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.