BOSTES HSC Physics 2015 Question 32

Question: 
This question is asked in the context of medical physics. Students are expected to explain the impact of advances in an understanding of waves on the development of imaging technologies. Three examples should be provided in the answer.

Marking Guidelines:

Criteria	Marks
Relate three imaging technologies to an understanding of waves. Assess the impact of advances on the development of imaging technologies.	6

(Source: https://www.boardofstudies.nsw.edu.au/hsc_exams/2015/guides/2015-hsc-mg-physics.pdf)

Possible answer:

There are more than dozens of specific applications of imaging technologies such as magnetic resonance imaging and positron emission tomography. Importantly, the answers should be related to an understanding of waves in different frequencies (or wavelengths). Below are three examples of imaging technologies that are closely related to medical physics:

1. Thermal (infrared) imaging: The thermal sensors essentially record the emitted infrared radiations from the skin surface of a patient. In some applications, thermal imaging provides an objective measurement of temperature changes that are clinically significant. Currently, the medical applications include not only fever screening but also inflammatory diseases and complex regional pain syndrome.

2. Ultrasound imaging: The depth of penetration of ultrasound waves is dependent on human tissues and the ultrasonic frequency. The principle of ultrasound is based on the reflection and refraction of ultrasound waves while propagating the tissues which have different densities. In Doppler-based modes, ultrasound waves help to determine the velocity of a moving tissue and the blood circulation in a baby during pregnancy.

3. X-ray imaging: Different organs and tissues have different sensitivities and absorptions of X-ray waves. Essentially, denser tissues such as bone can absorb more X-ray radiations as compared to other organs and tissues, and there is a greater attenuation of the X-ray waves. In X-ray imaging, the image of the human body has a higher resolution due to the shorter wavelengths of X-ray waves.

Feynman’s insights or goofs?:

Physics teachers may use Feynman’s lectures to explain the concept of waves in imaging technologies as shown below.

1. Thermal (infrared) imaging: Feynman says that “there are also infrared waves traveling from the warm foreheads to the cold blackboard (Feynman et al., 1964, section 20–2 Three-dimensional waves).” However, this does not mean that infrared waves only propagate from the warm bodies. Of course, infrared waves are emitted from the warm bodies as well as cold bodies and even dead bodies. Physics teachers should clarify that oscillations of molecules in bodies near room temperature can emit infrared waves. On the other hand, objects at a lower temperature can emit microwaves.

More importantly, Feynman adds that “[w]e are blind when we measure the infrared reflection coefficient of sodium chloride, or when we talk about the frequency of the waves that are coming from some galaxy that we can’t see — we make a diagram, we make a plot (Feynman et al., 1964, section 20–3 Scientific imagination).” That is, we can make a plot of different frequencies of the infrared waves and arbitrarily assign different colors to temperatures of bodies. It does help to visualize or distinguish the different temperatures of warm bodies.

Interestingly, Feynman suggests that “one day the physical review of the blind men might publish a technical article with the title ‘The Intensity of Radiation as a Function of Angle under Certain Conditions of the Weather’ (Feynman et al., 1964, section 20–3 Scientific imagination).” In a sense, we are also the blind men when the atmospheric radiations include infrared waves. However, we are not completely blind because we can visualize the intensity of atmospheric radiations as a function of wavelength and angle, under certain meteorological conditions.

2. Ultrasound imaging: According to Feynman, “waves like sound waves start out from such a source very much longer in wavelength than one usually considers in sound waves, but still they are sound waves, and they travel around in the earth. The earth is not homogeneous, however, and the properties, of pressure, density, compressibility, and so on, change with depth, and therefore the speed varies with depth. Then the waves do not travel in straight lines — there is a kind of index of refraction and they go in curves (Feynman et al., 1963, section 51–3 Waves in solids).” Similarly, ultrasonic waves travel in curves because of the changes in density of human tissues. Importantly, there are also reflections of waves and attenuations of amplitude due to density changes.

