Relativity 105a: Acceleration - Hyperbolic Motion and Rindler Horizon

0:00 Intro (Special vs General Relativity)
4:10 Acceleration in SR Intro
6:07 U·A = 0 proof
7:44 Proper Acceleration Definition
14:40 Accelerated motion is Hyperbolic Proof
25:11 Rindler Horizon
30:01 Summary

[davidzhichen]

Absolutely appreciated for this video! Professor Wolfgang Rindler was one of my favorite professor when I was working on my Ph.D in Physics. He was the one recruited me to chase my dream when I was young ... This video helped the rest of the people to understand "How to bridge the General relativity with Special relativity with gauge invariance. I learned when I was young and glad to see this video to resurface the beauty of Rindler's Horizon.

[bernardsmith]

The best set of lectures I've ever seen. I'm waiting anxiously for the ones to follow on GR. Great job.

[riemann]

@eigenchris your courses on Tensors(algebra+calculus) along with these Relativity series deserve to be put out in form of a Relativity Introduction book. Neither of books out there on relativity I have ever read, introduce in ways your courses do. Great Job!!!

[andrewrich]

Minor correction: at 27:00 where you show Rindler's acceleration stopping, his curve should not be a straight line vertically, but rather a straight line (or ray) tangent to the green curve at that point. It will still be true that all the light beams will cross this line eventually. Thanks.

[CallOFDutyMVP]

Great videos, I watched your Tensor Calculus series to get myself caught up because I know Einstein Field Equations have Tensors. Extremely great videos💯

[vkoptchev]

Just a note, at 26:57 the statement about Rindler stopping accelerating is correct, but the graph shows him stop moving. I love your series. Haven’t seen the material presented this way in textbooks or lectures.

[AswinMe]

I was waiting for this Chris, thank u.

[isma]

Extremely great videos. The full serie have helped me to understand the Special Relativity in great details

[md.shafiullahkhan]

This is so much educative that every student on phyics must learn this lecture.

[dXoverdteqprogress]

Excellent video! I was just working on a video about the Unruh effect; now I can skip its intro and just link to this video.

[imaginingPhysics]

23:57 an easy way to see this without hyberbolic identities is to note that d(S.S) =dS.S+S.dS.
Now, in the frame of accelerating Rindler, position S is purely spacelike (since S is parallel to acceleration A in Rindler coordinates), and dS is purely timelike (since in Rindler rest frame the velocity does not have space components). Therefore the dot products are zero and S.S is constant.

[PDavidJosephy]

Thanks! Leonard Susskind presents the same analysis in his "Theoretical Minimum" course ... but your presentation is much clearer!

[signorellil]

I was going to say "this is like porn" but I take that back, this is better

[AntiCitizenX]

I think you missed an opportunity at 7:45. The reason U dot A is zero has an important interpretation. Acceleration in special relativity is always a rotation. All objects are always moving at the same speed through spacetime. We can only ever “rotate” the direction. If U dot A we’re nonzero, it would imply an object moving “faster” or “slower” than c through spacetime, which can’t happen.

A perfect analogy in Newtonian physics would be rotation as well. It is as if the rules say we can only ever travel at the same speed, and we are only allowed to change direction. In that interpretation, U dot A is necessarily zero as well.

[BlueMoonshine]

Very well explained. I have rarely seen such well explained physics!

[WSFeuer]

Einstein (from his How I Created Relativity lecture): "I was dissatisfied with the special theory of relativity, since the theory was restricted to frames of reference moving with constant velocity relative to each other and could not be applied to the general motion of a reference frame."

I looked elsewhere for his opinion on this subject, since this quote makes its seem almost certain he did not believe special relativity could be extended to accelerated frames. In other quotes though he is careful not to say that the postulates or principles don't extend to accelerated frames, rather only the equivalency of frames, so this particular quote may only have been a thoughtless imprecision on his part. However, if you read his intro to his 1916 GR paper, or his explanation of the Twin Paradox where he invokes GR, both of these heavily imply that he was not happy with the idea of treating acceleration in SR. Likely this is due to his Machian influence and his belief, which I quoted in our comments below, that absolute acceleration made no kinematical sense.

[asmaiqbal]

your videos are really understandable. Could you tell any book or reference to study more about Rindler coordinates ?? That seems very interesting topic !!

[jensphiliphohmann]

26:55 f: _As soon as Rindler stops accelerating..._
Your diagram shows Rindler _stop moving_ which actually is a kind of infinite acceleration in the −x direction. Rindler stopping accelerating would look like the hyperbola at this point goes over into a straight line with the hyperbola's current slopes, without any sharp bend. This would still work since the slope is steeper than 45°, and the RINDLER horizon would vanish.

[jay]

Thank you for making these videos available on YouTube for free. Love your generous work.
I had a doubt:
In the video 'relativity 104f', to derive 4-velocity, we had used the fact that derivative of basis vectors (with respect to proper time) is zero as they are constant throughout. Hence we could show that Minkowski squared length of U is c*c.
But while dealing with non inertial frames, and accelerated motion, shouldn't the derivative of basis vectors be non zero? How can we still say that Minkowski squared length of U is c*c?

[nityadas]

Dear Chris, are you planning to discuss General relativity ?
I am waiting for Relativistic tensors like EM field and so on. You told that can be uploaded after X mas.