Mass in Special Relativity Theory
The word “mass” has two implications in special relativity: invariant mass (likewise called the rest mass) that is similar for all observers in all reference frames; while the relativistic mass is reliant on the velocity of the observer. As indicated by the idea of mass-energy relativity, invariant mass is identical to rest energy, while relativistic mass is identical to relativistic energy.
The expression "relativistic mass" tends not to be utilized in particle and nuclear physics. It is the mass of the body that changes with the change in the body’s speed as its speed approaches the speed of light, i.e., 3 × 108 m/s.
What Will You Learn Here?
This page will discuss the mass of light, a relativistic mass, relativistic speed, rest mass formula, and the relativistic mass formula.
Rest Mass
According to the theory of special relativity, the rest mass is called the invariant mass that remains invariant for all the observers in various frames of reference. The invariant mass is another name for the rest mass of particles inside the system. In contrast, the rest mass is preferred over the rest energy (E).
Hence, invariant mass is a characteristic unit of mass utilized for systems that are being seen from their focal point/centre of mass (COM frame).
Point To Note:
The idea of invariant mass doesn't need bound systems of particles. In such a case, it might likewise be applied to systems of unbound particles in high-speed relative motion.
Along these lines, it is regularly utilized in particle physics for systems that comprise broadly isolated high-energy particles.
Assuming such frameworks were obtained from a solitary particle, the calculation of the invariant mass of such frameworks, which is a never-changing quantity, will give the rest mass of the parent particle (since it is preserved over a long period).
Rest Mass Formula
It is helpful in computation that the invariant mass of a system is the total energy of the system divided by c2 in the COM frame (where, by definition, the momentum of the system is zero).
The rest mass is denoted by mo.
So, the rest mass formula is:
mo = E/c2
Rest Mass is a Conserved Mass
The invariant mass of any system is likewise a similar quantity in every single inertial frame, it is a quantity determined from the total energy in the COM frame.
Following the calculation of the rest mass in the aforementioned method, the rest mass is also used to compute system energies and momenta in other frames where the momenta are not zero, where the total energy will fundamentally be unexpectedly different as compared to the COM frame.
Similarly, as with energy and momentum, the invariant mass of a system (having multiple particles) can't be varied or changed, and it is in this manner monitored that the rest mass of the system cannot be destroyed or changed; thus, it remains conserved, as long as the system is not prone to all influences.
Relativistic Mass
From the above text, we understand that relativistic mass is studied under Einstein’s special theory of relativity. It is a mass that is associated with the body in motion.
Mass, in physics, is a quantitative proportion of idleness/inertia, an essential property of all matter. It is, as a result, the obstruction that a body of matter offers to an adjustment of its speed or position upon the action of force.
The quantifiable inertia and the distortion of spacetime by a body in a given frame of reference are controlled by its relativistic mass.
Relativistic Speed
Relativistic speed is the speed at which relativistic impacts become important to the ideal exactness of estimation of the phenomenon being noticed.
[Image will be Uploaded Soon]
Do You Know?
When any closed system (for instance a container of hot gas) is measured, which necessitates that the estimation is taken in the center of the momentum frame where the system has no net energy. In such a case, the invariant mass becomes equal to the relativistic mass, which is the total energy of the system divided by c2.
So, the relativistic mass is the sum total quantity of energy in a body/system divided by c2.
Mathematically, the relativistic mass formula is:
E = mREL c2
For a particle possessing finite rest mass “mo” moving at a speed “v”, i.e., relative to the observer, one finds the following relativistic mass formula:
mREL = \[\frac{m_{0}}{\sqrt{1-\frac{v^{2}}{c^{2}}}}\]
Where,
mREL = mass of an object in motion
mo = rest mass
Point To Note:
In the center of the momentum frame, the speed “v = 0”, and the relativistic mass equals the rest mass, while in other frames, the relativistic mass of a body or system of bodies includes a contribution from the "total" kinetic energy of the body, i.e., the kinetic energy of the center of mass of the body, and is larger the faster the body/system of bodies move.
Therefore, unlike the invariant mass, the relativistic mass relies on the frame of reference of the observer.
However, for a given single frame of reference and isolated systems, the relativistic mass also remains a conserved quantity. The relativistic mass is also the proportionality factor between velocity and momentum, which is given as per Newton’s second law of motion:
P = mRELv
Fun Fact
Do You Know What the Mass of Light is?
Well! Light is a bundle of photons. Photons (mass of light) have “mo = 0, “ i.e., zero rest mass; however, they do contribute to the inertia and possess weight in a gravitational field of any system comprising them.
FAQs on Relativistic Mass
1. What is meant by relativistic mass in Physics?
Relativistic mass is the mass of an object when it is in motion relative to an observer. According to Einstein's Special Theory of Relativity, an object's mass increases as its speed increases. This is different from its rest mass, which is the mass of the object when it is stationary.
2. What is the formula to calculate relativistic mass?
The formula for calculating relativistic mass (m) is:
m = m₀ / √(1 - v²/c²)
Where:
- m is the relativistic mass.
- m₀ is the rest mass of the object.
- v is the velocity of the object.
- c is the speed of light in a vacuum (approximately 3 × 10⁸ m/s).
3. What is the main difference between relativistic mass and rest mass?
The primary difference is that rest mass (also called invariant mass) is an intrinsic and constant property of an object, measured when it is at rest. In contrast, relativistic mass is not constant; it is the object's effective mass that depends on its velocity. Relativistic mass is always greater than or equal to the rest mass.
4. Why does an object's mass appear to increase as it approaches the speed of light?
This phenomenon is a direct consequence of the mass-energy equivalence principle (E=mc²). To accelerate an object, work must be done, which adds kinetic energy to it. This added energy increases the object's total energy, which in turn manifests as an increase in its mass. As the object's speed gets closer to the speed of light, the energy required for further acceleration becomes infinitely large, and so does its relativistic mass.
5. Has the concept of increasing relativistic mass been experimentally proven?
Yes, the concept has been repeatedly and precisely confirmed in numerous experiments. In particle accelerators like those at CERN, particles such as protons and electrons are accelerated to speeds very close to the speed of light. Scientists observe that it takes vastly more energy to increase their speed further, exactly as predicted by the relativistic mass formula, confirming that their effective mass has increased.
6. Since photons have no rest mass, do they have relativistic mass?
A photon has zero rest mass (m₀ = 0). However, since it travels at the speed of light and possesses energy and momentum, it has a non-zero relativistic mass. This mass can be calculated from its energy (E) using the formula E = mc², which means a photon's relativistic mass is m = E/c². This mass contributes to the total mass-energy of any system containing it.
7. Under what conditions do the effects of relativistic mass become significant?
The effects of relativistic mass are always present for any moving object, but they only become significant and measurable at very high speeds, often called relativistic speeds. These are speeds that are a noticeable fraction of the speed of light (e.g., above 10% of c). For everyday objects we encounter, the velocities are so low that the increase in mass is infinitesimally small and can be ignored.
8. How does relativistic mass relate to the famous equation E = mc²?
The equation E = mc² expresses the equivalence of mass and energy. In its most general form, the 'm' represents the relativistic mass, which accounts for the total energy of a body—both its intrinsic rest energy and its kinetic energy from motion. For a stationary object (v=0), the equation simplifies to E₀ = m₀c², where m₀ is the rest mass and E₀ is the rest energy.