In addition, Feynman’s explanation of Doppler effect of moving atoms is a good analogy for moving tissues. In Feynman’s own words, “[s]uppose that the atoms were emitting, instead of sine waves, a series of pulses, pip, pip, pip, pip, at a certain frequency ω₁. At what frequency would they be received by us? The first one that arrives has a certain delay, but the next one is delayed less because in the meantime the atom moves closer to the receiver. Therefore, the time between the “pips” is decreased by the motion. If we analyze the geometry of the situation, we find that the frequency of the pips is increased by the factor 1/(1−v/c) (Feynman et al., 1963, section 34–6 The Doppler effect).” That is, we can detect an increase in the frequency of reflected ultrasound waves when the tissues are moving toward the ultrasonic receiver.

3. X-ray imaging: Feynman clarifies that “[x]-rays are nothing but very high-frequency light. If we go still higher, we get gamma rays. These two terms, x-rays and gamma rays, are used almost synonymously. Usually, electromagnetic rays coming from nuclei are called gamma rays, while those of high energy from atoms are called x-rays, but at the same frequency they are indistinguishable physically, no matter what their source (Feynman et al., 1963, section 2–2 Physics before 1920).” Thus, physics teachers may explain that x-rays are basically higher frequency electromagnetic waves. Importantly, Feynman also distinguishes gamma rays from nuclei, cosmic rays, and artificial sources.

In defining x-rays, Feynman explains that “[w]here the ultraviolet stops, the x-rays begin, but we cannot define precisely where this is; it is roughly at 10⁻⁸ m, or 10⁻² μm. These are ‘soft’ x-rays; then there are ordinary x-rays and very hard x-rays; then γ-rays, and so on, for smaller and smaller values of this dimension called the wavelength (Feynman et al., 1963, section 26–1 Light).” In short, the hard x-rays have shorter wavelengths as compared to soft x-rays. This is because electromagnetic radiations that have shorter wavelengths behave more like particles. Simply put, x-rays appears to be soft particles or hard particles depending on their wavelengths.

References: 

1. 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. 

2. Feynman, R. P., Leighton, R. B., & Sands, M. (1964). The Feynman Lectures on Physics, Vol II: Mainly electromagnetism and matter. Reading, MA: Addison-Wesley.

BOSTES HSC Physics 2015 Question 31

Question: 
This question is asked in the context of geophysics. Students are expected to explain the impact of “remote sensing applications” on society. Three examples should be provided in the answer. 

Marking Guidelines:

Criteria	Marks
• Assess the impact of remote sensing applications on society. • Support the answer using three specific examples.	6

(Source: https://www.boardofstudies.nsw.edu.au/hsc_exams/2015/guides/2015-hsc-mg-physics.pdf)

Sample answer: 
1. Satellites have improved weather forecasts by capturing images that track weather events such as a hurricane or typhoon. This provides early warnings that help to save lives and protect properties.
2. Using infrared sensors to monitor vegetation helps to improve crop yields and plan for production shortages. This may allow food to be redistributed in areas where there are possible shortages.
3. Using magnetic sensors for mineral exploration such as detecting iron ore deposits. This can be done promptly such that societies have access to minerals efficiently.

Comments:

To achieve six marks in this question, students are expected to make informed judgments about the impact of the remote sensing applications on society and support their answers using three specific applications. However, there are more than hundreds of specific applications of remote sensing. For instance, we could classify applications of remote sensing in terms of electromagnetic waves. Importantly, according to Sabins (1997), “[r]emote sensing is the science of acquiring, processing, and interpreting images and related data, acquired from aircraft and satellites, that record the interaction between matter and electromagnetic energy (p. 1).” In other words, we can focus on common applications in which the basic principle involves electromagnetic waves. Below are three examples of remote sensing applications that are closely related to geophysics:

1. Visible light waves: This refers to satellite images that record visible light waves from the earth’s surface. For example, Google Earth allows everyone to view satellite images, maps, or terrains for purposes such as navigation. However, satellite images can also be used for monitoring of volcanic eruptions and island formations (natural or artificial).

