Thank you for reducing it down to only one dimension of space. That's the only reason I can even begin to understand some small part of this fascinating subject.
Additional dimensions of space should not be a problem for understanding. You just add few more equations. Although, it's harder to visualize that in your head. Scientists add 4+ dimensions and do a lot of things with them, despite not being able to visualize it
When I started this channel my objective was to explain everything in simple terms to anyone with a basic knowledge of algebra, calculus and trigonometry. I'm still working on how to do that for the field equations associated with general relativity.
Excellent place to start if you want to understand general relativity. Thank you for taking the time to produce these videos, they have enabled me to understand concepts I couldn’t previously understand. They are a good stepping stone to the rigours of academia.
That last explanation and the parallel to the 3-dimensional nature of gravity was absolutely brilliant. It is not a force that brought them closer together, but the nature of the area they were traversing, which is how curvature by gravity works.
I used to think that your channel is same as other physics channel but when I find out that you have topics about general relativity and Q.M I thought lets check your channel out and by just watching this video . My Mind =BLOWN . You describe on of the most versatile thoery of universe in an easy way Please keep making these kind of videos . Please read about string Theory and make us comperhend it as well
In general relativity everything moves through space time along a geodesic. Just as a straight line is the shortest distance between two points in flat space, so a geodesic is the shortest distance between two points in space time. In particular, the geodesic is the shortest distance between two points on a curve.
If I understand your question correctly you are asking one of the fundamental questions that we don't actually know the answer to. We can describe a force and its action on objects mathematically - but exactly why or how a force can cause two or more objects which are not in contact to move in a particular way remains a mystery.
Love you sir.. You taught me the gist of general relativity is such simple way. Thank you so much. Keep enlithing us about more in depth concepts of physics.
i was addressing what you talked about at around 8:00. you said that the force appears to be a consequence of moving in curved space. if we thought about it simply as an attraction between two objects then we can think that they're caused to move because of that force. but if the force is a consequence of moving in curved space then what caused them to move through curved space, because the force is just what it looks like once they're moving.
Very nice lecture, I have a little understand about this theory and every time I watch this, new thoughts just pop up making me check the math of this theory over and over too lol, hoping I found something interesting. I keep watching it over and over, good job and on behalf of general relativity lovers, like I am, thank you very much
The Einstein Field Equations reduce to Newtonian gravity but as I said in response to an earlier post I am still pondering how to explain all that with the simplicity that I am aspiring to achieve in this channel. The tensor equations are incredibly hard. But I'm working on it.
*Transcript* 0:00 Hello. Today we're going to look at curved or warped spacetime. 0:04 What gives us a clue that spacetime might be curved? 0:09 Well, in our previous videos on spacetime, there are 2 clues that we might've spotted. 0:16 The 1st is that if we draw a spacetime diagram - that is time placed against space & as usual we'll just do it in 1 dimension in space & 1 dimension in time to keep things simple. 0:29 If you draw an acceleration in spacetime, the curve looks like this. 0:36 What it means is that for any incremental unit in time, the distance that you travel is progressively further. 0:47 All this is really saying is that as you accelerate, you go further, faster - because you're speeding up. 0:54 But that curve is a curve & that's our 1st hint that we might have some kind of curvature in space. 1:03 & the reason for that is the principle of equivalence. 1:07 You'll remember that Einstein had said that a person standing in a box on the surface of the Earth but subject to the gravitational attraction is equivalent to a person who is in outer space in a rocket - here's the fuel - travelling or accelerating at g 1:31 & Einstein says those 2 things are equivalent - there is nothing that anybody inside that box could do to demonstrate whether they were either stationary on the Earth subject to a gravitational force, g or accelerating through space subject to an acceleration of g 1:50 Now, a person who is accelerating through space will travel through spacetime on the basis of this diagram here, like that. 2:01 That is their journey through spacetime if they are accelerating through space at g 2:07 & by the principle of equivalence, that must mean that the person who is stationary on the Earth but subject to the gravitational acceleration, must *also* be travelling through spacetime, even though apparently they're not moving, according to that curve. 2:28 The 2nd clue that we had in our previous videos, is just in relation to the spacetime diagram where you travel from this point here which we'll call point O to a point, P 2:44 We have travelled a distance x in a time t 2:49 But the problem is, of course, that another observer who is travelling at a speed relative to us, will not measure the same x & will not measure the same t - that's the problem. 3:02 But what we showed was that there was 1 value that everybody agrees on & that is that: [DrPhysicsA writes a formula:] S² = (ct)² - x² ess squared equals c, the speed of light, times t squared minus ex squared. 3:16 So, whatever values of x & t anybody measures, [DrPhysicsA points at the formula: S² = (ct)² - x² ] if you put them into that formula, they will all agree on the value of S² 3:27 But we've never actually said what S² is. [DrPhysicsA points at the term: ct in the formula: S² = (ct)² - x² ] 3:32 Well, ct is a measure of distance: speed times time gives you distance, [DrPhysicsA points at the: x in the formula: S² = (ct)² - x² ] & x is also a measure of distance. [DrPhysicsA points at the: S in the formula: S² = (ct)² - x² ] 3:41 So S must itself be a measure of distance. 3:45 & S is, in fact, the path... [On the screen it says: constant for all observers ] ...through spacetime. 3:51 Now, at 1st thought you might've expected that the distance through spacetime of travelling from point O to point P, if that distance is S that you might say that that ought to be - this distance here of course is: ct - we always multiply by c so that we've got the same units in the time direction as we have in the space direction so we can compare like with like - otherwise we're doing apples with pears. 4:22 You might expect that S could be described quite simply as: S² = (ct)² + x² which is just Pythagoras. 4:33 But in fact, the correct term is: S² = (ct)² - x² 4:40 & that's our 2nd clue because if you plot that on a spacetime diagram what you actually end up with is what they call 'Minkowski space' where every point on that hyperbola satisfies this equation: [DrPhysicsA points again at the formula:] S² = (ct)² - x² 5:07 But here's the problem: that that length & that length & that length & that length & that length are all different, & yet we're saying that they are the same. 5:18 & that suggests that this representation on a flat piece of paper isn't quite correct. 5:24 So, now we say that if acceleration through space has a curved effect on spacetime & gravity, by the equivalence principle, also has a curved effect on spacetime, then we need to ask ourselves the question: what causes gravity? 5:46 & the answer is: mass. 5:48 & so, we come to the conclusion that mass warps spacetime & its effect is to cause any body to follow a straight line which is curved by spacetime. 6:05 It's a little difficult to draw for someone like me who isn't really an artist, but if this is what one might call 'flat spacetime' then the idea is that a mass actually causes that spacetime to dip down. 6:22 It's rather like standing on a trampoline. 6:26 You depress the area where the trampoline is & so you cause a kind of a bit of a dip in the trampoline - in this case, a dip in the spacetime so that a particle - even a particle of light coming along will think it's continuing in a straight line but will be diverted around. 6:51 Imagine a golf ball that just skirts the edge of the hole & diverts its direction as a consequence - that's the effect of gravity. 7:01 I can try to describe it another way: let's just think about the Earth for a moment. 7:07 & the Earth has lines of longitude which are great circles going around the Earth. 7:14 There's also another great circle which is the equator. 7:17 & what we're going to do is we're going to get 2 people to start out on different lines of longitude. 7:24 Each of them is being told to face due North & each of them is told to walk in a straight line due North, & so each of them begins to walk along the line of longitude. 7:38 Now, what will happen as they walk along it? 7:40 They will find that they are getting closer & closer together. 7:45 & if they don't know why, they might come to the conclusion that there is a force which is attracting them as they move - they're both moving ostensibly in parallel lines due north & yet they are being drawn together. 8:01 Indeed when they get to the North pole, 1 will be facing in that direction & 1 will be facing in *that* direction. 8:09 Yet they both started out facing due North & yet when they get to the North pole, they're actually at an angle to 1 another. 8:17 & that they can ascribe to a force. 8:21 But in fact, it's not a force at all - it's just the consequence of going round a curved surface. 8:28 They travel in straight lines; parallel to 1 another & yet they are attracted together. 8:35 This illustrates the principle of curved space. 8:38 So effectively, Einstein's theory of general relativity says that gravity doesn't actually exist at all, as we understand it. 8:48 It is an illusion. 8:50 The illusion is caused when we follow a straight line in curved space.
