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Albert Einstein's theory of relativity asserts that space and time are relative and that all motion has to be relative to a frame of reference. It is a belief that laws of physics are universal, however, it is a hypothesis which appears to be straightforward yet it is difficult to grasp.
It states:
- The concept of absolute reference does not exist. If an object is in reference to another object, velocity may be measured as the reference to another object.
- Regardless of the measurement velocity, the speed of light remains constant.
The Theory of Relativity, developed by Albert Einstein, is divided into two parts:
- Special Relativity Theory
- General Relativity Theory
| Table of Content |
Key Takeaways: Relativity, Frame of Reference, Velocity, Speed of Light, Time Dilation, Length Contraction
Special Theory of Relativity
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In the year 1905, the term "relativity" was coined. The structure of space-time is the subject of this theorem. This theory was described by Einstein based on two postulates:
- Regardless of the observer's velocity, the rules of physics are the same for everybody.
- Regardless of whether the light source or the observer moves, the speed of light remains constant.
According to Einstein, when a person's velocity increases, the pace at which time tics drops. However, because the decrease in time is so little in comparison to the rise in time, this is difficult to perceive. So, it can be assumed that if the velocity of a person is made equal to the velocity of light, then that person will be in a situation where time is still. This phenomenon is termed as Time Dilation.Theory of special relativity says that the velocity of one reference frame is relative to another which affects the length, time, momentum, and energy. Relativity is a notion which asserts that moving things are relative to one another. Laws can be represented either as a mathematical expression or as an observation. In general, rules explain what will happen in a particular scenario using a particular equation, whereas theories explain how the phenomena occur. If a statement or mathematical expression meets the principle of relativity, we call it a law.
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What is Relativity?
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Relativity is a notion that asserts that moving things are relative to one another. On a bus, for example, person 1 throws a ball to person 2 while the vehicle is going at a constant speed of 50 mph, and the passengers are likewise moving at 50 mph even though they are standing still. As person 1 passes the ball to person 2 at 210 mph, an observer outside the truck calculates the ball's speed by combining the ball's speed and the bus's speed, which is given by,
50 mph + 10 mph = 60 mph
The human is also in continual motion due to the revolution of the planet and the sun as well as the rotation of the galaxy. As a result, nothing is completely still or moving. Things just move in relation to one another and this is known as the theory of relativity.
Theory of Relativity
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This theory has unexpected outcomes, such as -
- Relativity of simultaneity: This theory states that two actions, may be simultaneous for person 1, may not be simultaneous for person 1 in a relative motion.
- Length Shrinking: When an object moves in the same direction as another object it appears to be shorter in length.
- Mass-Energy Equivalence: The study of relativity led to one of the most important ideas, E = mc2, in which E stands for energy, m for mass, and c for light velocity.
General Theory of Relativity
General Theory of Relativity was developed between 1907 to 1915 by Einstein. This theory states that if an object is at rest in the gravitational field and accelerating are physically equal. For example, the free fall of the ball for an observer is the same on the rocket and on the earth. This is due to the rocket's acceleration of 9.8 m/s2. This theory relates to special relativity and Newton's gravitational theory.
The following are some of the theories related to general relativity:
- Gravitational Time Dilation: The progress of time is affected by gravity. Deeper gravity levels have slower clocks than ordinary gravitational levels.
- In the gravitational field, light rays bend.
- As the Universe expands the part of it moves away from the Earth at a speed faster than that of light.
Relativity Formula
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The theory of special relativity states that the length, time, momentum and energy have their dependence on the velocity of a frame of reference that is relative to another frame of reference. When the length, time, momentum and energy is measured by a person sitting in the spaceship moving at speed of light and a person outside the ship then the measurements will be different. When an object moves, the Lorentz factor (γ) is used to determine time, length and relativistic mass of the object.
The following equation is used in special relativity:
\(\gamma = \frac{1}{\sqrt{1-\beta^2}}\)
Where;
\(\beta = \frac{v}{c}\)
v = relative velocity (between two internal frames)
c = speed of light, value of c = 3 x 108 m/s
γ = 1; when two frames are at rest and increase with the relative velocity between two inertial frames.
γ → ∞; when velocity becomes nearly equal to speed of light
Some important formulas used in relativity are as follows:
Time Dilation
The time dilation is given by:
\(T = \frac{T_0}{\sqrt{(1-\frac{v^2}{c^2}})} \)
Where;
T = time observed
T0 = time observed at rest
v = velocity of the object
c = speed of light
Formula of Length Contraction
The length contraction is given by:
\(L = L_0{\sqrt{1-\frac{v^2}{c^2}}}\)
Where;
L = length of an object (with respect to relativistic speed)
L0 = length of an object at rest
c = velocity of light
v = velocity of the object
Relative Velocity Formula
Relative velocity can be defined as the speed of an object in relation to another object. The other object might be stationary, moving at a slow speed, same speed, fast, or in the opposite direction. An intermediate reference frame can be used to measure it. This may be expressed as the vector sum of the velocities. The formula for relative velocity is as follows:
VAC→= VAB→+ VBC→
Where;
VAB = velocity with respect to A & B
VBC = velocity with respect to B & C
VAC = velocity with respect to A & C
Things to Remember
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- The theory of relativity outlines how various sets of observers might estimate space and time differently for an object that moves relative to another.
