## Celebrating Einstein

### How High Up Is That Place?  How Far In The Future Is That Event?

"Up" is a direction that depends on where you stand.  "The future" is also a direction, and which direction it is depends on how you move.  The first idea is ancient; the latter realization we owe largely to a discovery of Albert Einstein.

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A.  Places and Times

You're a passenger in a car, taking a trip with some of your family, when you get a call on your mobile phone.  As the car continues down the road, you pick up the phone, talk, and then put the phone back where you picked it up.

Or did you?

Well, it was where you picked it up as far as you're concerned.  But keep in mind that you're in a vehicle traveling down the road.  In your frame of reference, the phone didn't move.  You put it back in exactly the same spot it was before.

But to someone watching from a car parked beside the road-a highway patrol officer, for example-you and the phone have both moved.  From his frame of reference, where the phone was when you picked it up is a very different place from where it was when  you put it down again.

The way that both events-picking up and putting down the phone-can occur in the same place and in different places is not hard to understand.  The difference in what constitutes "the same place" corresponds to a difference in frames of reference.  Whether or not two events are at the same place or at different places depends on your frame of reference.  And that frame of reference tells you what places to consider the same at different times.

Now let's assume that both you and your brother, sitting behind you in the same car, get phone calls at the same time.  Your calls are simultaneous, at least, as far as you and the rest of the family in the vehicle are concerned.  But in the reference frame of the patrol officer, it turns out that your brother's call actually occurred-however slightly-first.  And this has nothing to do with either you or the patrol officer making a faulty observation.  The difference in what constitutes "the same time" follows the difference in the frames of reference.  The difference turns out to be small, but nonetheless it is quite real.

On top of that, from the reference frame of anyone passing you while traveling down the road in the same direction, your call occurred before your brother's did.  Again, from this reference frame, the time between when your call came in and when your brother's did is very short, but the time span in real.  So, depending entirely on the frame of reference, either your phone rang first, or your brother's rang first, or both rang at the same time.  Whether the times are the same or different is determined similarly to the way places in space are determined to be the same or different.

This remarkable fact was brought to the world's attention by a discovery of Albert Einstein.  Einstein found that, just as one's frame of reference determines which places are the same at different times, it also determines which times are the same at different places.  He demonstrated this in his first paper on what came to be known as the Special Theory of Relativity.

This discovery seems odd at first glance, to put it mildly.  From our everyday experience, it's easy to see how places are the same or different depending on how we move, but we never notice events changing their sequence depending on how we move.  This difference in frames of reference depends on speed, and it turns out that changes in time sequence don't become obvious unless the speeds involved are quite large.

The fact that what came first for you may have come second for me is, perhaps, the one feature of Einstein's theory that most people find hardest to really believe, much less assimilate.  After all, in our usual experience, the differences in time order are so small that we don't even notice them; most things that occur in different order in our different reference frames are so nearly simultaneous that we never notice the difference.

On the other hand, there is more going on in the universe that what is obvious to us from our usual experience.  Some of these non-obvious events involve high spends and drastically different frames of reference in which differences in the order of events would be much clearer.

If our usual experience included moving around at much higher speeds that we actually do, the fact that events in different places can be simultaneous and sequential would be as obvious as the fact that events at different times can be at the same place and at different places.  We would have an equally intuitive grasp of both facts, instead of just one.  But, since we don't have that kind of experience, is there any way for us to get a handle on the concept, and get past any feeling that it just doesn't make sense?

Perhaps.  There is an analogy, within grasp of our ordinary intuition, that can at least give us a starting point.     (.....continued)

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