of time intervals differs when observers are in motion relative to one another.
To state Einstein’s thought experiment, we use a train and a platform beside the train. A
professor stands still on an open railcar at the middle of the train. Another observer,
Katherine, stands still at the middle of the platform. Two lightning rods, shown as gray
towers in Concept 2 and Concept 3, are equidistant from Katherine and the midpoint of
the platform.
We start this experiment with the train not moving, and the professor directly across
from Katherine, so he is also equidistant from the lightning rods. A lightning bolt strikes
each lightning rod. These lightning strikes cause flashes of light that will be visible to the
observers. Photons í packets of light í move from each lightning rod toward them.
Each lightning strike counts as one of the two spatially separated events we are
analyzing. We draw the photons from one rod in blue, and the photons from the other
rod in red, so that you can more easily distinguish them.
When will an observer conclude that the two events are simultaneous? The professor
concludes that the bolts struck simultaneously only if two photons reach him at exactly
the same moment. Why? Since both travel the same distance, the events are
equidistant from him. The professor reasons that if the photons reach him
simultaneously after traveling the same distance at the same speed, they must have
started their journey simultaneously.
Katherine also concludes that the bolts struck simultaneously only if two photons reach
her at a single instant in time. She too believes the events occurred simultaneously if
two photons, traveling the same distance and the same speed, reach her
simultaneously.
All this is “as expected”. Two lightning bolts strike rods, photons from the strike reach
each observer simultaneously, and they conclude that the two bolts struck
simultaneously because the photons traveled the same distance to each observer at the
same speed. This situation is shown in Concept 2, as the photons reach Katherine and
the professor.
Now, Einstein changed the scenario: He put the train in motion. Einstein asked again:
would they both say that the lightning bolts struck simultaneously? That the time interval
between the events was zero?
The answer, as illustrated by Concept 3 is: No. In the scenario we show, Katherine still
states that the lightning bolts struck simultaneously because both photons reach her
simultaneously. However, as you can see, the photons from the strike on the right have
reached the professor, but those on the left have not. His conclusion is that the strike on
the right occurred before the strike on the left.
Although they cannot be readily seen in the illustration, this time we have the strikes
make slight scorch marks on the train. The professor can later walk up and down the
train and reassure himself that the distance between each strike and his position as an
observer is the same.
Einstein’s thought experiment with the train showed that the perception of the time interval between events depends on the observer’s frame of
reference. Specifically, he showed how two events that are perceived as occurring simultaneously in one reference frame would be perceived
as occurring at two different moments in time (non-simultaneously) in another reference frame that is in motion with respect to the first.
Both observers were correct, based on observations in their own reference frames. This phenomenon is called the relativity of simultaneity. It
means that time intervals between events í something that Newton assumed was absolute í are actually relative, that is, they vary depending
on an observer’s state of motion.
As Einstein wrote: “Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment
also simultaneous relatively to the train? We shall show directly that the answer must be negative.”
An observer’s measurement of time intervals depends on his or her frame of reference. Time is relative. Motion alters time. This is a strange
conclusion, but it is true, and it changes our view of the universe. Few thought about it before Einstein, because in his day, the effect was
inaccessible to measurements at the low speeds humans were accustomed to observing. For instance, for a jogger moving at several meters
per second past a stationary observer, the difference is negligible (about one part in 10^16 ), but the effect becomes much more significant as the
relative speed between two observers increases.
Since Einstein’s time, technological advances have made it necessary to factor this effect into the design of certain systems. You may have
seen or used a Global Positioning System (GPS) unit, which receives signals from a network of orbiting satellites to pinpoint its location on the
Earth’s surface. The lightning strikes we considered are analogous to the signals that are emitted by satellites. The GPS unit works by
interpreting the time delays in the electromagnetic signals that are received from these fast-moving satellites whose positions are precisely
known. Relativistic considerations play a central role in making the system work.Train stationary relative to
observers
Light reaches each observer at an
instant in time
Both think the strikes occurred
simultaneouslyTrain moving relative to one
observer
Professor on train: Strikes NOT
simultaneous
Katherine on platform: Strikes
simultaneous
Observers disagree on whether events
are simultaneous(^642) Copyright 2007 Kinetic Books Co. Chapter 35