people often assume the because Paul is a scientist he will be using jargon and concepts that take a PhD to understand. that and many people feel thinking is too hard so they don't. before you say they won't amount to anything in life like that that they could clearly be president without having a single thought of their own.
I'm truly grateful for anyone that watches my little science videos. I'm not trying to be the biggest, just the best I can possibly be. That said, I really appreciate comments like this!
Some countries as the USA have no interest in educate their people. Even their president is a moron who doesn't understand science and brags that he loves the uneducated. " Give them bread and circuses and they never revolt". Juvenal
Wow. WOW!!!!!!!! You're an incredible educator. Krauss earned a reputation (well earned I believe) for making complicated/complex concepts relatable to anyone who may be interested in them. You're at least that good, just regrettably not as famous. Amazing.
Fascinating As an 70 year old, i have have been fortunate to see the amazing advance in science and space flight development starting before Sputnik to the advance in computers and internet communication over my years. Your lively lessons make me wish i was your age. I have always followed NASA and aircraft development . For the incredible achievements of man, science and knowledge like yours Paul would not have been possible. The only reason i stick around is to see what the hell will be invented next. I love it. Glad i wont be around though when the romantic Venus becomes a romantic planet earth when seen from a little cosy red cottage on Mars. I am a Boiler and Steam systems man who still uses Robert Louis Stevenson's principals. LoL Yet today are still in prolic use. Allister Thank you Paul
Love your videos as always. Have you had the chance to go over A Smooth Exit from Eternal Inflation? by S. W. Hawking and Thomas Hertog yet (Hawking's last published paper before his death)? I'm just curious where it sits in the grand scheme of current theories and progression.
Thanks! Yes, I've read over Hawking's last paper, which isn't very significant in the landscape but interesting nonetheless. I think talked about it a few weeks ago on Weekly Space Hangout.
Hey Paul! When we say there are no aliens in observable universe actually we mean there were no aliens 2 000-50 000( random number) years ago, and that doesnt mean that there is no aliens right now in the universe because for us to know that, light needs to travel to us so we can see them. So, there is possibility that universe is full of spaceships but we just dont know yet. Is that correct? Thank you :)
Yeah that's the Starwars Cantina hypothesis, that somehow all civilizations arise within a few thousand years of each other (so that the tech levels are about the same). Kind of like the Cambrian Explosion on earth. And yeah if they were all more than a few thousand lightyears away then we wouldn't know about it yet.
Haha, "why it's true" is a very difficult, and deeply philosophical, question :) It appears to be true given all available evidence, so we run with it!
Just because things converge and diverge while falling down doesn't mean that geometry must be at the root of it. Use magnetic force instead of gravitational force and you get the exact same result without any bending of space. So i appreciate your example and it does make things more clear, but only as an illustration, the movement of particles in gravity does not imply curvature, it's the same as if it's just a force.
You're absolutely right. The second ingredient that makes this thought experiment so powerful is the equivalence principle, which tells you that locally every test particle has a completely flat spacetime. Thus, their movements trace out the underlying structure of that spacetime, and it turns out that it's curved!
Equivalent principle supporting general relativity, theory by Sir Einstein according to which inertial mass and gravitational mass is identical. Different objects or paricles varies with their masses traces the gravitational field. Things that are initally parallel ends up converging and then diverging.Things closest to Earth accelerates faster with more gravitational force indicating that gravity is curvature of space time with the base concept of geomatry.. It was interesting to know more about gravity defined with geomatry. Thank you Sir.
What am I missing...?? A sense in which the equivalence principle does NOT hold. In a gravitational field, a structure (with vertical extent) does NOT have the same gravitional force at the bottom of the struture a at the top. (Greater at the bottom than at the top.) Very slight difference, sure, but still there. The identical structure, if accelerated at G, will have exactly the same acceleration at the bottom & the top of the stucture (once the structure has equilibrated to the acceleration). What am I missing??
tfk 052 After thinking about this, I THINK that I see my problem. If anyone can confirm or refute this, I’d appreciate a reply. I think that the issue is simply one of caluclus. The experiment (& the theory) applies in a limit, to tiny volumes of space as that volume approaches zero. Then the acceleration of gravity (& the equivalent external accleeration of the rocket) will also be very slightly different at the top & bottom of the structure. It’s a version of the classic calculaus of continuously varying properties (in this case, the curvature of space-time). The derivatives of those properties are defined as the volume of space-time approaches zero.
