For the Love of Physics
What is Time Dilation? In one of the most fascinating predictions of Special Theory of Relativity (STR), we see how the postulate of the constancy of speed of light shows that time measured by two different observers must be different.
RELATIVITY OF TIME :
In Newtonian or Classical Physics, time is considered to be absolute or independent of the observer (or reference frame). It means the measurement of time should be same for everyone. However Special Relativity challenges this idea of absolute time. According to STR time is neither absolute nor independent of the reference frame; rather it is very much dependent on the relative motion of the observer and the clock in which the physical events are taking place.
GEDANKEN EXPERIMENT / THOUGHT EXPERIMENT:
Such a radical idea of the relativity can also be proved with a very SIMPLE THOUGHT EXPERIMENT. Imagine a train moving with uniform velocity. Inside it, there is a setup of bulb (that can emit a photon and detector). As the bulb emits a light photon, it travels a certain distance to reach the detector. We can try to calculate the time taken by the light photon to reach the detector (a) from inside the train frame of reference, and (b) from an observer on the platform. The path lengths in both cases will be different due to the relative motion, and hence the time measured will be different (since speed of light remains constant). The time measured in a moving frame as compared to a rest frame will appear dilated, or stretched out. This is call Time Dilation. It simply means time as measured from a moving frame runs slower as compared to a rest frame of reference.
This is the incredible prediction of time dilation by relativity.
Experimental confirmation of time dilation is obtained by looking at the lifetimes of unstable (radioactive) nuclei. Unstable particles decay after a certain lifetime. Such particles have a different lifetime in a rest frame of reference, as compared to when they are moving through the atmosphere.
Can such a simple thought experiment make a general statement about the nature of time?
Yes. Time dilation is equally relevant whether we measure time by looking at the mechanics of clocks, or the motion of light, or the oscillation of pendulum, or any other time measuring systems. Time dilation affects the rate at which all physical systems evolve. It also affects our biological clocks.
In the above video, I have shown time dilation using a simple geometrical thought experiment. It can also be proved by other methods, namely using LORENTZ TRANSFORMATIONS or using the INVARIANT SPACE-TIME INTERVAL. I will create two separate videos in future to do the same.
STAY TUNED. PEACE…
Related Videos:
1. Special Theory of Relativity
https://youtu.be/RYIY4APbV5Q
2. History of Special Relativity (Part 1) – Galilean Invariance & Maxwell’s Equations
https://youtu.be/P79Ur8LVcy8
3. History of Special Relativity (Part 2) – Michelson Morley Experiment
https://youtu.be/FQGGSNIWm3o
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LINK TO OTHER VIDEOS
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What is a Geiger Muller Counter? – GM Counter
https://youtu.be/Qn8otCU5bhQ
The Four Fundamental Forces
https://youtu.be/e9zWwdDbnXw
Ehrenfest Theorem | Derivation using Schrodinger’s Picture
https://youtu.be/oKWCIf8cy5s
ObtainingTime Independent Schrodinger’s Equation from Time Dependent form
https://youtu.be/d8JXjrzy54w
Can electrons exist inside a nucleus?
https://youtu.be/0FCmKpPHveE
Electron Wave in Bohr Model of Atom!!
https://youtu.be/4qxfBTqBFn8
Inductor | Why Current Lags behind Voltage by 90 degrees?
https://youtu.be/VOgSpjZ1Vbo
Newton’s Laws of Motion
https://youtu.be/umJzxQHhKrA
Dynamics of a Point Mass Particle | Conservation of Linear/ Angular Momentum/ Energy
https://youtu.be/rQ8B_g3Vh6E
History of Special Relativity (Part 1) – Galilean Invariance & Maxwell’s Equations
https://youtu.be/P79Ur8LVcy8
History of Special Relativity (Part 2) – Michelson Morley Experiment
https://youtu.be/FQGGSNIWm3o
Special Theory of Relativity
https://youtu.be/RYIY4APbV5Q
What is Time Dilation? (Thought Experiment)
https://youtu.be/lBiAE4Lxy8g
What is Length Contraction? (Thought Experiment)
https://youtu.be/Ajjf_rIufb0
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CHANNEL: https://www.youtube.com/c/FortheLoveofPhysics
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FORWARD YOUR QUESTIONS HERE: http://www.8physics.com/
Source
Mu-meson paradox
A case of length contraction is discussed in respect of mu-meson surging towards Earth after its origin in upper atmosphere. It is argued that the space between Meson & Earth appears shrunken from the perspective of meson. This is perplexing. Is it the (hypothetical) measuring system in mu-meson is elongated ? This argument is some what like Geocentric Model of Universe where whole of the universe was considered revolving around Earth( It appears so to us on earth ).