Just a notice for viewers: when Drphysicsa says mass causes spacetime curvature, he is not being precise. The ultimate source of spacetime curvature is not mass, but energy. The term representing the components of energy in the field equations is the stress-energy tensor, which takes into account mass, pressure, shear stress, momentum flux, etc. The reason he says mass causes gravity is that mass dominates the stress-energy tensor. Think about e=mc^2. It gives rise to much larger values of energy than something like pressure or shear stress. Therefore mass is the main contributing term in the stress-energy tensor.
trancerchemist , what he's saying is the shortest distance between too points on A curved surface are geodesic in spacetime , and the mass of an object curves the geodesic paths traveled on A sphere . remember energy is equal to mass (E=Mc^2) . I imagine too really express the relationship would need the stress mass energy stress tensor ( Tuv) . Still very insightful . . .
@@cesarpinto3276 Dude he said it as to add to the explanation, no one is forcing you to get this into your understanding at the end of the video, still it's interesting to know that not only mass warps space, but also other types of energy, so get down your high horse and don't insult people for adding to an explanation.
S is the distance through space-time. It is therefore combination of travelling through distance and travelling through time. I developed this concept more clearly in my series of five videos on special relativity
In essence its two ways of looking at the same thing. Newton's gravity says that there is a force exerted between any two objects which is given by your formula. Einstein says that mass tells spacetime how to curve and curved spacetime tells mass how to move. So Einstein essentially says that what we think of as gravity is just a mass moving in a straight line in curved spacetime.
Yes. For slow moving low gravitational situations, the Newtonian picture of gravity works very well. But all of gravity can be explained using general relativity. We all move in space time notwithstanding that we may not move in space.
Thanks for getting back to me on these issues, I see what you mean about everything traveling through space time...good point. I appreciate that in the first Femtoseconds after the big bang all the forces were unified but gravity seems so so fundamentally different that it's hard it imagine it being part of the set...am I the only one who thinks that you can have EITHER the curvature of Space time OR the graviton but not both.
The curvature of space-time due to mass will depend on the distance from the mass in exactly the same way that gravitational strength depends on the distance. So although there is a black hole at the centre of our galaxy and it massively distort space time around it, the impact of that gravitational strength in our solar system is relatively modest and the sun's gravitational strength is dominant. Similarly it is the Sun's mass which has the dominant effect on space-time in our local region.
Light is an electromagnetic wave, it's out of photons, and a photon has no mass, although that it can't escape the gravity of the black hole, how is that? as if Einstein's general relativity only melt in the black hole. Please answer, thank you,
Oh and by the way " I am still pondering how to explain all that with the simplicity that I am aspiring to achieve in this channel" just to let you know your videos are pitched perfectly....I get a little lost during the math sometimes but I can feel my brain actually expanding as I watch :-)
There is a maximum velocity of 300,000 KM/S but there is no limit to the acceleration. The force which is generating the acceleration will not be able to cause the object which is being accelerated to exceed the speed of light.
but what caused the objects to follow the curvature, what makes the two people walk along the line to the top, that seems like the same force concept. also you do an amazing job of explaining things
If i lift up my keyboard it doesn't move through space but it is moving through time If i let go, my keyboard will fall down & strike my reproductive region my reproductive region is also moving through time. In 1 video DrPhysicsA says it's moving through time at the speed of light Imagine if we could see into the future. You would see your room with you in it right now - it's xmas day - merry xmas btw & you would see your room (or some other environment) with you in it on Boxing Day & you in your environment on Dec 27th, Dec 28th, Dec 29th, etc. A whole long stream of you & your environments - like pearls on a necklace - extending into the future - it's like looking down a corridor which is pointing due north. Thus my keyboard & my groin are like the 2 people heading due north. Let's make a table. .................................................................................................................the 2 people.........................................my keyboard & reproductive regions Heading due...?...........................................................................................North.................................................................... Future What curved object are they moving on/through?......................the surface of Earth.......................................................spacetime What caused the curvature.......................................planet formation & gravity made Earth spherical........mass somehow curved spacetime Why do they collide........................................................the curvature causes their paths to converge..............spacetime curvature causes their paths through time to converge Thus objects fall due to movement through spacetime + curvature of spacetime So my groin is heading due future at the speed of light. But what we mean is we are looking at 1 bit of the corridor & then another bit & then another bit & the speed at which we view these parts of the corridor is the speed of light. Really your question is why is there any speed at all? Why do we travel down the time corridor? i dunno but I think maybe if you meditated your mind would become still - it would focus on 1 thing & thus you'd be moving through the time corridor more slowly, maybe
I followed this up to the point where you said s squared is equal to ct squared minus x squared, rather than the more obvious Pythagorean result. I don't see the reason for that.
Should be up in a few days. It will be fairly basic albeit still quite challenging. But I will also point to the excellent series of lectures on General Relativity (which include the EFE) given by Leonard Susskind in 2008 which can be found on TH-cam.
Thanks. Good questions. And I'm not sure I can properly address them. Let's have a go. First, I take the point about the so called 4 forces. But I think the real issue is reconciling the apparent certainty of relativity (Einstein didn't like uncertainty "God does not play dice") with the inherent uncertainty of quantum mechanics. On the second point everything travels thro spacetime even if stationary in space.
It's still Pythagorean, just rearranged. You'd just need to plot s (cτ) vs x so that ct is your hypotenuse. I'm sure this is beyond the scope of the video but it's the same as switching between complex and split-complex numbers by multiplying by the Lorentz factor (γ=j/i where j²=1 and i²=-1) and looking at their magnitudes.
A boy falling to earth in a grav field will fall in a straight line in space (ignoring air resistance and terminal velocity). But it falls in a curved line in spacetime for the reasons shown in my graphs. Light curves around a massive body (ie as a consequence of the grav field) because of the principle of equivalence. As I show, the light travelling across a spaceship which is accelerating will appear to bend.
kind of confused here, are the S values all really the same or not? In this minkowski space diagram is S still referring to the distance to the origin? Is this like a space curve where S is the norm?
If I understand your question correctly the answer is that we don't know. We can produce a mathematical explanation that accounts for what we observe (whether it be Newton or Einstein mechanics). But just why nature makes things do that we dont know. The reason an object moves thro curved spacetime would be explained by energetics. The movement will achieve the lowest energy state.
