SPACETIME Interval & it's Physical Significance | Timelike, Lightlike & Spacelike Intervals
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- เผยแพร่เมื่อ 8 ก.ค. 2024
- SpaceTime Interval is the square of the interval between two points in Space-Time. It is a very important quantity in STR, because it is INVARIANT under a Lorentz Transformations. So, even though different observers do not agree upon the distance between two points in space, or the time interval between two physical events, they DO AGREE upon the SpaceTime Interval. Hence this physical quantity has it's own relevance. It also gives us an idea about the properties of 4 Dimensional SpaceTime.
00:00 Spacetime Interval
12:25 Spacetime Interval is invariant under LT
24:14 Physical Significance / Geometry of Space Time
32:06 Timelike, Spacelike, Lightlike Intervals
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PLAYLIST ON Special Theory of Relativity
• Special Theory of Rela...
-----------------------------------------------------
1. History of Special Relativity ► • History of Special Rel...
2. Michelson Morley Experiment ► • Michelson Morley Exper...
3. Special Theory of Relativity ► • Special Theory of Rela...
4. Time Dilation (Thought Exp) ► • What is Time Dilation?...
5. Length Contraction (Thought Exp) ► • What is Length Contrac...
6. Lorentz Transormations ► • Derive Lorentz Transfo...
7. Relativity of Simultaneity ► • Relativity of Simultan...
8. Can you prove E=MC² ► • Can you PROVE the most...
-----------------------------------------------------
9. Special Theory of Relativity ► • Special Theory of Rela...
10. Length Contraction ► • Length Contraction (Sp...
11. Length Contraction of Inclined Rod ► • Length Contraction (& ...
12. Time Dilation ► • The Mind Bending Predi...
13. Muon Decay Experiment ► • The Mind-Blowing Proof...
14. Relativistic Velocity Transformations ► • Derivation of Relativi...
15. Speed of light in moving medium ► • Speed of Light in a mo...
16. Relativistic Doppler Effect ► • What is Relativistic D...
17. Relativistic Mass? ► • What is Relativistic m...
18. Relativistic Kinetic Energy ► • Relativistic Kinetic E...
19. Relativistic Force ► • Relativistic Force
20. Relativistic Energy & Momentum ► • Relativistic Energy an...
21. Magnetism arises from Relativity ► • The Hidden Connection ...
22. GATE Physics question ► • GATE Physics: Problem ...
23. TIFR Physics question ► • TIFR Physics: Problem ...
24. Question on Volume contraction ► • Volume Contraction in ...
25. JEST Physics question ► • JEST Physics: Solving ...
26. NET Physics question ► • CSIR-NET Physics Probl...
27. Spacetime Invariant Interval ► • SPACETIME Interval & i...
28. Minkowski Spacetime ► • Minkowski SPACETIME, H...
29. Eucledian Space & Minkowski Spacetime ► • 5 Main Differences b/w...
30. Spacetime Diagrams ► • Time Dilation, Length ...
31. Four Vectors in Relativity ► • What are FOUR VECTORS ...
32. Doppler Effect using 4-vectors ► • How to use 4 VECTORS t...
33. Compton Effect using 4-vectors ► • How to prove Compton e...
34. Particle Decay using 4-vectors ► • Particle Decay in Rela...
35. (SHORTS) Does Light experience time ► • Does light photon expe...
36. (SHORTS) Light for moving observer ► • What is the speed of L...
37. (SHORTS) Nothing can travel faster than light ► • Why nothing can travel...
38. (SHORTS) What is farther away ► • What is farther away, ...
Minkowski Spacetime ► th-cam.com/video/-PV1JqV3blY/w-d-xo.html
professor, I am really sorry but at the 19:05, you take the dx.^2 /c.^2 as common, I dont understand how can you do it? can you share your secret please?
Because dear when u multiply that with what's inside the bracket you'll get the exact previous expression back.
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Because I don't know that about construction of space time
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29:56 Sir in some books, I read that that -ve sign before C²dt² is due the reason that we assume that temporal axis to be imaginary therefore after applying Pythagoras theorem , we will definitely get there -ve sign bcz of ( iC∆t)²
The temporal axis being imaginary is an oversimplification in some books.
The real reason for -ive before c²t² is so that speed of light is a constant for all observers.
For an observer in (x,ct) a light-front is represented by x² - c²t²=const. , and for another observer in (x',ct') it is x'² - c²t'² = const. So (x,ct) and (x',ct') must vary accordingly to keep the speed of light constant
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While talking about the separations of space-time, times of which frame do we use to decide whether two events are separated in time or not?
5:30 and of course the velocity of light, C
And subscribed and bell icon pressed. Hope to listen and learn from you standard physics.
14;35 Lorentz transformation given that moving frame is ONLY along X.
I have a doubt in finite potential well, can anyone explain, from where the potential comes and from which this potential related?
Give lectures on GR
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31:00, sir , can we take ict in place of ct so that we get ∆s²=∆x²+(ic∆t)² = ∆x²-c²∆t² ?
Sir , can we visualise the 4 dimensional space time as - the 3 dimensional Cartesian space moving on one line which we name the time axis ?