2. Infrared waves: The radiations recorded in the infrared satellite images can be a measure of temperature. It is also useful to use infrared light sensors to detect forest hot spots which could be caused by lightning or arson. Alternatively, infrared sensors can be used to monitor the temperature of earth’s surface to have a deeper understanding of global warming issues.

3. Radio waves: The altitudes of mountains, lands, and seas can be monitored by using radio waves. That is, radio waves are transmitted by satellites and the altitude of earth’s surface can be determined by measuring the time it takes the waves to reflect back to the radar. These altitude measurements can be useful for construction purposes such as building bridges or tunnels.

Applications of remote sensing include a wide range of fields such as agriculture, archaeology, cartography, hydrology, meteorology, and oceanography. However, students’ answers should be closely related to geophysics which is the context of the question. Importantly, the three examples should show significant impacts of remote sensing on society.

Feynman insights?: 

Remote sensing commonly involves the use of various instruments and electromagnetic waves to see earth’s physical processes. It should be insightful to explain this principle of remote sensing by using the following words of Feynman, “[t]he electromagnetic field can carry waves; some of these waves are light, others are used in radio broadcasts, but the general name is electromagnetic waves. These oscillatory waves can have various frequencies. The only thing that is really different from one wave to another is the frequency of oscillation. If we shake a charge back and forth more and more rapidly, and look at the effects, we get a whole series of different kinds of effects, which are all unified by specifying but one number, the number of oscillations per second. The usual ‘pickup’ that we get from electric currents in the circuits in the walls of a building have a frequency of about one hundred cycles per second. If we increase the frequency to 500 or 1000 kilocycles (1 kilocycle = 1000 cycles) per second, we are ‘on the air,’ for this is the frequency range which is used for radio broadcasts. (Of course, it has nothing to do with the air! We can have radio broadcasts without any air.) If we again increase the frequency, we come into the range that is used for FM and TV. Going still further, we use certain short waves, for example for radar. Still higher, and we do not need an instrument to ‘see’ the stuff, we can see it with the human eye. In the range of frequency from 5 × 10¹⁴ to 10¹⁵ cycles per second our eyes would see the oscillation of the charged comb if we could shake it that fast, as red, blue, or violet light, depending on the frequency. Frequencies below this range are called infrared, and above it, ultraviolet. The fact that we can see in a particular frequency range makes that part of the electromagnetic spectrum no more impressive than the other parts from a physicist’s standpoint, but from a human standpoint, of course, it is more interesting (Feynman et al., 1963, section 2-2 Physics before 1920).” Alternatively, a broader definition of remote sensing may include magnetic fields and gravitational fields in addition to electromagnetic fields.

Essentially, physics teachers should explain that remote sensing may involve electromagnetic waves such as visible light waves, infrared waves, or radio waves. Furthermore, all these waves, which contain a great amount of information, are the same kind of waves that differ in the wavelength or frequency. Interestingly, during a BBC interview, Feynman (1994) explains that “[t]he radio waves are just the same kind of waves, only much longer waves. Then there’s the radar from the airplane which is looking at the ground to figure out where it is, which is coming through this room too, plus X-rays, cosmic rays, all these other things which are exactly the same kind of waves, just shorter and faster, or longer and slower - it’s all the same thing. So this big field, this big area of irregular motions, this electric field, this vibration contains a tremendous information (p. 132).” However, Feynman may be perceived as sloppy when he uses terms such as longer waves instead of longer wavelengths.

References: 

1. Feynman, R. P. (1994). No Ordinary Genius: The Illustrated Richard Feynman. New York: W. W. Norton & Company. 
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. Sabins, F. F. (1997). Remote Sensing - Principles and Interpretation (3rd ed.). New York: W.H. Freeman. 