@DrPhysicsA I enjoyed the video. Can you explain to me why when I am standing on the earth I am being accelerated up. I know there is a normal force against the pseudo force created by curved spacetime. This acceleration shows up to me if someone falls off a building and so he is unhindered by force and sees the earth rushing up to him. what causes this expansion of the earth - electomagnetic? internal pressure?
nice explanation :) thanks a lot hehe .. i saw recently today you're putting up einsteins field equations, whens that gunna be btw? i rly can't wait lol, they confuse me so much
Just thinking about this more. If you are using rocket thrust(chemical, electromagnetic or nuclear) as you approach the speed of light, it takes more and more energy to increase your speed due to the realistic increase in mass. But the mass of the propellant increases also. What happens the potential energy in the chemical, electric forces or the weak/strong nuclear bonds. Assuming speed is relative does increasing your speed by 100m/s really depend on what speed you are doing. Why does the speed if the observer effect how much energy it takes to accelerate.
oh don't worry i've tried those up to like the 10th one on both and its still confusing to me lol.. i'm only just finishing alvls now and the concept of a tensor alone is just really peculiar
Random question. Based on Einstein's equivalence statement and that gravity distorts space and time, does that mean travelling with uniform acceleration also distorts space and time. As you reach relativistic speeds that exert time and length dilation WHAT DOES THE SPACE/TIME actually look like.
Well Einstein is effectively claiming that that which we call gravity is in fact a distortion of space time. And since by the equivalence principle gravity and acceleration are the same thing, then you are right.
DrPhysicsA Referring to what it looks like. In a frame of reference, you have parallel lines of space distortion at right angles to the direction you are travelling. Outside the elevator box, say, there is no space distortion. The rate of space distortion would be very high, at a molecular level. If you could stop suddenly, or even accelerate suddenly, would this create a gravitational wave?
following on from previous comment, it seems like we need the objects to first move through curved space and then they appear to just be moving towards each other. ie we need the two people to first walk up and them getting closer is the force. are we saying they're caused to walk by the curvature. sorry if im being tedious.
I got lost at about 6 minutes when he went from the t vs x explanation to the x,y versus something explanation. Now that I have had a good, long time to think about it and to rewatch the video, I see what he is saying, He actually does say it rather plainly in the video if you remember the right words when he goes to the membrane analogy. What is being plotted in the membrane picture is lines of equal changes in x and y, for equal changes in time as observed in our "stationary frame of reference" of an object (photon maybe) that would observe itself going in a straight line, moving equal distances in equal amounts of time in its constant velocity (but velocity near the speed of light) frame of reference. Throwing the Globe into the picture as shown in some of the representations on this TH-cam page is kind of phony if it makes you think of a heavy object pushing down on the membrane. But as the narrator draws it and most pictures show it, they just draw a drawing of space without actually showing the object that warps it.
Space is a calculation done by consciousness in order to interpret the data that comes into it. It is a mathematical function defined by the larger consciousness system (LCS). Scientists are expecting to see the edge of the Universe and they will never find it because is all virtual and it generates itself as long as you stare at it. It’s like AutoCAD model space. It’s infinite and a virtual generated space. As crazy as that sounds the Space is the same and consciousness is the computer.
If it's an illusion why are they looking to find the force in quantum mechanics. I agree it's an illusion but they say it holds everything together so what's up?
Can normal acceleration also be thought of as an illusion that is really just objects following the curve of space time? That is, if there is an accelerating space ship, can we imagine that the rocket engines are creating a 'dip' in front of the ship which it is constantly falling into? Thanks!
And second I can see how the curvature of space time influences objects with velocity by redefining what a straight line is but how does this curvature act on stationary objects sitting on a planet? Looking at conventional diagrams it's easy to think that the object sitting on the planet is at the bottom of the "gravity well" caused by a funnel of space time distortion but anything at the bottom of a well is held there by gravity. It doesn't seem to explain the situation. Thanks for your time
For an object not moving, but in a gravitational field, there is only motion in the time dimension. There is no movement in the spatial dimensions. How is that curved wrt space?
How do you get to the conclusion at 6:00 that gravity is caused by mass? I know but I am thinking how you make out mathematically? In between, That's really worth watching and understanding complex geometry in less time.
Hi Sir, seconds and minutes after the big bang we are already talking about gravity..where or what gave rise to Gravity at this early stage. Gravity is taught as curvature of space-time by mass..ibut doesw it mean anything to talk about space and time just seconds after the big bang? Where then does Gravity come into the picture? Tq !!
At 2:25 you state that, through the principle of equivalence, an object at rest on the earth is actually moving through spacetime along a curve where x changes with time. I must be wrong about this, but it seems to me that space would need to be sucked in, and not just curved, by the mass for x to change. Please explain. Similarly(?), how do a bullet and a ball each with no initial vertical velocity and differing horizontal velocities both follow straight lines through curved spacetime?
First let me say thanks for your excellent video's. If A level physics had been this clear I might have passed :-) Couple of things; I am puzzled about one thing (which you illustrate well in this video) in our obsession with uniting the 4 fundamental forces we always include (and it stymied by) gravity. (continues)
I feel a similar way. I studied Stroud's Engineering Maths which is a beautiful book that gently leads you up a "mountain" into degree level maths with many examples & problems that you can work through without a teacher. Once I finished the book I felt tempted to learn relativity & quantum mechanics as they have always fascinated me but the next books i got weren't that good including from the open universisty so i gave up & forgot 95% of what I learnt. Nowadays I would have put all the info through Supermemo which makes it impossible to forget what one has learnt. & years later I find these explanations by DrPhysicsA & which are of the same excellence as Stroud's & it makes me think if only these videos had been around years ago
I understand how gravity causes an object with velocity to go in curves or to orbit, due to the curvature of space-time: the object thinks that it's traveling in a straight line. But how does gravity (and curved space-time) cause an object to ACCELERATE towards the gravity source? The object was stationary. Why is this g-acceleration a "straight line" to the object even though it was originally stationary. Wouldn't to remain stationary be more of a "continuous motion" for it?
Maybe an analogy helps. Just think of a ball rolling down a hill, or a hole with increasing curvature, the ball will accelerate while moving closer to the center. The same way gravity curves space time, or we'll spacetime is curved giving rise to gravity.
@Mostwantedo Good question. if you have an object hovering in space & to its left is space & to it's right is compressed space then it would start to move toward the compressed space
How can s be constant for all values of x&t for an observer in one frame of reference? We have only established the fact that both the observers will agree on the equation (ct)^2-x^2 but have not proved that it always produces a constant value. That means the equation will produce varying values that are agreed by both the observers. So can it be a hyperbola? If yes , then the linear characteristics through spacetime is not at all possible right? What am I missing here??
INTERSTELAR TRAVEL This is how the element 115 gravity generators work. These amplifiers are located in front of space ship that create a distortion in the space-time continuum, so the craft follow a permanent downhill slope to infinity accelerating very fast…
But there must be a force or whatever else. Imagine an astronaut who can “walk” through space. When he’s far enough from Earth he can stop whenever he wants and he’ll be still. When he’s close to the Earth he will lose control of his movement and will start to fall down, he could not stop anymore. A curved space only suggests that his trajectory will be a curve as he approaches to the Earth, but it doesn’t explain what is pulling him toward the Earth.
