Section 15–4 Transformation of time

(Light clocks / Biological clocks / Experimental verification)

In this section, Feynman discusses light clocks, biological clocks, and experimental verification of length contraction.

1. Light clocks:

“… it is a rod (meter stick) with a mirror at each end, and when we start a light signal between the mirrors, the light keeps going up and down, making a click every time it comes down, like a standard ticking clock (Feynman et al., 1963, section 15–4 Transformation of time).”

According to Feynman, a light clock will work in principle as a rod (meter stick) with a mirror at each end in which we can send a light signal between the mirrors. Physics teachers should clarify that the idealized light clock relies on the principle of constant speed of light. Simply phrased, the light clock is an imaginary time-keeping instrument that is based on the motion of a light beam. Feynman could have explained that the units of space and time are dependent on the speed of the observer’s inertial frame of reference. In essence, the speed of light must appear the same to the observers (whether at rest or in motion) and the units of length and time can be defined by the motion of the light beam.

Feynman held the Richard Chace Tolman professorship in theoretical physics at the California Institute of Technology. In an article titled The Principle of Relativity, and non-Newtonian mechanics, Lewis and Tolman (1909) write that “… the velocity of light will seem the same to two different observers, even though one may be moving towards and the other away from the source of light, constitutes the really remarkable feature of the principle of relativity, and forces us to the strange conclusions which we are about to deduce. Let us consider two systems moving past one another with a constant relative velocity, provided with plane mirrors aa and bb parallel to one another and to the line of motion (Figure 1). An observer, A, on the first system sends a beam of light across to the opposite mirror, which is reflected back to the starting point…” The light clock is also known as Langevin clock, but Feynman could have coined the term Lewis-Tolman clock to recognize Lewis and Tolman for their contribution to the concept of light clock.

Note: Langevin’s paper on the evolution of space and time was published in 1911, two years after Lewis and Tolman’s (1909) paper.

2. Biological clocks:

“…the man’s pulse rate, his thought processes, the time he takes to light a cigar, how long it takes to grow up and get old—all these things must be slowed down in the same proportion… (Feynman et al., 1963, section 15–4 Transformation of time).”

Feynman explains that all phenomena such as a man’s pulse rate, his thought processes, and the time he takes to light a cigar must be slowed down in the same rate because he cannot tell whether he is at rest or moving. In one of his Messenger Lectures, he elaborates that “…if the clock is ticking and I look at the clock in the space ship, then I can see that it is going slow. No, your brain is going slow too! (Feynman, 1965, p. 92).” However, the physics of physical clocks is the same as the physics of biological clocks. Physics teachers should elaborate that daily phenomena such as a man’s pulse rate and his thought processes are mediated by electromagnetic waves that travel at the speed of light. Similarly, gravitational waves travel at the speed of light because gravitons have no mass (just like photons).

Feynman asks whether all moving clocks run slower and what if there is no way of measuring time that ticks at a slower rate. In a sense, it is potentially misleading for Feynman to say that all moving clocks run slower. Physics students may interpret this as a possibility to enjoy a longer lifespan. Specifically, a stationary biological clock tick at the same rate in the same stationary frame of reference. One may emphasize that the biological clock appears slower depending on the relative speed. (Feynman could have used the term relative speed instead of simply speed.) Therefore, physics students should not expect to live almost forever by developing a spacecraft that can move at close to the speed of light.

3. Experimental verifications:

“A very interesting example of the slowing of time with motion is furnished by mu-mesons (muons), which are particles that disintegrate spontaneously after an average lifetime of 2.2×10⁻⁶ sec. (Feynman et al., 1963, section 15–4 Transformation of time).”

Feynman cites an example of the slowing of time with motion using muons that disintegrate spontaneously after an average lifetime of 2.2 µs. To be precise, muons are produced during interactions of cosmic rays with particles near the top of the Earth’s atmosphere. (It is potentially confusing to say that “they come to the earth in cosmic rays” because muons are the products of cosmic rays.) Historically, Rossi and Hall (1941) compared the number of muons at Echo Lake (3240 m) and Denver (1616 m) in Colorado and determined the average lifetime of muons to be 2.4 µs. In a more precise experiment conducted at Mount Washington (using a difference in height of 1907 m), Frisch and Smith (1963) determined the average lifetime of muons (moving between 0.995 c and 0.9954 c) to be 2.2 µs.

Feynman explains that mu-mesons (muons) in their short lifetimes cannot travel much more than 600 meters even at the speed of light. (Based on current Standard Model, muons are no longer considered to be mesons.) Physics teachers should clarify that the distance from the Earth’s atmosphere to the ground appears contracted from the muon’s frame of reference. In other words, the length contraction can be explained as an effect due to the Earth moving toward the muons at a high speed. In summary, an experimenter on Earth observes the time dilation of muons, whereas another experimenter co-moving with a muon would deduce length contractions of mountains.

Questions for discussion:

1. What is the fundamental principle of a light clock?

2. Do moving clocks really run slower?

3. How would you explain that the time dilation can be verified experimentally?

The moral of the lesson: the fact that biological clocks function like a light clock can be experimentally verified using cosmic rays experiments in which muons are created in the Earth’s atmosphere.

References:

1. Feynman, R. P. (1965). The character of physical law. Cambridge: MIT Press.

2. Feynman, R. P., Leighton, R. B., & Sands, M. (1963). The Feynman Lectures on Physics, Vol I: Mainly mechanics, radiation, and heat. Reading, MA: Addison-Wesley.

3. Frisch, D. H., & Smith, J. H. (1963). Measurement of the relativistic time dilation using μ-mesons. American Journal of Physics, 31(5), 342–355.

4. Langevin, P. (1911). L’évolution de l'espace et du temps. Scientia, X, 31–54.

5. Lewis, G. N., & Tolman, R. C. (1909). The Principle of Relativity, and non-Newtonian mechanics. In Proceedings of the American Academy of Arts and Sciences.  44(25), 711-724. American Academy of Arts & Sciences.

6. Rossi, B., & Hall, D. B. (1941). Variation of the rate of decay of mesotrons with momentum. Physical Review, 59(3), 223–228.