Section 43–4 Ionic conductivity

Ionized gas / Electric current / Ohm’s law

 

In this section, Feynman begins with an ionized gas and uses the motion of its charged particles to derive an expression for electric current and show that, under simplifying assumptions, it obeys Ohm’s law. The logical progression is thus from ionized gas → drift velocity and mobility → electric current → electrical conductivity → Ohm’s law. Although the section is titled “ionic conductivity,” it is somewhat narrower than its actual scope. “Electrical Conductivity in an Ionized Gas” is an appropriate alternative title because it is broad enough to encompass the physical system, drift velocity, electrical mobility, electric current, and Ohm’s law.

 

1. Ionized gas

“Suppose we have a gas in a vessel in which there are also some ions—atoms or molecules with a net electric charge. We show the situation schematically in Fig. 43–2. If two opposite walls of the container are metallic plates, we can connect them to the terminals of a battery and thereby produce an electric field in the gas. The electric field will result in a force on the ions, so they will begin to drift toward one or the other of the plates. An electric current will be induced, and the gas with its ions will behave like a resistor. By computing the ion flow from the drift velocity we can compute the resistance (Feynman et al., 1963).”

 

A dilute ionized gas can be approximated as an ohmic resistor under three idealized conditions that suppress capacitive, inductive, and nonlinear plasma effects. First, the applied electric field must be strictly constant, so that all time-dependent effects vanish—displacement (capacitive) currents and induced electromotive forces become negligible, leaving conduction current as the sole transport mechanism. Second, the electric field must be sufficiently weak that the drift velocity of the ions remains linearly proportional to the field, avoiding nonlinear phenomena like avalanche ionization and electrical breakdown. Third, the current density must remain low enough to prevent space-charge accumulation, which would distort the electric field and alter the ions’ drift velocity. In most practical high-voltage discharges and plasma applications, however, these idealizations no longer hold, and the gas exhibits both resistive and reactive (capacitive and inductive) behavior.

 

Feynman’s characterization of an ionized gas as a resistor is therefore a valid first-order approximation for ion drift under steady DC conditions. From the broader perspective of classical electromagnetism and circuit theory, however, a dilute ionized gas confined between two electrodes is more accurately modeled as an equivalent RLC circuit. The gas possesses a finite resistance (or conductance) arising from collisional momentum transfer between drifting ions and neutral molecules. At the same time, the electrode-gas system has a finite capacitance originating from the electrode geometry and the formation of Debye sheaths near the electrode surfaces (Nation & Simpson, 1965). In addition, the current flowing through the gas generates a magnetic field, giving rise to a typically small self-inductance. Under time-varying conditions, both capacitive and inductive contributions become significant and must be included to accurately describe the system’s electrical response.

 

A more accurate introduction to the section might read: We now consider a dilute, weakly ionized gas confined between two metallic electrodes. The gas consists of neutral molecules together with a small concentration of ions. When a weak, constant electric field is applied, the ions drift through the neutral background molecules while undergoing frequent collisions, giving rise to an electric current. Under these conditions—constant ion density, constant mobility, and negligible space-charge effects—the gas behaves approximately as an ohmic conductor, allowing the resistance to be derived from the microscopic properties of the ions and their collisions. This wording makes explicit the assumptions that are only implicit in Feynman's presentation and clarifies that his derivation is intended for a weakly ionized dilute gas, not for a general plasma or strongly ionized gas.

 

2. Electric current

“The electric current to one of the plates is given by the total charge of the ions which arrive at the plate in a unit of time… If there are n_i ions per unit volume, the number which reach the plate in the time T is n_i⋅A⋅v_drift⋅T. The current I is the charge collected in T divided by T, so I=qn_iAv_drift (Feynman et al., 1963).”