Just a small quibble: 8:30 You say they travel in straight lines parallel to one another but at no point are they truly parallel to one another on a sphere. It's also debatable whether either of them can be said to be travelling in a straight line since they follow an arc. "Gravity is an illusion caused by following a straight line in curved space." Could that be rephrased as "gravity is the force experienced by any entity that deviates from its naturally curved trajectory through space" since everything is always orbiting something else i.e. subject to another thing's inertial frame of reference when either at rest or moving at constant velocity?
I'm a bit confused; if gravity is a consequence of the curvature of space-time rather than an actual force, then what's the point of the search for a gauge boson that carries the gravitational force in the Standard Model?
***** Thanks. Your idea (even if it's not a rigorously confirmed fact) kind of makes the relationship make a bit more sense. I was literally completely lost, I had forgotten to take into account the fact that no "information" can travel any faster than light and just assumed the particles should instantaneously react to the curvature.
Oners82 It seems to me (I'm not an expert, just throwing an idea out here) that while gravity isn't a force in precisely the way, say, electromagnetism is, it is still a force (causes objects to accelerate), and the curvature of space-time is merely the way we explain how that force arises.
+Prince Istalri A graviton is predicted by the standard model (which says that every force has a force carrier) that is why. Even though gravity is not a force in the sense Newton explained gravity, there still exist a force but it acts on space itself.
A curved graph of distance against time is not a 'hint' that space-time is 'curved'. Incidentally, it's normal to put the dependent variable on the vertical axis, not the horizontal axis. A person who is on the ground is not 'moving through space-time' as a result of being in the Earth's gravitational field. He is not moving at all.
There is a question in regards to inertia (conservation of motion). I am on the bus, I feel the bus accelerating, and I move backward. Is the bus producing a warped space time behind me? The thing that I don't understand is that the means (car, bus, train, bicycle...) are accelerating, but I doubt is a deformation of space-time anyhow. Answer?
For that you need to understand the theory more deeply, when you are in space time and you are stationary you just create a warped spacetime, but when you start moving you create waves in spacetime(which are called Gravitational waves), but this warped space is very very very small even smaller than the size of nucleus of an atom, a bus,car or any other thing on earth is just too small to just create a noticable ammount of warped space, for that you will need blackholes!! Simply, what you experience is just basic force of inertia it has nothing to do with warped spacetime!! Yes you create gravitational waves when you are in an accelerating bus but it is just too small to be significant.
The "space time", or at least how we represent it in a 3D fashion as a single plane thats curving. Technically theres an infinite amount of these planes in infinite amount of directions with technically no limit so does that indicate that space time is more of a fluid medium and gravity itself is more of a phenomena where this space time fluid "flow" is being interrupted by mass/energy? I mean, gravity still doesnt technically exist in the conventional form as a force itself but yeah
Oh my god. I was thinking the exact same thing. Or are we? I was thinking, if we are to take a sealed tank of water (or whatever fluid) into a vacuum, add a ball inside that tank of water, make that ball spin, maybe, the reaction of the water to the spinning ball inside it will show how spacetime reacts to the mass (say, earth) in it. I mean, I don't know if that even makes sense, but that is how I understand einstein's idea of gravity. The space (fluid) around us pushes us to the big mass that caused disturbance in it.
Paulo Villacorte I was thinking about this and, from my very limited understanding, I realize that we are not taking into account a 4D or even 5D universe. What we may perceive as a 3D fluid like properties of this structure may actually be something completely different. For example, length and time dilation and the physical shape of the universe being affected by mass counteract what we were thinking on the matter.
DaTurdburglar I suppose that curvature in spacetime causes the presence of mass. Mass in its ultimate form is nothing as you deep dive into the quantum world and you just see a while lot of nothingness as you navigate deep in an object. So the ultimate smallest unit of mass is just nothing. Then wat explains the presence of mass when its ultimate unit is nothing? It is the deformation of spacetime that creates mass.
since everything is relative then what this curve is relative to ? we do everything in spacetime then what does it mean by spacetime itself curve with respect to ?may be i am not able to fully explain my query...but please answer if you could get my question
is that why i cant go back in time...everything inflate….everything changes? what if i could go back to that point in Space maybe 10 yrs ago...would that bring me back to a time 10 year ago if i could travel instantly like a pair of entangled particle?…..
I ran out of space (no pun intended). Dark-M/E serves as a cushion gradually pushed by the bent space-time in "large mass areas" , in which while Black-Holes and their gravity will nullify the effects. /Crackpot Alert*
A railroad track is curved. A railroad car will follow that curve no matter what velocity. That is true curvature. With spacetime, the curvature is dependent upon the velocity of the object and their relative masses, it is variable. That is a mathematical curvature. Just because you were taught it doesn't make it true.
Plz dr physics explain it in Mathematical terms . True or ?? Dark Matter Ques , Galactical data shows That , The Galaxy don't follow The Law of kepler , newton and Einstein 's Orbital motion .and its graph is not as predicted , instead it's Linear . !!!!!!!And it said to be because of Darkmatters .So am asking? why , it is not because of Gravitational Time dilation or , relative time differences between two regions of spacetime in galaxys !!!!, May be it would be our wrong observation of orbital motion !!! Because Einstein has Said , Gravity Slowdown Theflow of Time , relative to Less gravitational Area . So .... May be it is the reasons , That's why we observing linear graph instead , predected Curve on graph !!!!
1:40 into this video DrPhysicsA quotes Einstein and says, "there's no experiment than can tell you whether you're accelerating through space, or on the ground". Yet in a previous video he talks about "tidal forces". So I have to disagree. You would not experience these tidal forces in a spaceship accelerating at 1 g. If you had a sensitive enough "gravitometer" you would predict tidal forces but observe "none" in a spaceship accelerating at 1g. Consider that this gravitometer is one you've calibrated yourself outside this "box" (or spaceship). If you can't reproduce these tidal forces like you did in a lab (at 1g), then you could easily conclude that the ship is accelerating. - Mike drop
If one could say that gravity that we feel here on earth would be same situation as in an accelerated elevator, couldn't we also say that we've been accelerating for the past 4.5 billions years? If so, by now, wouldn't we have a huge velocity with respect to some observer ?
Indeed, which is why stars/galaxies on the edge of the expansion of the universe will eventually move so fast they'll break the light speed barrier and their light will never reach our telescopes.
+Spell456 The curve DrPhysicsA draw at 4:52 is a _hyperbolic_ distances obeying the formula X^2 - Y^2 = C^2, where C is a constant. The dots he made on the curve are time points. The lines he draw to the curve are time lines of simultaneous time. The curve itself represent the _constant_ hyperbolic distance C (s^2 = (ct)^2 - x^2 in DrPhysicsA's notation) from origo over all time points in space. Therefore all the straight time lines he draw are of the same distance s. Take note that the axis marked t is not time - but time times c (ct), which is a distance. Also notice that s, unlike x, is not a distance in ordinary space with x/y axis but a space-time distance from origo to a point on the curve in _space-time_ - which per definition is a constant distance. If you were to draw such space-time curve in an ordinary x-y diagram, it would be a circle with the radius C, which could be thought about as a motion in space under constant acceleration but at a constant, radial, distance. Another way to think about it is to think about a hovering craft at a fixed height C above the surface in a gravitational field. In order to hover at the height C you will need to accelerate constantly to compensate the acceleration from the gravitational field. If you do that your position in space time will create the very same curved space-time diagram. You are now in a situation where you are under constant accelerate but your position x,y.z in space and as well your time flow t is constant so it follows that your space-time distance s also must be constant for all time points - even though you are accelerated!