You start with: . . . . (4 golf balls in a straight line) As they fall, if gravity was a straight line, they would all fall STRAIGHT down. So you would see a path something like: | | | | But you don't. You actually see something like: . . . . . . . . . . . . . . . . .... . So you can infer that the only way gravity could pull the golf balls down AND together is if it started at a single point (center of the earth) and went out in a curve and not a straight line. Though it could also be said to be an infinite number of straight lines that form a curve. Hope I didn't confuse you more, and hope I didn't get it wrong.
Alexander Krizel thanks, first let me say that I've never seen my golf balls fly in straight lines ;). I still see the balls falling down in straight lines which radius lines to the centre of the earth.
Lindsay Forbes LOL. I know what you mean. Maybe this: draw a line from the center of gravity to each ball. Now, make the lines equal length. The ends now for a curve. Why correct? That I don't think I can explain. I kind of understand, but not really. Weather finally broke out here, so maybe see you at the driving range. 😁
I think what is curved here is not the *trajectory* but the *geometry* in which that trajectory exists. Transforming the intuitive straight line into the slanted one would require you to curve that geometry.
Combine both of his thought experiments and construct a hollow square of glowworms 4x4. Now make a column of that hollow square infinitely (or sufficiently) high. Now drop it to earth, with you observing stationary but inside. You will see the walls of the column curving inwards to a single point as the glowworms reach the earth. I hope that helps.
Then we must be in a black hole if time space can only move in one direction as on a curve. That’s why it seem space time is accelerating that spaghetti effect ha sounds good anyway
Combine both of his thought experiments and construct a perfect 4x4x4 cube of 64 objects. Now allow the "cube" to drop to earth. The "cube" begins to look like a 4 sided pyramid, like if it were going down a drain or through a cone shape funnel. Since this would not happen in flat space, you must infer that you are now in curved space. The Earth has distorted the local flat spacetime and created a dimple, or gravity well due to it's mass. The objects "try" to move in a straight line, but earth deforms the local geometry (in a consistent and calculable way) so that the line is now a curve.
Dude, He spoon-fed you in the video, and then when you wanted more I tube-fed you in the comments. I'm not sure than even an IV drip would make you happy :( But lets try this: construct a hollow square of glowworms 4x4. Now make a column of that hollow square infinitely (or sufficiently) high. Now drop it to earth, with you observing stationary but inside. You will see the walls of the column curving inwards to a single point as the glowworms reach the earth. I hope that helps.
raven lord I can care less about equations made from something we can't even see. You don't agree? So you don't care if you can't find the curve but still bealive it?
That's the point, I CAN see it without the equations. His thought experiments can show this to someone with no math background. In the example he gave and the two I gave I can see the curve plain as day. I'll try one more and then you are on your own. Imagine a trampoline with a perfect grid of line painted on. Like a checker board but the colors are the same. Now take a 50 pound iron ball painted like the earth and gently place it in the center of the trampoline. what you see is the surface of the trampoline dip where the earth sits. The geometry is altered, including the shape and directions of the lines. Those near the earth are now curves bending towrds the earth. And if you shoot a row or string of marbles in that direction, you will see their shape and direction change too.
![⭐ฮิตในTikTok!! ( มะมะมะหมูเด้ง MooDeng ) Ver. แดนซ์ ReMix BY [ ดีเจกิต รีมิกซ์ ]](http://i.ytimg.com/vi/4noyAoMa7bQ/mqdefault.jpg)
It is an absolute travesty this channel has only 15k subs. Another great vid, thanks Paul!
Matthew Knight quite right. Only 15k subs, I don't get it
people often assume the because Paul is a scientist he will be using jargon and concepts that take a PhD to understand. that and many people feel thinking is too hard so they don't. before you say they won't amount to anything in life like that that they could clearly be president without having a single thought of their own.
I'm truly grateful for anyone that watches my little science videos. I'm not trying to be the biggest, just the best I can possibly be. That said, I really appreciate comments like this!