 

A key assumption underlying Feynman’s expression for electric current, I = n_i⋅A⋅v_d⋅q is that the ion density (n_i) is a fixed property of the gas—a prescribed constant independent of the applied voltage and resulting current. In a real ionized gas, however, ion density is a dynamic quantity governed by competing processes of ionization, recombination, and collection at the electrodes (Raizer & Allen, 1997). As ions drift toward the electrodes, they are neutralized upon contact. Unless the ions are continually replenished by ionization mechanisms—such as ultraviolet radiation, cosmic rays, or thermal ionization—the overall ion density will gradually decrease. Furthermore, increasing the applied voltage modifies not only the drift velocity—it accelerates ion collection at the electrodes, depleting the ion density at a faster rate. This depletion breaks the linear relationship between the electric current and applied voltage, giving rise to nonlinear conduction.

“An electric current I is the flow of charge in a unit time. The electric current to one of the plates is given by the total charge of the ions which arrive at the plate in a unit of time. If the ions drift toward the plate with the velocity v_drift, then those which are within a distance (v_drift⋅T) will arrive at the plate in the time T. If there are n_i ions per unit volume, the number which reach the plate in the time T is n_i⋅A⋅v_drift⋅T (Feynman et al., 1963).”

Feynman’s definition of electric current as “the flow of charge in a unit time” is correct at an introductory level, but it could be more precise. Formally, electric current is the time rate at which net electric charge passes through a specified surface: I = dQ/dt. However, this definition does not state the transport mechanism. In Maxwell’s electrodynamics, the total current may include both conduction current (arising from the motion of charged particles) and displacement current (associated with time-varying electric fields). Furthermore, in media containing multiple charge carriers—such as electrons, positive ions, and negative ions—the net current density is the vector sum of contributions from all charge carriers. Experimentally, the electric current can be measured by various instruments including ammeters based on the magnetic, resistive, Hall effect, or thermal principles, depending on the magnitude and nature of the current.

3. Ohm’s law

“We find that the current is proportional to the voltage, which is just the form of Ohm’s law, and the resistance R is the inverse of the proportionality constant: 1/R=μq²n_i(A/b). (43.20) (Feynman et al., 1963).”

 

Ohm’s law states that the current through a conductor is directly proportional to the voltage across it, provided the resistance remains constant. This proportionality is not a fundamental law of physics but an empirical relation that holds only under specific physical conditions. First, the conductor must be strictly ohmic, meaning its charge carrier density and mobility are independent of the applied electric field, so that the drift velocity scales linearly with the field strength. Second, the temperature must remain constant, because heating increases the lattice vibrations and collision rates, thereby modifying the resistance and current-voltage relationship. Third, the applied voltage must remain weak enough to avoid high field phenomena such as impact ionization, or space-charge injection, which introduce nonlinearities (Raizer & Allen, 1997). While Ohm’s law provides an accurate description under these idealized conditions, any non-ohmic devices—such as semiconductors, diodes, or electrolytes—requires a non-linear or complex impedance model.

 

Note: Ohm’s law is not strictly valid on very short timescales because it assumes that electrons reach a steady drift velocity instantaneously. In Griffith’s (2013) words, “N. Ashby, Am. J. Phys. 43, 553 (1975), points out that for good conductors t is absurdly short (10^-19 s, for copper, whereas the time between collisions is t_c = 10^-14 s). The problem is that Ohm's law itself breaks down on timescales shorter than t_c; actually, the time it takes free charge to dissipate in a good conductor is of order t_c, not t (p. 412).”

 

An ionized gas generally does not obey Ohm’s law for three fundamental reasons. First, the number of charge carriers is not fixed: increasing the applied voltage can produce additional electrons and ions through ionization, so the ion density becomes a function of the electric field. Second, the mobility of the ions is field-dependent: higher voltage (electric field) increases the ions’ kinetic energies and collision frequencies, making the drift velocity nonlinearly dependent on the electric field. Third, space-charge effects cause electrons and ions drift at different speeds, distorting the local electric field and producing non-uniform voltage drops across the gas. Since the ion density, mobility, and local field distribution all depend on the applied voltage, the current-voltage relationship is fundamentally nonlinear, and the ionized gas is, in general, a non-ohmic medium.

 

Key Takeaways:

1. An ionized gas conducts electricity because charged particles—electrons and ions—drift through the gas under an applied electric field while collisions with other particles impede their motion.