BOSTES HSC Physics 2015 Question 30

Question:
Explain how Newton’s Laws of Motion and Newton’s Law of Universal Gravitation were applied during the Cassini mission.

Marking Guidelines:

Criteria	Marks
• Explanation using Newton’s Three Laws of Motion and Newton’s Law of Universal Gravitation during the Cassini mission: (1) launch from Earth; (2) travelling to Saturn; and (3) orbiting Saturn.	6

(Source: https://www.boardofstudies.nsw.edu.au/hsc_exams/2015/guides/2015-hsc-mg-physics.pdf)

Sample answer:

Launching the probe from Earth’s surface requires the use of Newton’s third law of motion during the rocket’s operation. This occurs when exhaust gases are expelled downward and thus, there is an upward force on the rocket. During the launch, the rocket’s acceleration is dependent on its mass and the force of the engines as predicted by Newton’s second law of motion.

During the journey to Saturn, the probe does not experience air resistance and continues in its state of motion as described by Newton’s first law of motion.

The Slingshot effect utilizes Newton’s Law of Universal Gravitation as well as the Law of conservation of momentum (Newton’s Third Law of motion) to increase the velocity of the space probe.

A stable orbit can be predicted by using Newton’s Law of Universal Gravitation. The orbital velocity of the space probe is related to its orbital radius.

Comments:

Based on the marking guidelines, students are expected to explain how Newton’s Law of Universal Gravitation and Newton’s three laws of motion were applied to the three parts of the Cassini mission: launch, traveling to Saturn, orbiting Saturn. However, we can also explain Cassini mission by using the law of conservation of angular momentum and the law of conservation of energy. For instance, Warren (2003), a physics textbook author, writes that “[t]he probe picks up angular momentum from the planet (which loses an equal amount of angular momentum). Gravity allows the ‘coupling’ between the probe and planet to facilitate the transfer. For this reason, gravity-assist trajectories should more correctly be called angular momentum-assist trajectories (p. 30).” In short, Cassini increases speed by using the gravity-assist technique and the planet decreases speed based on the law of conservation of angular momentum or law of conservation of energy.

The sample answer (as mentioned above) with regard to the three parts of the mission: launch from Earth, traveling to Saturn, orbiting Saturn can be improved as follows:

1. Launch from Earth: During the launch of Cassini, the sample answer mentions that the acceleration of the rocket is described by Newton’s second law, and the upward force on the rocket is caused by the exhaust gases that are expelled downward based on Newton’s third law. However, the launch of the probe requires the upward force on the rocket to exceed the weight of the rocket which is governed by Newton’s law of universal gravitation. Furthermore, Newton’s third law can be expressed as a law of conservation of linear momentum such that the increase in forward momentum of the rocket equals to backward momentum of the exhaust gases.

2. Traveling to Saturn: The sample answer states that Newton’s first law of motion is relevant during the Cassini’s journey to Saturn because it does not experience friction or air resistance. On the contrary, Newton’s first law does not strictly apply to the Cassini mission because there are non-zero gravitational forces acting on Cassini everywhere. Importantly, we can explain that the resistive forces due to air resistance and gravitational forces are close to zero when it is reasonably far from the planets.

3. Orbiting Saturn: The sample answer specifies that a stable orbit can be predicted by using Newton’s law of gravitation and the orbital velocity determines the radius of the orbit. However, the orbit of the probe could be elliptical instead of circular based on Kepler’s laws of planetary motion.

Lastly, the sample answer states that the slingshot effect utilizes Newton’s law of gravitation and Newton’s Third Law to increase the velocity of Cassini. Nevertheless, the phrase slingshot effect is a misnomer and it could be replaced by a better term such as gravitational assist or simply gravity assist. However, the technique of gravity assist that increases the speed of Cassini is dependent on the gravitational force of a planet. For example, when Cassini is approaching Jupiter, there is an exchange of orbital kinetic energy and angular momentum between Cassini and Jupiter. Importantly, the total orbital kinetic energy remains constant: Cassini gains orbital kinetic energy whereas the planet loses its orbital kinetic energy.