I have developed a model based on a ‘Hypothetical Experiment’ conducted in a lab on mu-Meson generated in the upper atmosphere & moving towards earth. The Meson is moving towards Earth at .998c OR (299.4 mtrs/ micro-second w.r. to earth) Consider an Electro-Magnetic Pulse Genrator & Receiver (G-R) inside a lab on Meson sending pulse in the direction of motion. Let there be a Reflector ( R ) at 300 mtrs in Meson Scale ( 18.9642 mtrs on Absolute Scale or Earth’s Scale for all practical purposes)
e = v/c = 299.4/300 = 0.998
γ = √ (1-v2/c2) = √ ( 1- 0.9982 ) = 0.06321
Shrinkage Factor, S = 1 / γ = 15.8193.
i.e., 1 E-mtr = 15.8193 M-mtr, 1 E- mi-sec = 1/ 15.8193 M-mi-sec ( where E stands for measurement on Earths scale
& M stands for measurements on Meson scale.)
Dist GR to R = 300 M-mtr = 18.9642 E-mtr.
Speed of E-M pulse w.r.t G-R is 0.6 mtrs on earth’s scale.
Therefore to traverse 18.964 E-mtr time reqd = 18.9642 / 0.6 = 31.607 E. mi-sec = 1.998 M. mi-sec
Reverse journey time for Photon = 18.9642 / (300+299.4) = 0.03164 E. mi-sec = 0.002 M. mi-sec.
Total Journey time = 31.607+ 0.03164 = 31.63864 E. mi-sec = 1.998 + .002 = 2 M.mi-sec.
Bidirectional Speed of Light w.r.t Meson = 600 / 2 = 300 mtr / mi-sec.
Forward Speed of Light w.r.t Meson = 300 / 1.998 = 150.15 M-mtr / M. mi-sec.
Return Speed of Light w.r.t Meson = 300 / .002 = 150000 M-mtr / M. mi-sec.
Speed of Meson as measured on Earth with earth’s scale & clock ( which is at negligible speed ) = 299.4 mtrs / mi-sec
Speed of Light w.r.t Meson’s scale & clock = 299.4 * 15.8193 * 15.8193 = 74924.9256 mtrs/ mi-sec —- (1)
Distance to Earth in Meson’s measuring scale = 9500 * 15.8193 = 150283 mtrs —- (2)
Dividing (2) by (1) we get about 2.0058 mi-sec
Therefore from the above result it is evident that the Meson generated at upper atmosphere finds earth at about 150000 mtrs in its scale & it surges towards Earth at about 75000 mtrs/mi-sec in its measuring scale & clock to reach earth in 2 mi-sec on its clock.
From above approach it is clear that Light propogates with a CONSTANT RATE OF DISPLACEMENT form its origin unaffected by the motion of the source just like a wave in a Pond generated by a man sitting in a moving boat. Its bidirectional speed is 300 mtrs/sec to any observer in his scale & time but unidirectional speed is variable. The speed of Light is < 300 mtrs/mi-sec to an observer moving in the direction of light with minimum of 150 mtrs/mi-sec. to observers with speed greater than
mu-meson. Speed of Light approaches infinity to an observer approaching the light with speeds comparable to mu-meson speed.
I welcome opinion of viewers about correctness or otherwise of my analysis.
svaram55@gmail.com
Thank u sir
I am from Bangladesh.But i found these videos very much helpful.Thanks a lot.
Awesome sr
I really like the clarity of your explanation, thank you sir for making it easier to visualise
What is reflecting ferroeter ? Plz tell sir
Thank you
sir this is a mathematical conclusion of a assumption that speed of light is constant for everyone, I still can't able to understand how does that work
nice video.. my concepts are clear now.. thank you sir..