2. Electric current is more precisely defined as the time rate of net electric charge flow across a specified area (I = dq/dt). In general, electric current encompasses both the physical drift of charge carriers (conduction current) and time-varying electric fields (displacement current).

3. Ohm’s law is an empirical approximation valid only for ohmic conductors under strict conditions: constant resistance, constant temperature, and weak electric fields. While Feynman’s model holds for weak DC electric fields, real ionized gases are fundamentally non-ohmic—stronger fields can change the ion density and electrical mobility, whereas space-charge effects can distort the electric field.

 

The Moral of the Lesson: Physiological function as an electrical system

Ionic—or electrical—conductivity is far more than a laboratory curiosity: it keeps us alive. Every thought, heartbeat, and muscle movement depend on the controlled flow of ions across cell membranes. Sodium, potassium, chloride, and calcium ions within our cells and blood must be maintained in delicate balance. When an electrolyte imbalance occurs—whether from a poor diet, excessive sweating, or severe fluid loss—it affects nerve conduction, muscle contraction, and cardiac function.

 

Examples of Electrolyte Imbalances:

• Hyponatremia (Low sodium): Can cause headache, confusion, and seizures. Sodium is essential for generating action potentials across cell membranes.
• Hypokalemia (Low potassium): Can cause muscle weakness, cramps, and cardiac arrhythmias. Potassium plays a central role in establishing the resting membrane potential and repolarizing excitable cells.
• Hypocalcemia (Low calcium): Increases neuromuscular excitability, leading to muscle spasms, tingling, and tetany. Calcium is crucial for neurotransmitter release and muscle contraction.
• Hypochloremia (Low magnesium): May cause muscle weakness, tremors, and cramps. Magnesium is a cofactor for ATP-dependent enzymes and is essential for normal nerve and muscle function.

 

Dietary Sources and Maintenance

A healthy diet (e.g., Keto Diet as shown below) is your first line of defense against electrolyte imbalance. While severe imbalance cannot always be resolved by diet alone, daily food intake plays a vital role in maintaining normal electrolyte levels:

Source: Keto Diet Electrolytes: Why They Matter & How to Get Enough?

Eggs provide several minerals, including potassium, phosphorus, and calcium, along with protein and other nutrients—they may not be the top source of any single mineral or electrolyte, but they add variety and nutritional value to your diet. The secret to electrolyte balance isn't chasing one nutrient—it's eating a colorful, varied diet: fruits, vegetables, dairy or fortified alternatives, beans, whole grains, and protein-rich foods like eggs.

 

Conclusions:

Importantly, electrolytes are far more than dietary minerals—they are the body’s essential charge carriers whose concentrations and movement across cell membranes underlie much of the body’s physiological function. While a balanced diet and adequate hydration usually keep these ion concentrations within the acceptable range, severe imbalances can become life-threatening emergencies requiring medical intervention. In short, maintaining electrolyte balance is not merely an application of ionic conduction or healthy eating, but it is the foundation of life itself.

 

Review Questions:

1. Ionized Gas as a Resistor: Under what assumptions can a dilute ionized gas be treated as an ohmic resistor? Identify the conditions under which this approximation breaks down.

2. Definition of Electric Current: How would you define electric current, both conceptually and mathematically? Explain how the electric current I is related to the microscopic drift velocity of charge carriers.

3. Validity of Ohm's Law: Under what conditions does Ohm’s law hold, and what physical mechanisms cause deviations from linearity?

 

References

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.

Griffiths, D. J. (2013). Introduction to Electrodynamics (3^rd ed.). Prentice Hall.

Raizer, Y. P., & Allen, J. E. (1997). Gas discharge physics (Vol. 2). Berlin: Springer.

Kasper, D. L., Fauci, A. S., Hauser, S. L., Longo, D. L., Jameson, J. L., & Loscalzo, J. (2021). Harrison's Principles of Internal Medicine (21st ed.). McGraw-Hill.

