Special relativity concerns the principle that the speed of light in a vacuum is the same for inertial observers, and the consistency of physical laws. Even as an explanatory analogy, the expression “time as a photon experiences it” needs care: an inertial reference frame at rest alongside a photon cannot be defined.
When comparing time, it is more accurate to set out the comparison procedure before asking “Which clock is slow?” The question changes depending on whether we are watching images exchanged across a distance, discussing coordinate time corrected for signal travel, or placing two clocks side by side when they meet again. Even explanations using the same term “time dilation” can seem contradictory if this procedure is omitted. The numerical examples here are thought experiments that leave out effects such as gravity to examine the relationship for motion at constant velocity. When dealing with actual devices or journeys, the omitted conditions need to be included again.
1. Conditions for comparing time
To compare a moving clock with a stationary one, specify who is measuring and in which reference frame. The example of a light clock explains time dilation by considering both the path of light and its constant speed. A delay in light arriving from a distant place cannot by itself explain relativistic time dilation in its entirety.
2. When each observer describes the other clock as slow
Inertial observers moving at constant velocity relative to one another can each judge the other’s clock to run slowly. A journey in which they meet again to compare accumulated time requires examining the paths of departure, turnaround and reunion together. Applying a constant-velocity formula from just one side to the whole journey leaves out necessary conditions.
3. Distinguishing the speeds of light and matter
A massive object reaching the speed of light in a vacuum and light propagating through a medium are different problems. Reducing the propagation speed in a medium does not change the invariant speed in a vacuum. When explaining time dilation, identify the reference frame, path and measurement procedure first.
4. What a light clock actually compares
A light clock is an imagined device that counts time whenever light makes a round trip between two mirrors. In the frame moving with the clock, the light travels straight between the mirrors. In another frame, the mirrors also move sideways, making the path of the light appear longer. Applying the condition that the speed of light in a vacuum is the same in both frames produces a different relationship between the time intervals corresponding to the round trip. The explanation is not that the clock malfunctions or that light becomes tired and slows down.
For a simple numerical example, set the relative speed to 0.6 times the speed of light in a vacuum. Under ideal conditions of constant-velocity motion, the time dilation factor is 1 divided by the square root of 1 minus 0.6 squared, or 1.25. For two events at which the moving clock records an interval of 4 units at its own location, the coordinate time interval in the comparison frame is 5. These numbers are assumptions used to illustrate the principle, not a journey schedule that also calculates the acceleration and gravity experienced by an actual spacecraft.
What matters in the calculation is which two events are being compared. Distinguish the time measured by a clock between events at its own location from times assigned using synchronized clocks at different locations. Comparing clocks in different reference frames also involves the definition of simultaneity. This is why merely viewing one distant clock through a telescope cannot complete every comparison.
For example, without correcting for the delay in light’s arrival, images of a clock moving away and a clock approaching can show different changes. These observations include signal travel and Doppler effects. To explain the relativistic relationship between times, state how the travel time of light has been handled. A useful starting point is to avoid treating “looks like” and “is measured in the reference frame” as equivalent.
5. The round-trip path in the twin thought experiment
There is no logical contradiction in two observers passing each other at constant relative velocity each describing the other’s clock as slow. They group distant events as simultaneous in different ways. The problem of separating at the same starting point and then reuniting to compare clocks side by side includes additional conditions. Specify which observer changed direction and when, and which paths the two clocks followed through spacetime.
We can simplify a round trip by ignoring differences in gravity between Earth and the traveler and comparing the constant-velocity segments. The traveler changes their state of motion in order to return, so the whole process cannot be described using a single inertial frame. An accelerated segment is an important difference, but simply saying acceleration damages the clock and makes it slow misses the point. The problem is to compare accumulated proper time along each path.
In the earlier example at 0.6 times the speed of light, if the total Earth-frame time for the constant-velocity segments is set to 10, the sum of the traveler’s clock times for the corresponding segments is 8. This is an idealized example in which the turnaround is short enough to neglect. An actual journey needs to include accelerated segments, gravity and the details of the path. Although the numbers help explain the idea, they must not be read as capabilities already demonstrated by a real mission.
When drawing the thought experiment, mark the events of departure, turnaround and reunion first. Then record which frame describes each segment and the time actually recorded by the clock. Checking whether a diagram compares only communication images during the journey or also the accumulated times of clocks at reunion makes it easier to understand why different explanations give different numbers.
6. Common misconceptions about a photon’s viewpoint and light in a medium
Accelerating a massive object to the vacuum speed of light is a different problem from light that propagates at that speed from the outset. Transformations between inertial frames in special relativity cannot be applied unchanged to an observer at rest alongside light. Presenting “the universe as a photon sees it” as the experience of a rigorously defined observer therefore creates a problem. Even when used as an analogy, the expression needs an explanation that this is not an actually definable reference frame.
How proper time is described along a photon’s path and whether a photon has consciousness and experiences time are entirely different questions. Turning the mathematical properties of a physical quantity into a human experience easily introduces a clock or observer that does not exist. What can be explained are the relationships between the speed of light, energy and signals measured by observers. However engaging the wording, do not treat a viewpoint without a measurement procedure as a physical fact.
The fact that light propagates more slowly in water or glass than in a vacuum also does not mean the invariant vacuum speed has changed. This is a problem with additional conditions involving interactions between light and the medium. An explanation that particles can move faster than light in a medium therefore must not be turned into a claim that they have exceeded the vacuum speed-of-light limit. First write down which speeds are being compared and relative to what.
The final check when reading about time dilation is to distinguish the reference frame, the two events, the clock and the signal. Without these four items, numbers and analogies become difficult to understand. Effects in special relativity concerning constant-velocity motion and effects in general relativity that include gravity should also be explained separately as appropriate to the situation. Establishing the observational procedure first turns “time slows down” from a vague impression into a physical claim that can be compared.