One objection to the Kalam Cosmological Argument is that it requires an A Theory of time, but most physicists reject the A theory because of special relativity. Though the main idea of special relativity – that the laws of physics are the same for all observers (in uniform motion), so a microwave oven works just fine on a planet that is moving very fast relative to Earth – is simple, it has strange consequences for our concept of time. When we understand these consequences, we can see why special relativity undermines the A Theory of time.
Last time, I said that the time interval between two events must be different for two observers who are in motion relative to each other. Today I will show why this must be true, using an illustration borrowed from Richard Wolfson‘s excellent book, Simply Einstein.
Imagine you’re holding a long box with a laser at one end, and a mirror at the other end. Here’s how it works: A beam of light departs from the laser. Let’s call that Event A. The light travels “vertically” to the other end of the box, bounces off the mirror, and returns to the source. When the light returns to the source, that’s Event B.
This round trip takes some time, however small. Consider the time interval between events A and B relative to the reference frame of the light box. Let’s say that interval was 6 nanoseconds, since light travels about a foot in one nanosecond. Since you are standing at rest relative to the light box, you will observe that the interval between events A and B is 6 nanoseconds.
Now, imagine that you and the light box are floating past me in deep space, very fast. Equivalently, I am floating past you at that very same speed. Now, what interval will I observe between events A and B?
From my reference frame, the light has further to travel than it does in your reference frame, because from my reference frame, after the light departs from the laser, the box moves “horizontally” before the light beam hits the mirror. So the light beam moves vertically and horizontally to reach the mirror – a longer distance than it had to move from your reference frame. And the same is true for its return trip back to the laser:
(The length of the box is L and the speed at which we are passing each other is v. The three boxes on the right illustrate that the box is in three different positions relative to me at Event A, when the light hits the mirror, and at Event B.)
Since light moves at a constant speed, but it has further to go from my reference frame than it does from your reference frame, that means that if for you the interval between events A and B is 6 nanoseconds, the interval is going to be longer than that for me.
And again, it’s not the the time interval between the two events is “really” 6 nanoseconds. There is no privileged reference frame. You are moving relative to me in just the same way that I am moving relative to you. So both time intervals are correct, with respect to each reference frame, which is the only kind of time interval there is.
Time intervals between events must always be given with respect to a chosen reference frame, because there is no “absolute” reference frame. That’s the whole point of special relativity.
Intuitively, this doesn’t make sense. How can there be two different time intervals between the exact same two events? We assume this is impossible. We assume the passage of time is absolute and consistent across the universe as a whole, so there is always one correct time interval between any two events. There is a kind of “universal clock” that ticks away forever, and after each tick the present moves one step into the past, and one moment of what was once part of the future is now the present, and the moment that had just been the present has moved into the past… across the universe as a whole.
But this is not so. Time, too, is relative. Time is different in each reference frame.
One more illustration, also from Wolfson’s book. Let’s say we have three identical clocks. Two of them, C1 and C2, are floating in deep space, at rest relative to each other. A third clock, C3, is moving – relative to the reference frame of C1 and C2 – such that it passes C1 at Event A and it passes C2 at Event B.
When C3 passes C1 (Event A occurs), it just so happens that all three clocks read the same time: noon. That is, an observer that is equally distant from C1 and C2 reads those two clocks as giving the same time, and an observer that is equally distant from C1 and C3 reads them as giving the same time.
By the time C3 passes C2 (Event B occurs), four hours have elapsed for clock C2, but only two hours have elapsed for clock C3.
This is not because one of the clocks is broken, but because C3 has literally experienced less time relative to C1 and C2.
Note that Event A and Event B occurred at the same place relative to C3: namely, it happened very near the location of C3. But the interval between these two events was two hours, in C3′s reference frame.
In contrast, in a reference frame relative to C1 and C2, events A and B occurred at different times and different places. Event A occurred near C1, and event B occurred near C2. Moreover, the time interval between events A and B was four hours in the reference frame of C1 and C2.
“Moving Clocks Run Slowly”?
Why is this? Many physics textbooks say it’s because “moving clocks run slowly,” but that makes no sense. It wouldn’t be correct to say that clock C3 is moving and clocks C1 and C2 are floating still. Rather, C3 is moving relative to C1 and C2, and C1 and C2 are moving relative to C3. That’s the whole point of relativity. There is no privileged reference frame.
No, this “time dilation” occurs because
Given uniformly moving reference frames (no acceleration), the time between two events is shortest when measured in a reference frame where the two events occur at the same place.
So, the time interval between events A and B was shorter when it was measured from C3′s reference frame (where the two events occurred at the same place) than when it was measured from the reference frame of C1 and C2, from which the two events did not occur at the same place.
The exact same thing happened with the light box. There, the time interval between events A and B was shortest when it was measured from your reference frame, because from your reference frame events A and B occurred at the same place (since you were holding the light box). The time interval was longer when it was measured from my reference frame, because in my reference frame, events A and B occurred at slightly different places, since from my reference frame the light box was moving while the light was traveling from the laser (Event A) to the mirror and then back to the laser again (Event B).
Perhaps you’re beginning to see why special relativity is a problem for the A Theory of time, and thus for the Kalam Cosmological Argument (KCA). But we have a few more things to discuss before we explain the tension between special relativity and the KCA.
Finally, for good measure, here’s a video making roughly the same point:
Or, more abstract:
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