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Sir can we say incase of time like interval two different event happening at different time but in same location??
It's the opposite
❤
Sir I have a confusion about minkowski space....there are two ways to describe or demonstrate minkowski frame one is x' vs ct amd another x' vs ict..so which one is authentic...and how can we established Lorentz eqn by minkowski frame....? If we want to established then which frame should we take x' vs ct or x' vs ict.....
Some books take x v/s ict to approximate minkowski spacetime as eucledian space, since the square of distance between two points in such a space is x² + (ict)² = x² - (ct)²
However it's only a simplification for beginner level students. The correct approach is x v/s ct with the understanding that minkowski spacetime geometry is not same as that of flat space. In minkowski spacetime, the distance b/w two points (in general any inner product) is different from eucledian space (ex. there's a negative sign before time-component. This goes to the metric tensor of such spacetime)
Thanks sir....
Will you make videos on these topic also...? Some advanced STR like that....!...
@@tushardey7653 I will continue this topic a bit further. try to explore the necessary subject
Why distances are taken in squre root form?
Damnn, that was some tricky and speedy algebra hahaha
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What if, two events happening at the same space like in a repeatative reference and considered light like?
two events happening in the same place for one observer S, may not be happening in the same place for another moving observer S'
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But sir in some books (del s)^2 >0
For timelike interval....and for sapcelike interval (del s)^2 < 0
Depends on which convention is used (+++-) or (---+) Both are valid in their respective conventions. I used (+++-) for the space time interval
Tell reference book
5:00 You should be a marriage councillor! :-) .... 'appreciation of their Children' So the spacetime interval is the child of space and time united. 9:36 So time could be real yet the spacial dimensions be 'imaginary' ... and not the other way around,? In a cartoon Donald Duck said look at that Mountain, it ain't changing is it. Bugs Bunny having grown up in a fertile river valley said: I 'Imagine' it might ...hence the imaginary time axis :-) 14:20 I missed the bit where yo said the motion was along the x axis only.. 20:33 the penultimate line is hilarious but that's because you are having so much fun. 21:17 Please don't think me being picky or pedantic here but whilst I agree that the spacetime interval is invariant is it not just so by dint of its definition and formulation and hence not necessarily being due to the temporal axis being given an 'imaginary' property? What came first , the Interval or the Hyperbolae? Silly question I suppose: Is there a description of how Human's perceive the spacetime interval or is it abstract? (hahahaha you just said we don't need to worry ..OK). 27:20 You are now defining the spacetime interval as the geometric distance between events in spacetime a priori. 30:35 It certainly isn't Euclidean so what is it? What type of geometry is it? I can see where you are going now.
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Brovo!
But sir according to our book space time interval value in rest frame is equals to zero every time! Plz reply it, will clarify doubt of lakhs of students
It's only zero for a moving light photon.
What is physics ?
I understand this channel is about "education" and that requires one not to question the material.
However, that is a problem if the entire theory is wrong.
I suspect Future generations may find videos like this rather humorous (as I do)
Lets say we have two clocks A (stationary) and B (moving) with constant velocity differing by 161,000 miles/second.
At the instant at which B passes A both clocks read 12.00 mid-day.
According to special relativity :
- At the instant when B reads 1:00 PM . The clock at A must read 2.00 PM .
This is a calculation based on the Lorentz contraction (obviously an idea dependent on the existence of a absolute frame of reference) that time passes slower (50% of the rate) for the “moving” clock.
Now, we have a problem ………
- Because according to relativity movement is relative.
- There is no difference between A moving away from B (at a certain velocity) compared to B moving away from A (at that same velocity).
Hence if we repeat the same calculations for the Clock at A (according to special relativity):
- We must conclude that at the instant when A reads 1.00 PM . The clock at B must read 2.00 PM
Your final conclusion about Clock A and B does not violate relativity. It is infact a prediction of relativity, that both their measurements are correct (acc to each observer).
I think you need to read a little bit more before making such comments.
why you blur the video
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This is silly. Not any wonderful aspect of Physics as is claimed. First, you apply a fudge factor to a result (the original lorentz fudge ratio) to a value, then later you apply the reverse of that fudge to the result thus getting the original result back... and that is just application of a math process, not anything to do what Physics. So you don't have "something that both observers can agree on" at all. Actually there is no valid reason to even apply the Lorentz transformation equation for Length or Time or Mass in the first instance. Its only useful if applied to wave forms.- doppler.
There begins no new world, Sir. That has nothing to do with a „different geometry“. Thats sheer nonsense. What do you mean? Riemann geometry? No. „Minkowski geometry“? Whats that? Hyperbolas? No. Of course does the „spacetime interval“ depend on Pythagoras. It i s P.!But its an illegal move to write s^2 at the hypotenuse. Thats simply plain wrong. Think about it.
You sir are a BRILLIANT and gifted teacher. And I'm saying this having had experience with dozens of different university professors. I was completely absorbed. I am certainly joining, with pleasure.
Thank you sir
But, what will be the reference frame according to which del x, del y and del z was measured.