Intervals of Time

by Luke Muehlhauser on October 18, 2010 in Science

One objection to the Kalam Cosmological Argument is that it requires an A Theory of time, but most physicists reject the A Theory. To explain why, I explained Galilean relativity and then Einstein’s theory of special relativity.

Hopefully you remember that special relativity merely asserts that the laws of physics work the same for all reference frames in uniform motion; that is, a microwave oven works just fine on a distant planet moving very fast relative to Earth.

That seems obvious. So why did it take a genius like Einstein to come up with special relativity? On reason is that the implications of this simple hypothesis are very strange, and Einstein’s stroke of insight occurred when he was able to throw out his intuitions about time and follow the data instead.

The speed of light

According to Einstein, the laws of physics, and therefore the speed of light, must be the same for all reference frames; for all observers (from here on out, I’ll drop the “in uniform motion” bit and take it to be assumed).

But if all observers will measure the same speed for light (speed c), then even two observers that are moving relative to each other will observe the same speed for light. And that’s where it gets weird.

Remember my story about the Nerf dart gun. If you’re standing still and I drive toward you in a car and shoot you with a Nerf dart gun, the dart will hit you with greater speed than if I had shot you while standing next to you. And if I pass you and look back and shoot you with the Nerf dart while driving away from you, then (assuming no air resistance and that my gun is powerful enough) the dart will hit you with less speed than if I had shot you while standing next to you.

But that’s not true for light. Let’s say you’re tethered to a space station in deep space, and I fly my spaceship toward you at 100 million miles per hour with my headlights on. The light from my headlights will go past you at 671 million miles per hour, or “speed c.” But if I park my ship next to you and turn on the headlights, that light will still go by you at speed c. And if I zoom past you at 100 million miles per hour and shine a light back at you, that light will go by you at speed c, too.

That seems really weird. How can that be?

It’s a simple consequence of the fact that the laws of physics are the same for all observers, and the speed of light is one of the laws of physics. (The speed of a Nerf dart is not one of the laws of physics.)

Intervals of time

The reason this seems weird is that the fastest we ever travel relative to Earth is only about 600mph, which is not even close to 1% of the speed of light. If we regularly traveled at 80% the speed of light, special relativity would be intuitively obvious to us. But we don’t. So to understand relativity, we need to do what Einstein did: we need to ignore our intuitions and follow the science instead.

To see what simple relativity does to our notion of time, we need to talk about events. Events occur at a certain place and a certain time. The event of the nuclear bombing of Hiroshima occurred at Hiroshima, Japan at 8:15 (Japan time) August 6th, 1945.

We also need to talk about intervals of time. If I take a sip of wine in my apartment at 8:15:40 and a second sip of wine at 8:15:45, the interval between those two events is five seconds.

The weird thing is that according to relativity, the interval between two events cannot be the same for two observers who are moving relative to each other.

If you run past me while I’m taking those two sips of wine, and the interval between the two sips in my reference frame is exactly 5 seconds, then the interval between the two sips in your reference frame will not be exactly 5 seconds (though it will be very, very close to 5 seconds, especially since you’re moving so slowly relative to me).

Moreover, we cannot say that the interval between the two sips was “really” exactly 5 seconds, because that would be claiming there is some absolute or privileged reference frame. But there isn’t. You may be moving relative to me, but all the same, I am moving relative to you, even if I’m sitting still relative to Earth. So there is no “really” to be found. There are, quite simply, two different intervals of time between these two events, and both are equally valid. (In fact there are more than two intervals of time between the two sips, because there are many other reference frames, but for now let’s keep things simple.)

In the next post, we’ll look more closely at why the intervals of time between my two sips of wine must be different for observers who are moving relative to each other.

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{ 9 comments… read them below or add one }

Hermes October 18, 2010 at 7:12 am

One common example of this is used in the design of consumer grade GPS networks.

The clocks in the satellites move relative to each other and the Earth based stations. This movement must be kept in mind with the design of the clocks — they use a different frequency to set the tick rate depending on where the satellite is deployed — to improve accuracy.

Yet, it’s important to know that the rate time passes for each satellite as opposed to the Earth is not a substantial factor at the moment of calculation. It is a factor that has to be accounted for over time if adjustments such as in the tick rate aren’t made in the design of the satellite.

[ Note that I am intentionally leaving out other issues with GPS systems as they detract from the the point about time. ]





Chip October 19, 2010 at 10:06 am

Nitpick: actually, there is a “privileged” time interval between the two sips. It’s the time that passed in the reference frame of the wine glass. This interval is known as the “proper time”, and it measures time as it “feels” to the wine glass. Any other observers would generally measure a different time, true, but the proper time is the smallest possible time between those two events.

Interesting consequence: many people think the distance you could travel in your lifetime is limited by the speed of light. If you live for t=100 years, then you could never hope to reach any position further than 100 light years. This is actually wrong: there is no limit to the distance you can cover in 100 years of proper time. But the time that passes in the rest frame of your destination will be tremendous compared to the time it feels like to you.

So: the Laws Of Physics(TM) do not prevent you from travelling 2 million light years towards the galaxy of Andromeda in your 100-year lifespan… but don’t expect it to be the same by the time you get there!


scott mc laughlin October 19, 2010 at 12:31 pm

I thought I knew this but I clearly don’t, I’m confused, isn’t the speed of light in a vacuum an absolute value?

In the penultimate paragraph you say there’s no absolute reference point, but is this only because you’re talking in seconds, and the definition of a second is relative? What if we defined time relative to the speed of sound in a vacuum, isn;t that absolute? and then would those two timings of the sips of wine be the same?


lukeprog October 19, 2010 at 1:25 pm

scott mclaughlin,

There’s no ‘absolute’ or ‘special’ reference point in spacetime. But yes, the speed of light in a vacuum is absolute.


bossmanham October 20, 2010 at 10:31 am

scott mclaughlin,There’s no ‘absolute’ or ‘special’ reference point in spacetime.

Of course, this is simply assumed in Einstein’s work.


Hermes October 20, 2010 at 12:50 pm
mojo.rhythm October 21, 2010 at 11:24 pm

You folks will probably like this. It’s finally a YouTube video discussing the presentist presuppositions in the Kalam, and how Dr. Craig employs one giant argu-circle in making the case for the tensed view.


Hermes October 22, 2010 at 4:17 am

Mojo, yep; good video.


mojo.rhythm October 22, 2010 at 9:20 pm

scott mclaughlin,There’s no ‘absolute’ or ‘special’ reference point in spacetime. But yes, the speed of light in a vacuum is absolute.  

Velocity of light dude, there is a difference.



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