Mahan, L. K., & Raymond, J. L. (2020). Krause and Mahan's Food and the Nutrition Care Process (15th ed.). Elsevier.

Nation, J. A., & Simpson, D. (1965). A measurement of the effective thickness of the plasma sheath at a cold electrode. British Journal of Applied Physics, 16(11), 1705-1709.

Section 43–3 The drift speed

S-molecules / Drift velocity / Mobility

 

In this section, Feynman introduces the concepts of S-molecules, drift velocity, and mobility (electrical and generalized). Although the section title is “The drift speed,” Feynman later shifts to using “drift velocity” in the text. This transition aligns with the standard physics term because the phenomenon is inherently directional, arising from an asymmetric external force. Conversely, "drift speed" is simply the scalar magnitude of that vector, a term best reserved for contexts where directional orientation is irrelevant. 

 

1. S-molecules

“We shall refer to the “majority” molecules as the “background” molecules, and we shall call the molecules which are different from the background molecules “special” molecules or, for short, the S-molecules (Feynman et al, 1963).”

 

The term S‑molecules (special molecules) serves as a shorthand for identifying the particle under study, distinguishing it from background molecules without lengthy descriptions. This abstraction unifies the treatment of diffusion of gases, centrifugal separation, and ionic conduction, under a framework, providing an intuitive explanation of drift velocity. However, the term is nonstandard in the broader literature, where expressions such as test particles or tagged particles could be used. Its use may confuse readers and inadvertently suggest that S‑molecules possess unique properties, but it is merely an analytical description. Furthermore, the model assumes a dilute system in which the S-molecules neither disturb the background molecules nor interact with one another, which is unlikely to happen in the real world. Here’s a fun twist, in the Audio Recordings of this lecture, Feynman did not use the term “S‑molecules”, but relied instead on phrases like “this thing,” “heavy object,” or simply “it.” He did, however, explicitly introduce the “fresh start” assumption—the idea that molecules do not remember their acceleration after each collision.

 

The limitations of the “fresh start” assumption can be illustrated with a bowling ball analogy: a heavy particle moving through a sea of lighter molecules behaves like a bowling ball rolling through bowling pins—each impact alters its motion only slightly. The assumption of a "fresh start" after every collision is unrealistic because the particle’s momentum remains highly correlated from one collision to the next; a single collision is usually insufficient to erase the memory of its prior motion. Instead of adopting t as the mean time between consecutive collisions, we can reframe it as the momentum relaxation time—the characteristic time over which cumulative collisions dissipate the particle’s initial directed momentum. This approach preserves the structure of the simple formula while incorporating the cumulative effects of many collisions, making the model both intuitive and more realistic. A rigorous treatment of this process is provided by the Boltzmann equation, Langevin equation, or Green-Kubo relations.

 

“We shall not work out the details, but just state that the result is equivalent to replacing τ, the average collision time, by a new—and longer—τ which corresponds to the average ‘forgetting time,’ i.e., the average time to forget its forward momentum (Feynman et al., 1963).”

 

It is worthwhile to clarify the distinction between the mean collision time and the momentum relaxation time (Feynman’s "forgetting time"). The mean collision time is a kinematic quantity that measures the average time between consecutive collisions and characterizes the frequency of collision events. By contrast, the momentum relaxation time is a transport quantity that measures the average time required for cumulative collisions to “erase” a particle’s directed momentum and establish a new equilibrium. The two timescales are identical if each collision completely randomizes the particle’s momentum. In real gases, liquids, and plasmas, momentum is lost gradually through a succession of small-angle deflections. Consequently, the momentum relaxation time is typically longer than the mean collision time, serving as the appropriate parameter for describing drift velocity and mobility.

 

2. Drift velocity

“We say that there is a drift, superposed on its random motion. We would like to know what the speed of its drift is—its drift velocity—due to the force F (Feynman et al, 1963).”

