledge.

Of course, one might retort that I’m only looking at the first half of the quote from Dr. Craig which launched this article, and that the second half justifies his claim. After all, if there could have been a universe in which– for example– Special Relativity does not apply, then the fact that something is logically impossible given Special Relativity does not make it logically impossible in all cases– that is to say, a metaphysical impossibility. However, notice that there is a subtle but extremely significant difference in the way I have formulated this objection to the way in which Dr. Craig did. Where he claimed, “there could have been a universe,” I instead made the conditional proposition, “if there could have been a universe.” That, my friends, is a very big “if.”

Dr. Craig gives us no reason to think that there actually could be universes which are not subject to Special Relativity. He simply makes the bald assertion that such universes could exist. I would very much like to see how Dr. Craig justifies that claim.

Certainly he wouldn’t justify it by appealing to the fact that we know of no reason why such a universe cannot exist. That would be a blatant Argument from Ignorance fallacy. The fact that we do not know X is impossible does not imply that X is therefore possible. I would like to give Dr. Craig the benefit of the doubt and assume that he would not appeal to such an obviously flawed bit of reasoning.

Similarly, I don’t think Dr. Craig would justify it by appealing to the fact that we can imagine such a world. It’s quite obvious that our ability to imagine things does not mean that those things are therefore possible. If, for example, I were to say that I can fairly easily imagine a world in which no deity exists, I’m sure Dr. Craig would not take this as proof that God is therefore not a metaphysically necessary being.

Nor am I aware of any evidence from contemporary cosmology which would indicate that a universe which is not subject to Special Relativity could exist. Insofar as I am aware, all of the tenable models of the universe currently under research tend to model space-time as a Minkowski space (or similar geometric object). Special Relativity would apply on all such models. If Dr. Craig is aware of any models which do not treat the universe in this manner, he hasn’t presented them in any of the books, articles, papers, talks, or debates which I have seen. I would certainly welcome such an interesting view, if he can present it.

All of this is a Red Herring, though, because even if it is physically possible in some other universe with different laws, it still stands that it is logically impossible to attain the speed of light in our universe, and it similarly still stands that Dr. Craig should have been aware of this fact.

Now, again, this was just a minor, tangential point, and doesn’t necessarily do much (if anything) to refute the rest of what Dr. Craig said in his Excursus, Part 6. However, I feel that it was a fairly important thing for me to nitpick. You see, a very large part of William Lane Craig’s work is dependent upon his view of the metaphysics of Time, and that view is informed by Dr. Craig’s attempts to comprehend Relativity. The fact that he has, once again, shown himself to be rather ignorant in regards to Relativity casts some very reasonable doubts upon his conclusions about the metaphysics of Time, which in turn makes quite a bit of Dr. Craig’s philosophical and theological work entirely dubious.

## 4 thoughts on “WLC on the Speed of Light”

1. If, for example, I were to say that I can fairly easily imagine a world in which no deity exists, I’m sure Dr. Craig would not take this as proof that God is therefore not a metaphysically necessary being.

Nicely played, sir… Very nicely played, indeed!

2. Awesome, as always.

And I need to figure out how to write equations like that in WordPress.

• It’s inline LaTeX coding. WordPress supports it by default, I believe.

• Thank you, I’ve refrained from posting many equations because they look so sloppy with the native WordPress toolbar. Thanks much, I need to learn LaTeX.