Feynman’s insights or goofs?: 

Firstly, Feynman mentions that “a rocket of large mass, M, ejects a small piece, of mass m, with a terrific velocity V relative to the rocket. After this the rocket, if it were originally standing still, will be moving with a small velocity, v. Using the principle of conservation of momentum, we can calculate this velocity to be v = (m/M)⋅V. So long as material is being ejected, the rocket continues to pick up speed. (Feynman et al., 1963, section 10–4 Momentum and energy).” Note that the velocity of the ejected material (V) is relative to the rocket instead of the Earth. However, to be more precise, we can explain that the initial gain in velocity is (m/M)⋅V, but the subsequent gain in velocity can be increased because of the decrease in the total mass of the rocket, M. 

Furthermore, in An Introduction to Mechanics, Kleppner and Kolenkow (2014) write that “[t]he law is often stated in words such as ‘A uniformly moving body continues to move uniformly unless acted on by a force,’ but the underlying concept is really the idea of an isolated body… Newton’s first law raises a number of questions such as what we really mean by an ‘isolated body’ (p. 51).” In other words, there is a problem of defining an isolated body. Similarly, Feynman (1995) explains that “as soon as we allow the presence of gravitating masses anywhere in the universe, concept of such truly unaccelerated motion becomes impossible, because there will be gravitational fields everywhere (p. 93).”

On the other hand, Feynman mentions that “if we can remember some of Kepler’s laws, and add some other laws like the conservation of energy - we can figure out that if the particle didn’t escape, it would make an ellipse, and we can figure out how far away it would get, and that’s what we’re going to do now. If the perihelion of the ellipse is a, how far is the aphelion, b? (Feynman, Gottlieb, & Leighton, 2006, p. 72).” Simply phrased, the probe’s orbital motion is elliptical. More importantly, the terms aphelion and perihelion should be used instead of radius. The aphelion is a point in the orbit of a planet (or a probe) that is furthest from the sun, whereas perihelion is a point in the orbit that is nearest to the sun.

Note:

In Genius: Richard Feynman and modern physics, Gleick (1992) writes that

“Feynman’s spacecraft would use the outer edges of the earth’s atmosphere as a sort of warm-up track and accelerate as it circled the earth. An atomic reactor would power the jet by heating the air that was sucked into the engine. Wings would be used first to provide lift and then, when the speed rose beyond five miles per second, ‘flying upside down to keep you from going off the earth, or rather out of the atmosphere.’ When the craft reached a useful escape velocity, it would fly off at a tangent toward its destination like a rock from a slingshot. 

Yes, air resistance, heating the ship, would be a problem. But Feynman thought this could be overcome by delicately adjusting the altitude as the craft sped up—‘if there is enough air to cause appreciable heating by friction there is surely enough to feed the jet engines’ (p. 219).”

References: 

1. Feynman, R. P., Gottlieb, M. A., & Leighton, R. (2006). Feynman’s tips on physics: reflections, advice, insights, practice: a problem-solving supplement to the Feynman lectures on physics. San Francisco: Pearson Addison-Wesley.

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. Feynman, R. P., Morinigo, F. B., & Wagner, W. G. (1995). Lectures on gravitation (B. Hatfield, ed.). Reading, MA: Addison-Wesley. 

4. Gleick, J. (1992). Genius: Richard Feynman and modern physics. London: Little, Brown, and Company. 

5. Kleppner, D., & Kolenkow, R. (2014). An Introduction to Mechanics (2nd ed.). Cambridge: Cambridge University Press. 

6. Warren, N. (2003). Excel HSC Physics. Glebe, NSW: Pascal.

BOSTES HSC Physics 2015 Question 29

Question:

In the Large Hadron Collider, protons move at a speed about 0.99999 c.
(a) What are the advantages of using superconductors to produce magnetic fields in the Large Hadron Collider? 