Gravity is the bent space time done in the presence of a mass according to general theory of relativity. Only impressive math skills you have to have. Tensors, derivatives, fields. Imagine a rubber sheet the Sun a cannon ball and the Earth like a marble rotating around it. There is not an attraction force per say like Newton thought although is very intuitive, but rather the Earth moves on curved space-time geodetic lines that Sun bends. It’s like it always chasing a valley.
A wizard did it. If we think about the trampoline model at 6:00 we have our weight stretching the fabric of the trampoline In this analogy the fabric of the trampoline is like spacetime This implies that each bit of space is connected to each other bit of space It's said that the trampoline model isn't as accurate as this image: 64.media.tumblr.com/659da12fac7582bf5c47f4efbb2152d9/tumblr_o5ee0gLt591s5nl47o1_500.gifv by 1ucasvb here we see a ball compressing the space around it like a penis becoming floppy Let's imagine that we are directly above a gigantic penis looking down on it. What do we see? Just the tip We see the circular head of the penis. The "glans" if you will. In the penis analogy, erections stretch the penis like an elastic band & when the blood leaves the penis, elastic forces pull the penis back down to it's original size. Thus we can imagine our planet, Earth attached to each bit of space with an elastic band, pulling on each bit of space bringing them inwards like a giant space penis.
+standingunder If space-time is curved it means it contains energy, and if there is energy in space-time it curves space-time. In Einsteins general theory, gravity is not a force but a property (curvature) of space-time itself. Mass tells space-time how to curve. In turn the curvature of space-time tells the masses show to move in space-time.
+standingunder Yes, it's saying gravity is not a force. Objects are coming near each other due to them travelling through space. But we thought they were moving in the first place because of gravity. It seems to me they move through space and if they try to occupy the same position they are stuck to each other and that's how we're stuck to the earth. Now the question is. Why are we all moving, maybe even why does light move?
So, in motion, the number of cycles is less than the actual according to special relativity, is that correct? Motion effects the transition of atom,doesn't it?
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Thank you for reducing it down to only one dimension of space. That's the only reason I can even begin to understand some small part of this fascinating subject.
Additional dimensions of space should not be a problem for understanding. You just add few more equations. Although, it's harder to visualize that in your head.
Scientists add 4+ dimensions and do a lot of things with them, despite not being able to visualize it
When I started this channel my objective was to explain everything in simple terms to anyone with a basic knowledge of algebra, calculus and trigonometry. I'm still working on how to do that for the field equations associated with general relativity.
I watched them. You rocked! Too bad no more new videos :(
Excellent place to start if you want to understand general relativity. Thank you for taking the time to produce these videos, they have enabled me to understand concepts I couldn’t previously understand. They are a good stepping stone to the rigours of academia.
That last explanation and the parallel to the 3-dimensional nature of gravity was absolutely brilliant.
It is not a force that brought them closer together, but the nature of the area they were traversing, which is how curvature by gravity works.
I used to think that your channel is same as other physics channel but when I find out that you have topics about general relativity and Q.M I thought lets check your channel out and by just watching this video . My Mind =BLOWN . You describe on of the most versatile thoery of universe in an easy way Please keep making these kind of videos . Please read about string Theory and make us comperhend it as well
In general relativity everything moves through space time along a geodesic. Just as a straight line is the shortest distance between two points in flat space, so a geodesic is the shortest distance between two points in space time. In particular, the geodesic is the shortest distance between two points on a curve.
Fcking hell this feels so intuitive, it feels like this is exactly was going through the mind of Einstein.
If I understand your question correctly you are asking one of the fundamental questions that we don't actually know the answer to. We can describe a force and its action on objects mathematically - but exactly why or how a force can cause two or more objects which are not in contact to move in a particular way remains a mystery.
Love you sir.. You taught me the gist of general relativity is such simple way. Thank you so much. Keep enlithing us about more in depth concepts of physics.
i was addressing what you talked about at around 8:00.
you said that the force appears to be a consequence of moving in curved space. if we thought about it simply as an attraction between two objects then we can think that they're caused to move because of that force. but if the force is a consequence of moving in curved space then what caused them to move through curved space, because the force is just what it looks like once they're moving.
Very nice lecture, I have a little understand about this theory and every time I watch this, new thoughts just pop up making me check the math of this theory over and over too lol, hoping I found something interesting. I keep watching it over and over, good job and on behalf of general relativity lovers, like I am, thank you very much
The Einstein Field Equations reduce to Newtonian gravity but as I said in response to an earlier post I am still pondering how to explain all that with the simplicity that I am aspiring to achieve in this channel. The tensor equations are incredibly hard. But I'm working on it.
*Transcript*
0:00
Hello. Today we're going to look at curved or warped spacetime.
0:04
What gives us a clue that spacetime might be curved?
0:09
Well, in our previous videos on spacetime, there are 2 clues that we might've spotted.
0:16
The 1st is that if we draw a spacetime diagram - that is time placed against space & as usual we'll just do it in 1 dimension in space & 1 dimension in time to keep things simple.
0:29
If you draw an acceleration in spacetime, the curve looks like this.
0:36
What it means is that for any incremental unit in time, the distance that you travel is progressively further.
0:47
All this is really saying is that as you accelerate, you go further, faster - because you're speeding up.
0:54
But that curve is a curve & that's our 1st hint that we might have some kind of curvature in space.
1:03
& the reason for that is the principle of equivalence.
1:07
You'll remember that Einstein had said that a person standing in a box on the surface of the Earth but subject to the gravitational attraction is equivalent to a person who is in outer space in a rocket - here's the fuel - travelling or accelerating at g
1:31
& Einstein says those 2 things are equivalent - there is nothing that anybody inside that box could do to demonstrate whether they were either stationary on the Earth subject to a gravitational force, g or accelerating through space subject to an acceleration of g
1:50
Now, a person who is accelerating through space will travel through spacetime on the basis of this diagram here, like that.
2:01
That is their journey through spacetime if they are accelerating through space at g
2:07
& by the principle of equivalence, that must mean that the person who is stationary on the Earth but subject to the gravitational acceleration, must *also* be travelling through spacetime, even though apparently they're not moving, according to that curve.
2:28
The 2nd clue that we had in our previous videos, is just in relation to the spacetime diagram where you travel from this point here which we'll call point O to a point, P
2:44
We have travelled a distance x in a time t
2:49
But the problem is, of course, that another observer who is travelling at a speed relative to us, will not measure the same x & will not measure the same t - that's the problem.
3:02
But what we showed was that there was 1 value that everybody agrees on & that is that:
[DrPhysicsA writes a formula:]
S² = (ct)² - x²
ess squared equals c, the speed of light, times t squared minus ex squared.
3:16
So, whatever values of x & t anybody measures,
[DrPhysicsA points at the formula: S² = (ct)² - x² ]
if you put them into that formula, they will all agree on the value of S²
3:27
But we've never actually said what S² is.