Some countries as the USA have no interest in educate their people. Even their president is a moron who doesn't understand science and brags that he loves the uneducated. " Give them bread and circuses and they never revolt". Juvenal
Incredibly profound stuff. Thanks.
Awesome!! I love your channel! Mind blowing every time!
I just love they manner in which you explain complicated ideas to make them understandable to a "dummy" like me. Awesome video. Thanks, Paul. 👍🏾
I don't think anyone is a dummy but I appreciate it, thanks!
Wow.
WOW!!!!!!!!
You're an incredible educator. Krauss earned a reputation (well earned I believe) for making complicated/complex concepts relatable to anyone who may be interested in them. You're at least that good, just regrettably not as famous. Amazing.
Thanks! Let's hope I, uh, don't follow in ALL of Krauss' footsteps...
Paul M. Sutter
Ok so........yea. I could have picked a different example perhaps. Oops! I meant well 😶
Fascinating
As an 70 year old, i have have been fortunate to see the amazing advance in science and space flight development starting before Sputnik to the advance in computers and internet communication over my years. Your lively lessons make me wish i was your age. I have always followed NASA and aircraft development . For the incredible achievements of man, science and knowledge like yours Paul would not have been possible. The only reason i stick around is to see what the hell will be invented next. I love it.
Glad i wont be around though when the romantic Venus becomes a romantic planet earth when seen from a little cosy red cottage on Mars. I am a Boiler and Steam systems man who still uses Robert Louis Stevenson's principals. LoL Yet today are still in prolic use.
Allister
Thank you Paul
You are a great teacher sir. Keep these videos coming please!!!!
Thank you, I plan on it :)
I like his channel because I didn’t learn higher maths and how to read it
Great explanation! You rock!
Thank you1
Awesome i now have a basic understanding. Thanks!!
Awesome, a good start :)
Yeah but you have been promising complete knowledge of time and space, so you don't get to stop just yet!
Love your videos as always. Have you had the chance to go over A Smooth Exit from Eternal Inflation? by S. W. Hawking and Thomas Hertog yet (Hawking's last published paper before his death)? I'm just curious where it sits in the grand scheme of current theories and progression.
Thanks! Yes, I've read over Hawking's last paper, which isn't very significant in the landscape but interesting nonetheless. I think talked about it a few weeks ago on Weekly Space Hangout.
Hey Paul! When we say there are no aliens in observable universe actually we mean there were no aliens 2 000-50 000( random number) years ago, and that doesnt mean that there is no aliens right now in the universe because for us to know that, light needs to travel to us so we can see them. So, there is possibility that universe is full of spaceships but we just dont know yet. Is that correct? Thank you :)
Yeah that's the Starwars Cantina hypothesis, that somehow all civilizations arise within a few thousand years of each other (so that the tech levels are about the same). Kind of like the Cambrian Explosion on earth. And yeah if they were all more than a few thousand lightyears away then we wouldn't know about it yet.
So why is the Equivalence Principle True? It is possible that small violation in EP can describe the dark matter?
Haha, "why it's true" is a very difficult, and deeply philosophical, question :) It appears to be true given all available evidence, so we run with it!
In a grid?
Just because things converge and diverge while falling down doesn't mean that geometry must be at the root of it. Use magnetic force instead of gravitational force and you get the exact same result without any bending of space. So i appreciate your example and it does make things more clear, but only as an illustration, the movement of particles in gravity does not imply curvature, it's the same as if it's just a force.
You're absolutely right. The second ingredient that makes this thought experiment so powerful is the equivalence principle, which tells you that locally every test particle has a completely flat spacetime. Thus, their movements trace out the underlying structure of that spacetime, and it turns out that it's curved!
❤
Equivalent principle supporting general relativity, theory by Sir Einstein according to which inertial mass and gravitational mass is identical. Different objects or paricles varies with their masses traces the gravitational field. Things that are initally parallel ends up converging and then diverging.Things closest to Earth accelerates faster with more gravitational force indicating that gravity is curvature of space time with the base concept of geomatry.. It was interesting to know more about gravity defined with geomatry. Thank you Sir.
No polytopes on a grid
What am I missing...??
A sense in which the equivalence principle does NOT hold.