(b) Discuss concepts in special relativity that are related to the high speed of protons in the Large Hadron Collider.

Marking Guidelines:

29(a) Criteria	Marks
• Identify two advantages	2
• Identify an advantage	1

Sample answer:

Strong magnetic fields are required to guide the path of protons due to their high speeds and the mass dilation of protons. To produce strong magnetic fields, very high electric currents are required and this is feasible by using superconductors.

29(b) Criteria	Marks
• Discusses concepts in special relativity that are related to high speed of protons in the Large Hadron Collider.	3

Sample answer:

The protons are moving at almost the speed of light and this is related to the concept of mass dilation. Mass dilation implies that an increase amount of electrical energy is needed to accelerate the protons. (Physics teachers may accept answers that include length contraction/time dilation or non-inertial frame of reference.)
(Source: https://www.boardofstudies.nsw.edu.au/hsc_exams/2015/guides/2015-hsc-mg-physics.pdf)

Comments:

There are at least three advantages of using superconductors to produce the magnetic fields and guide protons around the Large Hadron Collider may include strong magnetic fields, minimal generation of thermal energy, and lower electrical power consumption.

1. Strong magnetic fields: The magnetic fields of Large Hadron Collider can be as high as about 8 Teslas and it is about 10 000 times stronger than the earth’s magnetic fields. Strong magnetic fields are required to deflect the protons that are moving at high speeds. To produce strong magnetic fields, high electric currents are required and superconductors allow very high electric currents.

2. Minimal generation of thermal energy: As mentioned earlier, high electric currents are required to achieve strong magnetic fields. If there is electrical resistance in the magnets, there will be ohmic heating, and thus, an increase in temperature of the magnets or even overheating. However, the electrical resistance of a superconductor is effectively zero, and the generation of thermal energy is minimal.

3. Lower electrical power consumption: In the words of Lederman (1993), “[o]ne could ramp the model magnets from zero current to 5,000 amperes in 10 seconds, and the superconductivity persisted. In 1978-79 a production line began producing twenty-one-foot magnets with excellent properties, and in 1983 the Tevatron began operating as a superconducting ‘afterburner’ at the Fermilab complex. The energy went from 400 GeV to 900 GeV, and the power consumption was reduced from 60 megawatts to 20 megawatts, with most of that used to produce liquid helium (p. 234).” In other words, the reduction in electrical power consumption also results in cost savings.

In part (b) of the question, students are expected to discuss the application of special relativity to the protons in the Large Hadron Collider. The sample answer involves the concept of mass dilation that means an increasing amount of energy is needed to accelerate the proton. However, in an article titled The concept of mass (mass, energy, relativity), Okun (1989) writes that “there is in the theory of relativity essentially just one term, mass, and all the others come ‘from the devil’ (p. 118).” In other words, he disagrees with the use of terms such as relativistic mass, transverse mass, and longitudinal mass. 

Okun (1989) has five arguments against the concept of relativistic mass and the definition of mass in terms of E = mc². The five arguments are summarized as shown below:

1. Aesthetic: The equations E² – p² = m² and p = Ev are elegant rather than E = mc².

2. Ethical: It creates the illusion that E/c² is a universal measure of inertia or universal gravitational mass.

3. Philosophical: There is not a complete equivalence of mass and energy as suggested by E = mc².

4. Terminological: There are confusions in the notation and terminology. Okun prefers the equation E₀ = mc² instead of E = mc².

5. Pedagogical: Students who learn the concept of relativistic mass cannot truly understand the essence of the theory of relativity.

On the contrary, in an article titled In defense of relativistic mass, Sandin (1991) writes that “The one equation nearly every student brings to an introductory treatment of relativity is E = mc². From the pro-relativistic mass point of view (the pro-view), this famous equation states with elegant simplicity that energy and mass are equivalent (p. 1032).” Sandin’s arguments to support relativistic mass are shown below:

1. Aesthetic: The equation E = mc² is elegant and simple.

2. Ethical: It is consistent to accept the equivalence of inertial mass and gravitational mass (both equal to E/c²).

3. Philosophical: Energy and mass are equivalent as suggested by E = mc². Thus, there is a direct proportionality between energy and mass.