[DrPhysicsA points at the term: ct in the formula: S² = (ct)² - x² ]
3:32
Well, ct is a measure of distance: speed times time gives you distance,
[DrPhysicsA points at the: x in the formula: S² = (ct)² - x² ]
& x is also a measure of distance.
[DrPhysicsA points at the: S in the formula: S² = (ct)² - x² ]
3:41
So S must itself be a measure of distance.
3:45
& S is, in fact, the path...
[On the screen it says: constant for all observers ]
...through spacetime.
3:51
Now, at 1st thought you might've expected that the distance through spacetime of travelling from point O to point P, if that distance is S that you might say that that ought to be - this distance here of course is: ct - we always multiply by c so that we've got the same units in the time direction as we have in the space direction so we can compare like with like - otherwise we're doing apples with pears.
4:22
You might expect that S could be described quite simply as: S² = (ct)² + x² which is just Pythagoras.
4:33
But in fact, the correct term is: S² = (ct)² - x²
4:40
& that's our 2nd clue because if you plot that on a spacetime diagram what you actually end up with is what they call 'Minkowski space' where every point on that hyperbola satisfies this equation:
[DrPhysicsA points again at the formula:]
S² = (ct)² - x²
5:07
But here's the problem: that that length & that length & that length & that length & that length are all different, & yet we're saying that they are the same.
5:18
& that suggests that this representation on a flat piece of paper isn't quite correct.
5:24
So, now we say that if acceleration through space has a curved effect on spacetime & gravity, by the equivalence principle, also has a curved effect on spacetime, then we need to ask ourselves the question: what causes gravity?
5:46
& the answer is: mass.
5:48
& so, we come to the conclusion that mass warps spacetime & its effect is to cause any body to follow a straight line which is curved by spacetime.
6:05
It's a little difficult to draw for someone like me who isn't really an artist, but if this is what one might call 'flat spacetime' then the idea is that a mass actually causes that spacetime to dip down.
6:22
It's rather like standing on a trampoline.
6:26
You depress the area where the trampoline is & so you cause a kind of a bit of a dip in the trampoline - in this case, a dip in the spacetime so that a particle - even a particle of light coming along will think it's continuing in a straight line but will be diverted around.
6:51
Imagine a golf ball that just skirts the edge of the hole & diverts its direction as a consequence - that's the effect of gravity.
7:01
I can try to describe it another way: let's just think about the Earth for a moment.
7:07
& the Earth has lines of longitude which are great circles going around the Earth.
7:14
There's also another great circle which is the equator.
7:17
& what we're going to do is we're going to get 2 people to start out on different lines of longitude.
7:24
Each of them is being told to face due North & each of them is told to walk in a straight line due North, & so each of them begins to walk along the line of longitude.
7:38
Now, what will happen as they walk along it?
7:40
They will find that they are getting closer & closer together.
7:45
& if they don't know why, they might come to the conclusion that there is a force which is attracting them as they move - they're both moving ostensibly in parallel lines due north & yet they are being drawn together.
8:01
Indeed when they get to the North pole, 1 will be facing in that direction & 1 will be facing in *that* direction.
8:09
Yet they both started out facing due North & yet when they get to the North pole, they're actually at an angle to 1 another.
8:17
& that they can ascribe to a force.
8:21
But in fact, it's not a force at all - it's just the consequence of going round a curved surface.
8:28
They travel in straight lines; parallel to 1 another & yet they are attracted together.
8:35
This illustrates the principle of curved space.
8:38
So effectively, Einstein's theory of general relativity says that gravity doesn't actually exist at all, as we understand it.
8:48
It is an illusion.
8:50
The illusion is caused when we follow a straight line in curved space.
The Earth's gravitational field will also have an effect on space-time and cause some curvature but it will be much less than that of the sun.
The gravity is an illusion - it is caused when we followed a straight line in curved space. Now I got it!
Just a notice for viewers: when Drphysicsa says mass causes spacetime curvature, he is not being precise. The ultimate source of spacetime curvature is not mass, but energy. The term representing the components of energy in the field equations is the stress-energy tensor, which takes into account mass, pressure, shear stress, momentum flux, etc. The reason he says mass causes gravity is that mass dominates the stress-energy tensor. Think about e=mc^2. It gives rise to much larger values of energy than something like pressure or shear stress. Therefore mass is the main contributing term in the stress-energy tensor.
trancerchemist , what he's saying is the shortest distance between too points on A curved surface are geodesic in spacetime , and the mass of an object curves the geodesic paths traveled on A sphere . remember energy is equal to mass (E=Mc^2) . I imagine too really express the relationship would need the stress mass energy stress tensor ( Tuv) . Still very insightful . . .
@@cesarpinto3276 Dude he said it as to add to the explanation, no one is forcing you to get this into your understanding at the end of the video, still it's interesting to know that not only mass warps space, but also other types of energy, so get down your high horse and don't insult people for adding to an explanation.
S is the distance through space-time. It is therefore combination of travelling through distance and travelling through time. I developed this concept more clearly in my series of five videos on special relativity
Without any graphical illustration you just clearly taught amazing 👌👌
Thanks you very much. Your way of explanation is enjoyable
In essence its two ways of looking at the same thing. Newton's gravity says that there is a force exerted between any two objects which is given by your formula. Einstein says that mass tells spacetime how to curve and curved spacetime tells mass how to move. So Einstein essentially says that what we think of as gravity is just a mass moving in a straight line in curved spacetime.
Yes. For slow moving low gravitational situations, the Newtonian picture of gravity works very well. But all of gravity can be explained using general relativity. We all move in space time notwithstanding that we may not move in space.
Thanks for getting back to me on these issues, I see what you mean about everything traveling through space time...good point. I appreciate that in the first Femtoseconds after the big bang all the forces were unified but gravity seems so so fundamentally different that it's hard it imagine it being part of the set...am I the only one who thinks that you can have EITHER the curvature of Space time OR the graviton but not both.
amazing explanations...very intuitive presentations,...congratulations...Nothing like pen and paper and sketches...
The curvature of space-time due to mass will depend on the distance from the mass in exactly the same way that gravitational strength depends on the distance. So although there is a black hole at the centre of our galaxy and it massively distort space time around it, the impact of that gravitational strength in our solar system is relatively modest and the sun's gravitational strength is dominant. Similarly it is the Sun's mass which has the dominant effect on space-time in our local region.
Light is an electromagnetic wave, it's out of photons, and a photon has no mass, although that it can't escape the gravity of the black hole, how is that? as if Einstein's general relativity only melt in the black hole. Please answer, thank you,
Oh and by the way " I am still pondering how to explain all that with the simplicity that I am aspiring to achieve in this channel" just to let you know your videos are pitched perfectly....I get a little lost during the math sometimes but I can feel my brain actually expanding as I watch :-)
Very good finally someone made it simple
There is a maximum velocity of 300,000 KM/S but there is no limit to the acceleration. The force which is generating the acceleration will not be able to cause the object which is being accelerated to exceed the speed of light.
but what caused the objects to follow the curvature, what makes the two people walk along the line to the top, that seems like the same force concept. also you do an amazing job of explaining things
If i lift up my keyboard it doesn't move through space but it is moving through time
If i let go, my keyboard will fall down & strike my reproductive region
my reproductive region is also moving through time. In 1 video DrPhysicsA says it's moving through time at the speed of light
Imagine if we could see into the future. You would see your room with you in it right now - it's xmas day - merry xmas btw
& you would see your room (or some other environment) with you in it on Boxing Day
& you in your environment on Dec 27th, Dec 28th, Dec 29th, etc. A whole long stream of you & your environments - like pearls on a necklace - extending into the future - it's like looking down a corridor which is pointing due north.