In a gravitational field, a structure (with vertical extent) does NOT have the same gravitional force at the bottom of the struture a at the top. (Greater at the bottom than at the top.) Very slight difference, sure, but still there.
The identical structure, if accelerated at G, will have exactly the same acceleration at the bottom & the top of the stucture (once the structure has equilibrated to the acceleration).
What am I missing??
tfk 052 After thinking about this, I THINK that I see my problem. If anyone can confirm or refute this, I’d appreciate a reply.
I think that the issue is simply one of caluclus. The experiment (& the theory) applies in a limit, to tiny volumes of space as that volume approaches zero. Then the acceleration of gravity (& the equivalent external accleeration of the rocket) will also be very slightly different at the top & bottom of the structure. It’s a version of the classic calculaus of continuously varying properties (in this case, the curvature of space-time). The derivatives of those properties are defined as the volume of space-time approaches zero.
I don't see a curve. All the objects are falling straight down to the centre of the earth. What have I missed?
You start with: . . . . (4 golf balls in a straight line)
As they fall, if gravity was a straight line, they would all fall STRAIGHT down.
So you would see a path something like: | | | |
But you don't.
You actually see something like:
. . . .
. . . .
. . . .
. . . .
....
.
So you can infer that the only way gravity could pull the golf balls down AND together is if it started at a single point (center of the earth) and went out in a curve and not a straight line. Though it could also be said to be an infinite number of straight lines that form a curve.
Hope I didn't confuse you more, and hope I didn't get it wrong.
Alexander Krizel thanks, first let me say that I've never seen my golf balls fly in straight lines ;). I still see the balls falling down in straight lines which radius lines to the centre of the earth.
Lindsay Forbes LOL. I know what you mean. Maybe this: draw a line from the center of gravity to each ball. Now, make the lines equal length. The ends now for a curve. Why correct? That I don't think I can explain. I kind of understand, but not really. Weather finally broke out here, so maybe see you at the driving range. 😁
I think what is curved here is not the *trajectory* but the *geometry* in which that trajectory exists.
Transforming the intuitive straight line into the slanted one would require you to curve that geometry.
Combine both of his thought experiments and construct a hollow square of glowworms 4x4. Now make a column of that hollow square infinitely (or sufficiently) high. Now drop it to earth, with you observing stationary but inside. You will see the walls of the column curving inwards to a single point as the glowworms reach the earth. I hope that helps.
Then we must be in a black hole if time space can only move in one direction as on a curve. That’s why it seem space time is accelerating that spaghetti effect ha sounds good anyway
yeah find me a curve
Combine both of his thought experiments and construct a perfect 4x4x4 cube of 64 objects. Now allow the "cube" to drop to earth. The "cube" begins to look like a 4 sided pyramid, like if it were going down a drain or through a cone shape funnel. Since this would not happen in flat space, you must infer that you are now in curved space. The Earth has distorted the local flat spacetime and created a dimple, or gravity well due to it's mass. The objects "try" to move in a straight line, but earth deforms the local geometry (in a consistent and calculable way) so that the line is now a curve.
raven lord do u know how many experiments you can do to proove flat? Come on. I need to see man give me that evidence
Dude, He spoon-fed you in the video, and then when you wanted more I tube-fed you in the comments. I'm not sure than even an IV drip would make you happy :( But lets try this: construct a hollow square of glowworms 4x4. Now make a column of that hollow square infinitely (or sufficiently) high. Now drop it to earth, with you observing stationary but inside. You will see the walls of the column curving inwards to a single point as the glowworms reach the earth. I hope that helps.
raven lord I can care less about equations made from something we can't even see. You don't agree? So you don't care if you can't find the curve but still bealive it?
That's the point, I CAN see it without the equations. His thought experiments can show this to someone with no math background. In the example he gave and the two I gave I can see the curve plain as day. I'll try one more and then you are on your own. Imagine a trampoline with a perfect grid of line painted on. Like a checker board but the colors are the same. Now take a 50 pound iron ball painted like the earth and gently place it in the center of the trampoline. what you see is the surface of the trampoline dip where the earth sits. The geometry is altered, including the shape and directions of the lines. Those near the earth are now curves bending towrds the earth. And if you shoot a row or string of marbles in that direction, you will see their shape and direction change too.