I just wanna note that the dot product isn’t a random definition. It’s a generalized operation for getting frame-invariant quantities. It’s easy to prove with a bit of calculus. Technically you could *define* an arbitrary binary operator that takes two vectors to the reals, but there’s no reason for us to expect our answer to be the same once we go to a different coordinate system. If you tried to build an operator that took two vectors to the reals and gave the same number in different reference frames, you would get the dot product. So it’s not a coincidence that we use the dot product to define lengths: they constitute a property of space time that shouldn’t vary. Hope this helps someone who finds the definitions kind of arbitrary at first glance, as I once did. After learning tensor calculus, I see why these definitions make sense. Best wishes, friends.
if we assume that S1 and S2 are inertial frame of reference and a photon emitting source is also their initialy both S1 and S2 frame are coinside each other and photon emitting source is placed at X distance far from S1 & S2 frame and S1,S2 & emitted photon are movable in only x-direction this setup is initially given after that this setup is released then velocity of S1 is Zero and velocity of S2 is V and only we consider one photon emitted by source that moving towards S1 and S2 with speed of light then calculate velocity and time taken by S1 & S2 to reach that emitted photon from the frame of reference of emitted photon ?
I just wanna note that the dot product isn’t a random definition. It’s a generalized operation for getting frame-invariant quantities. It’s easy to prove with a bit of calculus. Technically you could *define* an arbitrary binary operator that takes two vectors to the reals, but there’s no reason for us to expect our answer to be the same once we go to a different coordinate system. If you tried to build an operator that took two vectors to the reals and gave the same number in different reference frames, you would get the dot product. So it’s not a coincidence that we use the dot product to define lengths: they constitute a property of space time that shouldn’t vary. Hope this helps someone who finds the definitions kind of arbitrary at first glance, as I once did. After learning tensor calculus, I see why these definitions make sense. Best wishes, friends.
these lectures if seen in conjunction with a good book really help you clarify the concepts.thank you sir :)
The way he explained ❤️❤️❤️❤️ thank-you sir for this beautiful series
thank you thank you thaaank youu, you explain perfectly
thank u very much sir.u clear my concept .....
if we assume that S1 and S2 are inertial frame of reference and a photon emitting source is also their initialy both S1 and S2 frame are coinside each other and photon emitting source is placed at X distance far from S1 & S2 frame and S1,S2 & emitted photon are movable in only x-direction this setup is initially given after that this setup is released then velocity of S1 is Zero and velocity of S2 is V and only we consider one photon emitted by source that moving towards S1 and S2 with speed of light then calculate velocity and time taken by S1 & S2 to reach that emitted photon from the frame of reference of emitted photon ?
THNX SIR BEST EXPLANATION
If these are proper time then why events are not happen in same place???
It should be 1-B^2 not (1-B)^2
True, thank you!