Very useful video, helped a lot when reading through the last few chapters of Penrose's 2011 book 'Cycles of time' in which he discusses his Conformal Cyclic Cosmology theory'. Note that he calls Penrose diagrams, Conformal diagrams. Thanks. Just watched the video again: At 7:09: Presumably the reason for both scaling time and distance axes is simply that Tan 0 to Pi/2 (Pi/2 radians = 90 deg.) makes for a convenient scale. A more familiar Log scale, would be not be steep enough in getting to infinity I guess.
I found that very informative, thank you! I don't get the topology of the spread out singularity but I'm working on that. I get the impression that at a sufficient time in the future we will be able to see a sufficient proportion of the past, even though folks say that there are limits to our visible Universe. Anyway that's another matter. From observing the length of the singularity in a Penrose diagram, Susskind has wondered what happens when it get longer and has latched upon Feynman's exponential increase in quantum states and is proposing something like Quantum Complexity as being a quantum analogue of The Second Law of Thermodynamics. Given that Penrose's zig zag line is a mere consequence of the chosen graphical representation isn't it likely that Lenny is chasing widgets for fun and publicity?
@@ExplainingScience Invisible AND VISIBLE SPACE in fundamental equilibrium and BALANCE IS E=MC2 AS F=ma, AS ELECTROMAGNETISM/energy is gravity. Indeed, the ultimate mathematical unification (AND UNDERSTANDING) of physics/physical experience combines, BALANCES, AND INCLUDES opposites. (Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black.) WHY AND HOW ELECTROMAGNETISM/energy is gravity, AS E=MC2 IS NECESSARILY F=MA: TIME DILATION ULTIMATELY proves ON BALANCE that E=mC2 IS F=ma, AS ELECTROMAGNETISM/energy is gravity. INDEED, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=mc2 is F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy. E=mc2 is F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE.) Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. BALANCE AND completeness go hand in hand. It ALL CLEARLY makes perfect sense. Great !!! Gravitational force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS E=mc2 is F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=mc2 is F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/energy is gravity. The Earth AND the Sun are CLEARLY E=MC2 and F=ma IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky. GREAT !! By Frank DiMeglio
Thank you for the Penrose diagram explanation. Makes sense to me now. But the black hole part at 11:45 was too fast for me. Because this is true for everything, as everything has a light cone. So e.g. everything inside my own light cone cannot get outside of it.
Thanks for your nice comment. I’m really glad you enjoyed the video. You may want to look at some more of the videos on czcams.com/users/explainingscience or subscribe to the channel.
So in a flat universe with a big bang and no dark energy (the last example), at infinite time in the future all points could have communicated with eachother!? I suppose thats cuz without dark energy theier would be no faster than light space expansion? Great video btw
You would have to know the green rings where in fact physically documented to follow this any further. At least that’s what I believe was indicated. It is a very deep subject and even the beginning premise can point to different ways of approaching the time theme.
Thanks for the video. However at 4:45 into the video, you state that it would not be possible "to travel between A and D", citing an example of an event taking place on Alpha Centauri in 5 minutes. But I don't understand why this would not be possible, because it would just be a matter of waiting for the light to travel from Alpha Centauri to earth, which would take approx 4 years and 5 minutes. Also, at 7 minutes into the video you introduced the concept of an "inverse tangent function", but as there was no explanation of what that means I completely gave up at that point, which is a shame as I find this subject interesting. I would say this video is only really suitable for those with advanced maths knowledge, so not really an "Introduction to Penrose Diagrams".