- Albert Einstein developed the equation E = mc2 in 1905. He described the link between energy and mass using this equation.
- Energy and mass are interchangeable, according to Einstein's equation E = mc2. It is a specific relativity theory that describes how space and time are related in the case of an object travelling at the speed of light.
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Sample Questions
Ques. The velocity of an electron is 0.990 × c. Calculate the relativistic factor γ using the Relativity Formula. (3 Marks)
Ans. v = 0.990×c
\(\gamma = \frac{1}{\sqrt{(1-\frac{v^2}{c^2}})} \)
= \( \frac{1}{\sqrt{(1-\frac{(0.990c)^2}{c^2}})} \)
= \( \frac{1}{\sqrt{(1-(0.990)^2}} \)
= 7.0888
The relativistic factor is 7.0888.
Ques. Can the concepts of general relativity be used in the fields of biology? (2 Marks)
Ans. The concepts of general relativity are currently not applicable in the field of biology. For general relativity to be applicable, the gravitational field must be a strong and massive body like a planet, whereas in the case of the human body (in biology) it is very small and has a negligible gravitational field of its own.
Ques. What will be the expression for the variation in mass of a particle in relation to the velocity. (2 Marks)
Ans. When a particle moves towards the speed of light, its mass gets large and it can’t go faster with respect to the speed of light. This required expression is:
\(Mt = \frac{M}{\sqrt{(1-(\frac{v}{c})^2})} \)
Where;
Mt = transverse mass
M = original mass
Ques. The threshold frequency for a certain metal is 3.3 x 1024 Hz. If light of frequency 8.2 x 10-4 Hz is incident on the metal, predict the cut off-voltage for the photoelectric emission. (2 Marks)
Ans. Given;
V = 3.3x10 Hz
V = 8.2x10 Hz
Cut-off voltage - eV =h(V-VO)
Substituting the values Vo = 2.03 eV
Ques. Light of wavelength 488 nm is produced by an argon laser which is used in the photoelectric effect. When light from this spectral line is incident on the emitter, the stopping (cut-off) potential of photoelectrons is 0.38 V. Find the work function of the material from which the emitter is made. (3 Marks)
Ans. Given: \(\lambda\) = 488 nm
Vo = 0.38 V
We Know;
eVo = \(hv-\phi_0\)
Or
\(\phi\)o = hc /\(\lambda\) - eVo
= 3.46 x 10-19 J
= 2.16 eV
Ques.
a) For what kinetic energy of a neutron will the associated de Broglie wavelength be 1.40 x 10 m-30?
b) Also find the De Broglie wavelength of a neutron, in thermal equilibrium with matter, having an average kinetic energy of (3/2) K T at 300 K. (5 Marks)
Ans. Given; \(\lambda\)=1.4 x 10-30m
- Now, K = p2 / 2m
And p = h/\(\lambda\)
Therefore;
K = h2/2m\(\lambda^2\)
Or K = 6.686x10-21J
- Kinetic Energy
K= (3/2) kT
where;
k = Boltzmann constant = 1.381x10
T = 300K
So,
K = 6.21x10-21J
Now, \(\lambda\) = \(\frac{h}{\sqrt2mK}\)=0.145nm
Ques. Ultraviolet light of wavelength 2271 \(\bar{A}\) from a 100 W mercury source irradiates a photocell made of molybdenum metal. If the stopping potential is -1.3 V, estimate the work function of the metal. How would the photo-cell respond to a high intensity (105 W m-2) red light of wavelength 6328 ? produced by a He-Ne laser? (5 Marks)
Ans. Wavelength of ultraviolet light, \(\lambda\) = 2271\(\bar{A}\) = 2271 x 10-30m Stopping potential of the metal, Vo = 1.3 V
Planck's constant, h = 6.6 x 10
Charge on an electron, e = 1.6 x 10-19C
Work function of the metal= \(\phi_0\) Frequency of light = v
We have the photo-energy relation from the photoelectric effect as:
\(\phi_0\)-hv-evo
=(hc/\(\lambda\)) - eVo
Let Vo be the threshold frequency of the metal.
\(\phi_0\) = hVo
Vo = \(\phi_0\)/h
= \(\frac{6.64 \times 10^{-39}}{6.6 \times 10^{-34}}\)
= 1.006x1015 Hz
Wavelength of red light \(\lambda\)c = 6328\(\bar{A}\)
Frequency of red light = 6328 10-10 m
3x108 / 6328x10-10 = 4.74x1034 Hz
Since vo > vr, the photocell will not respond to the red light produced by the laser.
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