 

A comprehensive definition of Drift velocity

Drift velocity is the average, directed velocity acquired by charged particles (such as electrons or ions) when subjected to an external electric field—a slow, systematic drift superimposed upon their much larger, random thermal motion (typically averages to zero in the absence of a field). Microscopically, it arises from the acceleration by the applied force (typically F= qE) during the brief intervals between collisions and molecular force from each collision. Macroscopically, the drift velocity is directly proportional to the applied electric field and is related to the electric current density by J = nqv, where n is the charge carrier density. Although the random thermal speeds of particles are typically orders of magnitude larger than the drift velocity, it is this tiny net motion that is responsible for macroscopic electrical conduction, diffusion, and other transport phenomena. In electrical circuits, this allows the drift velocity to bridge the microscopic molecular collisions to the measurable electrical currents in response to applied fields.

 

“So between the two collisions it has, on the average, a velocity one-half of the final velocity, so the mean drift velocity is ½ Fτ/m. (Wrong!) This result is wrong and the result in Eq. (43.13) is right, although the arguments may sound equally satisfactory…… Short times occur more often but make less contribution to the drift velocity because they have less chance “to really get going.” If one takes proper account of the distribution of free times between collisions, one can show that there should not be the factor ½ that was obtained from the second argument. The error was made in trying to relate by a simple argument the average final velocity to the average velocity itself (Feynman et al., 1963).”

 

Feynman warns that the drift velocity cannot be obtained by simply halving the final velocity, but he only mentions the “distribution of free times” without showing the calculation. A more instructive approach uses the exponential distribution of free-flight times. Although the mean time between collisions is the constant t, individual free-flight times t are random and vary from one collision to another. They follow the probability density function p(t) = (1/t)e^{-t/t}, which arises from the assumption that collisions occur randomly and independently—a Poisson process (Feller, 1968). Immediately after a collision, the probability that the next collision occurs between t and t + dt is p(t)dt. During this interval, the particle accelerates under a constant force F, gaining an additional velocity (F/m)t. Averaging over all possible free-flight times gives the drift velocity:

Thus, the drift velocity is determined by the mean of the exponential free-flight distribution—not by assuming that every molecule accelerates for the same duration. However, while this approximation is valid for dilute gases, it becomes less reliable in dense fluids or systems with correlated collisions.

 

Note: In the Audio Recordings (26 min: 55 sec) of this lecture, Feynman mentions that the ½ factor error could be due to the textbook of Resnick and Halliday, or others.

 

Alternatively, Feynman could have clarified that a molecule’s initial velocity immediately after a collision is not zero. More precisely, after each collision, a molecule moves with a random (initial) velocity v₀, which is typically several orders of magnitude larger than the drift velocity. Between successive collisions, the external force F imparts a small systematic velocity increment Dv = (F/m)t where t is the time elapsed since the last collision. The molecule’s actual (instantaneous) velocity is therefore: v = v₀ + (F/m)t. The crucial assumption is that the post-collision initial velocities are isotropically distributed (equally likely in any direction), meaning their statistical average is zero (<v₀> = 0). This does not imply that each molecule has zero initial velocity after a collision; rather, the random directions of many molecules cancel statistically. Thus, the drift velocity arises solely from the small, nonzero average produced by the force-induced term. The macroscopic drift represents a small directional bias superimposed on the much larger random thermal motion.

 

3. Mobility

“If in an electrical problem the force is written as the charge times the electric field, F=qE, then the constant of proportionality between the velocity and the electric field E is usually called the “mobility.” In spite of the possibility of some confusion, we shall use the term mobility for the ratio of the drift velocity to the force for any force. We write v_drift = μF (43.14). in general, and we shall call μ the mobility (Feynman et al., 1963).”

 

Perhaps Feynman could have distinguished between electrical mobility and generalized mobility. His discussion begins with an electrical problem in which the force on a charged particle is electrical (F = qE). In this context, the proportionality constant between the drift velocity and the electric field is the electrical mobility, typically denoted as m_e, giving the equation v_d = m_eE. Electrical mobility is a physical property that quantifies how fast a charged particle drifts through a medium under an applied electric field. Mathematically, it is defined as the ratio of the drift velocity to the electric field strength: m_e = v_d/E. Experimentally, it can be measured by several techniques, including electrical mobility analyzers (EMAs) or Hall-effect measurements. Electrical mobility is a key transport parameter in semiconductor and ionized gases, and it plays a central role in the design of electronic devices such as transistors, diodes, and solar cells.