I think with the first question, he meant that because it takes 4 years for light to travel between Earth and Alpha Centauri, an event on Earth can't have affected an event on Alpha Centauri 5 minutes later. These diagrams are used for examining causal effects it seems, hence. With the second question, an inverse tangent function is like y = tan^-1(x), with x the variable, as shown in text in the video. It's what you get when you ask 'What angle would x be the tangent (tan) of?' as seen in this image www.skillsyouneed.com/images/trig/sin-cos-tan-unit-circle.png This results in the diagram as seen in the video, which shows y-values for all x-values from -infinity to +infinity being between a finite range [-pi/2, +pi/2]. This, in other words, makes it usable as a finite projection of infinity (if you embrace mathematics as your saviour), like infinite space or infinite time. I personally got such trigonometry in early high school, but such practices might not be commonplace depending on the kind of school, country, time, or other factors. Perhaps the creator had similar school experience for said material, hence the title of the video. It requires some stoppages to digest the information though, math doesn't follow intuition per se. If something still troubles you about the video, don't mind asking. I'm no physicist though, so I have my limits ':-)
Inverse Tangent is well understood (in high school Math) but perhaps it wasn't explained very well for why Penrose chose that transformation. I assumed that it enabled him to map an infinite canvas into something drawable?
Better the little that the righteous have than the wealth of many wicked; for the power of the wicked will be broken, but the Lord upholds the righteous. Psalm 37:16-17
thank you for this excellent intro! Now I feel confident enough to watch the continuation of the topic with Frederic Schuller
Very useful video, helped a lot when reading through the last few chapters of Penrose's 2011 book 'Cycles of time' in which he discusses his Conformal Cyclic Cosmology theory'. Note that he calls Penrose diagrams, Conformal diagrams. Thanks.
Just watched the video again:
At 7:09: Presumably the reason for both scaling time and distance axes is simply that Tan 0 to Pi/2 (Pi/2 radians = 90 deg.) makes for a convenient scale. A more familiar Log scale, would be not be steep enough in getting to infinity I guess.
Excellent explanation of what was a difficult topic for me. Many Thanks.
Thank you
I wish I had this in high school... Not that I would have understood it, but it was better than what the 2003 world wide web had to offer.
I found that very informative, thank you! I don't get the topology of the spread out singularity but I'm working on that. I get the impression that at a sufficient time in the future we will be able to see a sufficient proportion of the past, even though folks say that there are limits to our visible Universe. Anyway that's another matter. From observing the length of the singularity in a Penrose diagram, Susskind has wondered what happens when it get longer and has latched upon Feynman's exponential increase in quantum states and is proposing something like Quantum Complexity as being a quantum analogue of The Second Law of Thermodynamics. Given that Penrose's zig zag line is a mere consequence of the chosen graphical representation isn't it likely that Lenny is chasing widgets for fun and publicity?
I love that spacetime physics are half philosophy
Great video. Clear to follow
Glad you enjoyed it!
@@ExplainingScience Invisible AND VISIBLE SPACE in fundamental equilibrium and BALANCE IS E=MC2 AS F=ma, AS ELECTROMAGNETISM/energy is gravity. Indeed, the ultimate mathematical unification (AND UNDERSTANDING) of physics/physical experience combines, BALANCES, AND INCLUDES opposites. (Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black.)
WHY AND HOW ELECTROMAGNETISM/energy is gravity, AS E=MC2 IS NECESSARILY F=MA:
TIME DILATION ULTIMATELY proves ON BALANCE that E=mC2 IS F=ma, AS ELECTROMAGNETISM/energy is gravity. INDEED, TIME is NECESSARILY possible/potential AND actual IN BALANCE; AS E=mc2 is F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity IS ELECTROMAGNETISM/energy.
E=mc2 is F=ma. This NECESSARILY represents, INVOLVES, AND DESCRIBES what is possible/potential AND actual IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky, AS E=MC2 IS F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. (Energy has/involves GRAVITY, AND ENERGY has/involves inertia/INERTIAL RESISTANCE.) Very importantly, outer "space" involves full inertia; AND it is fully invisible AND black. BALANCE AND completeness go hand in hand. It ALL CLEARLY makes perfect sense. Great !!!
Gravitational force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE, AS E=mc2 is F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE, AS E=mc2 is F=ma; AS ELECTROMAGNETISM/ENERGY IS GRAVITY. "Mass"/ENERGY IS GRAVITY. ELECTROMAGNETISM/energy is gravity. The Earth AND the Sun are CLEARLY E=MC2 and F=ma IN BALANCE, AS ELECTROMAGNETISM/energy is gravity. The stars AND PLANETS are POINTS in the night sky. GREAT !!