Thus my keyboard & my groin are like the 2 people heading due north. Let's make a table.
.................................................................................................................the 2 people.........................................my keyboard & reproductive regions
Heading due...?...........................................................................................North.................................................................... Future
What curved object are they moving on/through?......................the surface of Earth.......................................................spacetime
What caused the curvature.......................................planet formation & gravity made Earth spherical........mass somehow curved spacetime
Why do they collide........................................................the curvature causes their paths to converge..............spacetime curvature causes their paths through time to converge
Thus objects fall due to movement through spacetime + curvature of spacetime
So my groin is heading due future at the speed of light. But what we mean is we are looking at 1 bit of the corridor & then another bit & then another bit & the speed at which we view these parts of the corridor is the speed of light. Really your question is why is there any speed at all? Why do we travel down the time corridor? i dunno but I think maybe if you meditated your mind would become still - it would focus on 1 thing & thus you'd be moving through the time corridor more slowly, maybe
I followed this up to the point where you said s squared is equal to ct squared minus x squared, rather than the more obvious Pythagorean result. I don't see the reason for that.
He derives it in earlier videos on relativity
zarchy55
sorry
Ok, I will drink a beer and challenge myself with understanding this video.
Should be up in a few days. It will be fairly basic albeit still quite challenging. But I will also point to the excellent series of lectures on General Relativity (which include the EFE) given by Leonard Susskind in 2008 which can be found on TH-cam.
I really like your videos, thanks my friend.
2:30 Holy crap that just made so much sense!
Thanks. Good questions. And I'm not sure I can properly address them. Let's have a go. First, I take the point about the so called 4 forces. But I think the real issue is reconciling the apparent certainty of relativity (Einstein didn't like uncertainty "God does not play dice") with the inherent uncertainty of quantum mechanics. On the second point everything travels thro spacetime even if stationary in space.
Where did you get the equation s²=(ct)² - x² from? It came out of nowhere from your explanation..
These video's are great.
beautiful as always
It's still Pythagorean, just rearranged. You'd just need to plot s (cτ) vs x so that ct is your hypotenuse. I'm sure this is beyond the scope of the video but it's the same as switching between complex and split-complex numbers by multiplying by the Lorentz factor (γ=j/i where j²=1 and i²=-1) and looking at their magnitudes.
A boy falling to earth in a grav field will fall in a straight line in space (ignoring air resistance and terminal velocity). But it falls in a curved line in spacetime for the reasons shown in my graphs. Light curves around a massive body (ie as a consequence of the grav field) because of the principle of equivalence. As I show, the light travelling across a spaceship which is accelerating will appear to bend.
kind of confused here, are the S values all really the same or not? In this minkowski space diagram is S still referring to the distance to the origin? Is this like a space curve where S is the norm?
Thanks a lot ,Sir!
If I understand your question correctly the answer is that we don't know. We can produce a mathematical explanation that accounts for what we observe (whether it be Newton or Einstein mechanics). But just why nature makes things do that we dont know. The reason an object moves thro curved spacetime would be explained by energetics. The movement will achieve the lowest energy state.
Brilliant explanation.
Great explanation!
Good, very good.
@DrPhysicsA I enjoyed the video. Can you explain to me why when I am standing on the earth I am being accelerated up. I know there is a normal force against the pseudo force created by curved spacetime. This acceleration shows up to me if someone falls off a building and so he is unhindered by force and sees the earth rushing up to him. what causes this expansion of the earth - electomagnetic? internal pressure?
nice explanation :) thanks a lot hehe .. i saw recently today you're putting up einsteins field equations, whens that gunna be btw? i rly can't wait lol, they confuse me so much
Just thinking about this more. If you are using rocket thrust(chemical, electromagnetic or nuclear) as you approach the speed of light, it takes more and more energy to increase your speed due to the realistic increase in mass. But the mass of the propellant increases also. What happens the potential energy in the chemical, electric forces or the weak/strong nuclear bonds. Assuming speed is relative does increasing your speed by 100m/s really depend on what speed you are doing. Why does the speed if the observer effect how much energy it takes to accelerate.
Very Nice!
oh don't worry i've tried those up to like the 10th one on both and its still confusing to me lol.. i'm only just finishing alvls now and the concept of a tensor alone is just really peculiar
Random question. Based on Einstein's equivalence statement and that gravity distorts space and time, does that mean travelling with uniform acceleration also distorts space and time. As you reach relativistic speeds that exert time and length dilation WHAT DOES THE SPACE/TIME actually look like.
Well Einstein is effectively claiming that that which we call gravity is in fact a distortion of space time. And since by the equivalence principle gravity and acceleration are the same thing, then you are right.
DrPhysicsA Referring to what it looks like. In a frame of reference, you have parallel lines of space distortion at right angles to the direction you are travelling. Outside the elevator box, say, there is no space distortion. The rate of space distortion would be very high, at a molecular level. If you could stop suddenly, or even accelerate suddenly, would this create a gravitational wave?
Amazing.Thankyou
following on from previous comment,
it seems like we need the objects to first move through curved space and then they appear to just be moving towards each other. ie we need the two people to first walk up and them getting closer is the force. are we saying they're caused to walk by the curvature.
sorry if im being tedious.
I got lost at about 6 minutes when he went from the t vs x explanation to the x,y versus something explanation. Now that I have had a good, long time to think about it and to rewatch the video, I see what he is saying, He actually does say it rather plainly in the video if you remember the right words when he goes to the membrane analogy.
What is being plotted in the membrane picture is lines of equal changes in x and y, for equal changes in time as observed in our "stationary frame of reference" of an object (photon maybe) that would observe itself going in a straight line, moving equal distances in equal amounts of time in its constant velocity (but velocity near the speed of light) frame of reference.
Throwing the Globe into the picture as shown in some of the representations on this TH-cam page is kind of phony if it makes you think of a heavy object pushing down on the membrane. But as the narrator draws it and most pictures show it, they just draw a drawing of space without actually showing the object that warps it.
Space is a calculation done by consciousness in order to interpret the data that comes into it. It is a mathematical function defined by the larger consciousness system (LCS). Scientists are expecting to see the edge of the Universe and they will never find it because is all virtual and it generates itself as long as you stare at it. It’s like AutoCAD model space. It’s infinite and a virtual generated space. As crazy as that sounds the Space is the same and consciousness is the computer.
If it's an illusion why are they looking to find the force in quantum mechanics. I agree it's an illusion but they say it holds everything together so what's up?
x=x0+v0t+1/2gt2 the equation of space with respect to time in a uniform accelerated motion is a parabola therefore space-time is warped or curved
Can normal acceleration also be thought of as an illusion that is really just objects following the curve of space time? That is, if there is an accelerating space ship, can we imagine that the rocket engines are creating a 'dip' in front of the ship which it is constantly falling into?