 

Note: In his Lectures on Computation, Feynman (1996) explains: “Drawing on engineering practice, we can write the drift velocity v_d in terms of the mobility m of the charge carriers as v_d = m_eE, E is the electric field across the drain/source (p. 225).”

 

When Feynman introduces the general equation v_d = mF, the quantity m does not represent electrical mobility but a generalized (or mechanical) mobility. This transport coefficient relates the drift velocity to any applied force—electrical, gravitational, or chemical. Under an electric field, where F = qE, this equation becomes v_d = mF = m(qE). Comparing this with the definition of electrical mobility, v_d = μ_eE, gives: μ_e = qm. Thus, a particle’s electrical mobility is simply its generalized mobility multiplied by its charge. The generalized mobility is also the quantity that appears in the Einstein diffusion relation, D = mkT, where D is the diffusion coefficient. Expressed in terms of the electrical mobility, the relation becomes D = μ_ekT/q. In summary, the generalized mobility is the more general charge-independent transport coefficient, while the electrical mobility is a special case that describes a particle’s response specifically to an electric field.

 

Key Takeaways (In Feynman’s Tone):

1. The "Special Molecule" Idea

Suppose you've a gas with an enormous number of molecules, all flying about, colliding with one another, and changing their directions every instant. Trying to follow every molecule would be hopeless. Instead, we single out one molecule—the special molecule, or S-molecule—and ask only what happens to it. Maybe it’s heavier than the others, maybe it carries a charge, or maybe it’s being pushed by an electric force while the background molecules simply collide with it. By focusing on this one molecule, we can understand the basic ideas behind many transport phenomena—diffusion, electrical conduction, and sedimentation. It's not the whole truth—it's an approach to get started.

 

2. Where the Drift Comes From

Now consider what happens to the S-molecule. Between collisions it is accelerated by an applied force, but every collision sends it off again in a new random direction. The collisions randomize the motion; the external force biases the direction.

The result is a tiny average velocity—the drift velocity—superimposed on the molecule’s much larger random thermal motion. You can barely see it, but it's this small average motion that produces measurable phenomena such as electric current, diffusion, and sedimentation.

 

3. Mobility: How Easily a Molecule Drifts

How fast does the molecule drift for a given force? That depends on the mobility, which is how readily the molecule moves through a medium. Here's the catch: you have to be careful what you mean by "mobility."

• If you define it as the drift velocity per unit force, we'll call it the generalized mobility—it works for any force, electric or others: m = v_d /F .
• If you define it as the drift velocity per unit electric field, we call that the electrical mobility: m_e = v_d /E.

They're simply related: μ_e = qm. Thus, the electrical mobility is just the generalized mobility multiplied by the charge. So if you know one, you know the other. It's not two different physical properties—it's the same mechanism, just calibrated for different kinds of forces.

 

The Moral of the Lesson: From Drift Velocity to Cholesterol Transport

Cholesterol does not circulate through the bloodstream as isolated molecules. Because it is a hydrophobic lipid, it must be packaged into spherical vehicles known as lipoproteins—such as low-density lipoproteins (LDL) and high-density lipoproteins (HDL). From a physicist’s perspective, these lipoproteins can be viewed as Feynman’s "special molecules" (S-molecules) moving through a complex fluid environment crowded with background molecules. Just like the S-molecule, each lipoprotein undergoes continual collisions with surrounding water molecules, plasma proteins, and blood cells, while external forces—whether drag, gravity or electrical—can affect its motion.