4. Terminological: To be precise, one may use equations such as Δm = ΔK_i/c².or Δm = E_ex/c².

5. Pedagogical: The concept of relativistic mass is consistent and simple within relativity, whereas four-vectors can be unnecessarily complicated for students.

There is no agreement on the use of terms such as relativistic mass among physicists. Some physicists are also against teaching the concept of length contraction and time dilation in the theory of special relativity.

Feynman’s insights or goofs?:

Feynman states that “[t]he mass varies with velocity according to the law m = m₀/√(1−v²/c²) where m₀ is the mass of the body at rest and c is the speed of light (Feynman et al., 1963, section 10-5 Relativistic momentum).” In other words, Feynman is open to the concept of relativistic mass or velocity-dependent mass. Furthermore, Feynman explains that “[i]n the Einstein relativity theory, anything which has energy has mass — mass in the sense that it is attracted gravitationally. Even light, which has an energy, has a ‘mass’ (Feynman et al., 1963, 7–8 Gravity and relativity).” That is, it is possible that a beam of light has ‘mass’ because it has energy. This is based on the principle of equivalence of energy and mass. However, this approach is objected by particle physicists such as Okun.

On the contrary, Feynman also provides the alternative view: “the following relations are easily proved, and turn out to be very useful: E² − P²c² = m₀²c⁴ and Pc = Ev/c (Feynman et al., 1963, section 16–5 Relativistic energy).” In other words, the two equations do not need the concept of mass dilation or relativistic mass. Simply put, Feynman does not care so much about terminologies and he has a pragmatic attitude toward physics. (In short, it is more important for him to check whether the equations work.) Similarly, in his Nobel speech, Feynman (1965) opines that “[m]any different physical ideas can describe the same physical reality (p. 30)” and that “equation guessing might be the best method to proceed to obtain the laws for the part of physics which is presently unknown (p. 31).”

Note: 

1. Okun (1989) quotes Einstein’s letter to Barnett in 1948, “It is not good to introduce the concept of the mass, m_r = m₀ /√(1 – v²/c²) of a moving body for which no clear definition can be given.” However, in Autobiographical notes, Einstein is supportive of the idea of how kinetic energy may contribute to mass: “…the theory had to combine the following things: 1. From general considerations of special relativity theory it was clear that the inert mass of a physical system increases with the total energy (therefore, e.g., with the kinetic energy). 2. From the very accurate experiments… it was empirically known with very high accuracy that the gravitational mass of a body is exactly equal to its inert mass (Einstein, 1949, p. 61).” 

2. In Lederman’s (1993) words, “[t]he system is self-correcting. If the particle gains too much energy (mass), its radius will increase and it will arrive later at the gap and see a decelerating voltage, which will correct the error (p. 219).” Lederman was the director of Fermilab and he was awarded Nobel (Physics) Prize 1988 for the neutrino beam method and the demonstration of the doublet structure of the leptons through the discovery of the muon neutrino. 

References:

1. Einstein, A. (1949/1979). Autographical notes (Translated by Schilpp). La Salle, Illinois: Open court.

2. Feynman, R. P. (1965). The development of the space-time view of quantum electrodynamics. In Brown, L. M. (ed.), Selected papers of Richard Feynman. Singapore: World Scientific.

3. 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. 

4. Lederman, L. & Teresi, D. (1993). The God Particle: If the universe is the answer, what is the question?. New York: Delta Books.

5. Okun, L. B. (1989). The concept of mass (mass, energy, relativity). Soviet Physics Uspekhi, 32(7), 629.

6. Sandin, T. R. (1991). In defense of relativistic mass. American Journal of Physics, 59(11), 1032-1036.