By Frank DiMeglio
@@ExplainingScience In 7:08, just to be more precise, you can say maps the infinite domain(not range) of values since that is for the horizontal axis.
Thank you for the Penrose diagram explanation. Makes sense to me now. But the black hole part at 11:45 was too fast for me. Because this is true for everything, as everything has a light cone. So e.g. everything inside my own light cone cannot get outside of it.
Better explanation of Penrose diagrams than those on PBS Spacetime.
Thank you
Great explanation thank you
Glad you enjoyed the video. You may want to look at some more video on
czcams.com/users/explainingscience
or subscribe to the channel
Excellent, thank you
You are welcome! and please spread the word about the channel
how does line x = constant change to curved line? If we apply the transformation X = atan(x + t) + atan(x - t) and T = atan(x + t) - atan(x - t) ?
Brilliant explanation!
Thanks for your nice comment. I’m really glad you enjoyed the video. You may want to look at some more of the videos on
czcams.com/users/explainingscience
or subscribe to the channel.
Maybe it was not correctly mentioned that inside the ergosphere time and space dimensions swap? I think the green line should be drawn differently?
Thankyou. Very nice. 👍
Thank you. Long topic. 👍
So in a flat universe with a big bang and no dark energy (the last example), at infinite time in the future all points could have communicated with eachother!? I suppose thats cuz without dark energy theier would be no faster than light space expansion?
Great video btw
You would have to know the green rings where in fact physically documented to follow this any further. At least that’s what I believe was indicated. It is a very deep subject and even the beginning premise can point to different ways of approaching the time theme.
Great explanation. Thank you.
Thanks for the video. However at 4:45 into the video, you state that it would not be possible "to travel between A and D", citing an example of an event taking place on Alpha Centauri in 5 minutes. But I don't understand why this would not be possible, because it would just be a matter of waiting for the light to travel from Alpha Centauri to earth, which would take approx 4 years and 5 minutes.
Also, at 7 minutes into the video you introduced the concept of an "inverse tangent function", but as there was no explanation of what that means I completely gave up at that point, which is a shame as I find this subject interesting.
I would say this video is only really suitable for those with advanced maths knowledge, so not really an "Introduction to Penrose Diagrams".
I think with the first question, he meant that because it takes 4 years for light to travel between Earth and Alpha Centauri, an event on Earth can't have affected an event on Alpha Centauri 5 minutes later. These diagrams are used for examining causal effects it seems, hence.
With the second question, an inverse tangent function is like y = tan^-1(x), with x the variable, as shown in text in the video.
It's what you get when you ask 'What angle would x be the tangent (tan) of?' as seen in this image www.skillsyouneed.com/images/trig/sin-cos-tan-unit-circle.png
This results in the diagram as seen in the video, which shows y-values for all x-values from -infinity to +infinity being between a finite range [-pi/2, +pi/2]. This, in other words, makes it usable as a finite projection of infinity (if you embrace mathematics as your saviour), like infinite space or infinite time.
I personally got such trigonometry in early high school, but such practices might not be commonplace depending on the kind of school, country, time, or other factors. Perhaps the creator had similar school experience for said material, hence the title of the video. It requires some stoppages to digest the information though, math doesn't follow intuition per se.
If something still troubles you about the video, don't mind asking. I'm no physicist though, so I have my limits ':-)
Inverse Tangent is well understood (in high school Math) but perhaps it wasn't explained very well for why Penrose chose that transformation. I assumed that it enabled him to map an infinite canvas into something drawable?
Im subscriber 342 👍🏻
thanks you for subscribing!
Perfection a point of 0
Better the little that the righteous have
than the wealth of many wicked;
for the power of the wicked will be broken,
but the Lord upholds the righteous.
Psalm 37:16-17