 

One laboratory technique that illustrates this idea is electrophoresis, in which an electric field causes charged molecules to migrate through a supporting medium. Because different types of lipoproteins possess distinct surface charges arising from their apolipoproteins, they experience different electrical forces. After a brief period of acceleration, the electrical force is balanced by the viscous drag of the medium, causing each molecule to reach a constant drift velocity. The ratio of this drift velocity to the applied electric field is called the electrophoretic mobility. Although electrophoresis is used mainly for specialized lipoprotein analysis rather than routine cholesterol testing, it provides a real-world example of Feynman’s discussion of drift velocity and mobility.

 

Note on Density: The terms “low‑density” and “high‑density” originated from the separation of these molecules via an analytical ultracentrifugation. In a centrifuge, lipoproteins are segregated by their density—not by electrophoretic mobility.

 

The "Drift Velocity" Analogy for Atherosclerosis

The concept of drift velocity also provides a useful analogy for understanding atherosclerosis. LDL molecules do not simply “flow” passively through the bloodstream; rather, they undergo continual random motion while being transported by the flowing blood. The probability that a LDL molecule interacts with the arterial wall increases with its concentration and the condition of the vessel wall.  Consider a mechanical analogy: a healthy artery has a smooth endothelial lining (like a new road), while a damaged one has a rough, permeable surface where molecules can become trapped. Over time, as LDL molecules “drift” through the bloodstream, a higher concentration of them—akin to high traffic density—leads to more interactions with the artery wall. When too many LDL molecules accumulate in a damaged artery wall, they can become trapped and oxidized, triggering an inflammatory immune response that contributes to atherosclerosis. For this reason, many scientists consider the number of LDL molecules to be a better indicator of cardiovascular risk than the total amount of cholesterol—but LDL molecules can be further classified into several subclasses with differing biological properties.

 

The Science of Temporary LDL Increase After Intense Exercise

Intense exercise can cause a temporary increase in measured LDL cholesterol levels. This short term elevation is generally attributed to two physiological mechanisms rather than to any harmful effect of exercise. 

Hemoconcentration: Strenuous exercise, such as long-distance running, results in substantial fluid loss through sweating and respiration. The reduction in plasma volume temporarily increases the concentration of the blood, meaning that about the same number of LDL molecules remain within a smaller volume. Consequently, a lipid panel may show a transient increase in measured LDL concentration. In one study, total plasma cholesterol rose by 24% immediately post-exercise, with LDL-C increased by about 20% (Krum et al., 1991).

 

These changes are short-term physiological responses to intense exercise rather than evidence that exercise is harmful. As hydration is restored and the body recovers, lipid concentrations generally return to their usual baseline. More importantly, the long-term effects of regular physical activity maintain healthy lipid metabolism and reduce cardiovascular risk.

 

Summary and Takeaways

Distinguishing short-term transport phenomena from long-term equilibrium behavior is important in both physics and medicine. The short-term “rise” in LDL after intense exercise is a normal physiological response—not a sign that exercise is harming your heart. When you are well-rested and hydrated, regular exercise has a proven beneficial effect on cholesterol profiles, which is why doctors recommend it for heart health.

To ensure clinical accuracy and eliminate transient variables, cholesterol levels should be measured under consistent conditions—well-rested, fully hydrated, and following a standard 12-hour fast. Thus, doctors should advise the public to avoid strenuous or exhaustive exercise for 12-24 hours prior to a blood test. This precaution ensures that temporary transport dynamics do not obscure the patient’s true, steady-state lipid profile.

 

Review Questions:

1. Why did Feynman introduce the concept of the S-molecule, and what is the purpose of the "fresh start" assumption?

2. Why is it incorrect to assume that the average drift velocity is simply one-half of the final velocity between collisions?

3. How would you distinguish between generalized (mechanical) mobility and electrical mobility?

 

References

Feller, W. (1968). An Introduction to Probability Theory and Its Applications (Vol. 1, 3rd ed.). Wiley.

Feynman, R. P. (1996). Feynman lectures on computation. Reading, Massachusetts: Addison-Wesley.

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.

Krum, H., Conway, E. L., & Howes, L. G. (1991). Acute effects of exercise on plasma lipids, noradrenaline levels and plasma volume. Clinical and experimental pharmacology and physiology, 18(10), 697-701.