Thanks!
And second I can see how the curvature of space time influences objects with velocity by redefining what a straight line is but how does this curvature act on stationary objects sitting on a planet? Looking at conventional diagrams it's easy to think that the object sitting on the planet is at the bottom of the "gravity well" caused by a funnel of space time distortion but anything at the bottom of a well is held there by gravity. It doesn't seem to explain the situation.
Thanks for your time
For an object not moving, but in a gravitational field, there is only motion in the time dimension. There is no movement in the spatial dimensions. How is that curved wrt space?
Is there a difference in saying “I’m at this point in space and time” vs “I’m at this point in space and space is at this point in time”?
How do you get to the conclusion at 6:00 that gravity is caused by mass? I know but I am thinking how you make out mathematically?
In between, That's really worth watching and understanding complex geometry in less time.
Hi Sir, seconds and minutes after the big bang we are already talking about gravity..where or what gave rise to Gravity at this early stage. Gravity is taught as curvature of space-time by mass..ibut doesw it mean anything to talk about space and time just seconds after the big bang? Where then does Gravity come into the picture?
Tq !!
At 2:25 you state that, through the principle of equivalence, an object at rest on the earth is actually moving through spacetime along a curve where x changes with time. I must be wrong about this, but it seems to me that space would need to be sucked in, and not just curved, by the mass for x to change. Please explain.
Similarly(?), how do a bullet and a ball each with no initial vertical velocity and differing horizontal velocities both follow straight lines through curved spacetime?
First let me say thanks for your excellent video's. If A level physics had been this clear I might have passed :-)
Couple of things; I am puzzled about one thing (which you illustrate well in this video) in our obsession with uniting the 4 fundamental forces we always include (and it stymied by) gravity. (continues)
I feel a similar way. I studied Stroud's Engineering Maths which is a beautiful book that gently leads you up a "mountain" into degree level maths with many examples & problems that you can work through without a teacher. Once I finished the book I felt tempted to learn relativity & quantum mechanics as they have always fascinated me but the next books i got weren't that good including from the open universisty so i gave up & forgot 95% of what I learnt. Nowadays I would have put all the info through Supermemo which makes it impossible to forget what one has learnt. & years later I find these explanations by DrPhysicsA & which are of the same excellence as Stroud's & it makes me think if only these videos had been around years ago
I understand how gravity causes an object with velocity to go in curves or to orbit, due to the curvature of space-time: the object thinks that it's traveling in a straight line. But how does gravity (and curved space-time) cause an object to ACCELERATE towards the gravity source? The object was stationary. Why is this g-acceleration a "straight line" to the object even though it was originally stationary. Wouldn't to remain stationary be more of a "continuous motion" for it?
Maybe an analogy helps.
Just think of a ball rolling down a hill, or a hole with increasing curvature, the ball will accelerate while moving closer to the center. The same way gravity curves space time, or we'll spacetime is curved giving rise to gravity.
@Mostwantedo Good question. if you have an object hovering in space & to its left is space & to it's right is compressed space then it would start to move toward the compressed space
5:50 How does that "lead to the conclusion that mass bends Spacetime"??
Infact you are really a Doctor physics...
How can s be constant for all values of x&t for an observer in one frame of reference? We have only established the fact that both the observers will agree on the equation (ct)^2-x^2 but have not proved that it always produces a constant value. That means the equation will produce varying values that are agreed by both the observers. So can it be a hyperbola?
If yes , then the linear characteristics through spacetime is not at all possible right?
What am I missing here??
May be we can see you sometime!!
the space time graph shows time as the y-axis instead of the x axis that you see everywhere else why is that? Why is time the y-axis?
INTERSTELAR TRAVEL
This is how the element 115 gravity generators work. These amplifiers are located in front of space ship that create a distortion in the space-time continuum, so the craft follow a permanent downhill slope to infinity accelerating very fast…
But there must be a force or whatever else. Imagine an astronaut who can “walk” through space. When he’s far enough from Earth he can stop whenever he wants and he’ll be still. When he’s close to the Earth he will lose control of his movement and will start to fall down, he could not stop anymore. A curved space only suggests that his trajectory will be a curve as he approaches to the Earth, but it doesn’t explain what is pulling him toward the Earth.
In your drawing gravity seems to curve the 2D space time into a third dimension, does that mean that gravity curves a 4D spacetime into a fifth?
Just a small quibble: 8:30 You say they travel in straight lines parallel to one another but at no point are they truly parallel to one another on a sphere. It's also debatable whether either of them can be said to be travelling in a straight line since they follow an arc.
"Gravity is an illusion caused by following a straight line in curved space."
Could that be rephrased as "gravity is the force experienced by any entity that deviates from its naturally curved trajectory through space" since everything is always orbiting something else i.e. subject to another thing's inertial frame of reference when either at rest or moving at constant velocity?
No.
I would phrase is as ''gravity is a force which impacts the space on which you are travelling'', rather that it impacting matter.
I'm a bit confused; if gravity is a consequence of the curvature of space-time rather than an actual force, then what's the point of the search for a gauge boson that carries the gravitational force in the Standard Model?
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Thanks. Your idea (even if it's not a rigorously confirmed fact) kind of makes the relationship make a bit more sense. I was literally completely lost, I had forgotten to take into account the fact that no "information" can travel any faster than light and just assumed the particles should instantaneously react to the curvature.
Oners82
It seems to me (I'm not an expert, just throwing an idea out here) that while gravity isn't a force in precisely the way, say, electromagnetism is, it is still a force (causes objects to accelerate), and the curvature of space-time is merely the way we explain how that force arises.
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Haha, thanks, that's one of the best ways to intuitively visualize the idea I've heard ^_^
+Prince Istalri A graviton is predicted by the standard model (which says that every force has a force carrier) that is why. Even though gravity is not a force in the sense Newton explained gravity, there still exist a force but it acts on space itself.
+Oners82 Mass asserts a force but it is not acting on other masses but on space itself.
A curved graph of distance against time is not a 'hint' that space-time is 'curved'. Incidentally, it's normal to put the dependent variable on the vertical axis, not the horizontal axis.
A person who is on the ground is not 'moving through space-time' as a result of being in the Earth's gravitational field. He is not moving at all.
Actually ,since you are on Earth, and Earth is moving you are moving too
There is a question in regards to inertia (conservation of motion). I am on the bus, I feel the bus accelerating, and I move backward. Is the bus producing a warped space time behind me? The thing that I don't understand is that the means (car, bus, train, bicycle...) are accelerating, but I doubt is a deformation of space-time anyhow. Answer?
For that you need to understand the theory more deeply, when you are in space time and you are stationary you just create a warped spacetime, but when you start moving you create waves in spacetime(which are called Gravitational waves), but this warped space is very very very small even smaller than the size of nucleus of an atom, a bus,car or any other thing on earth is just too small to just create a noticable ammount of warped space, for that you will need blackholes!!
Simply, what you experience is just basic force of inertia it has nothing to do with warped spacetime!! Yes you create gravitational waves when you are in an accelerating bus but it is just too small to be significant.
The "space time", or at least how we represent it in a 3D fashion as a single plane thats curving. Technically theres an infinite amount of these planes in infinite amount of directions with technically no limit so does that indicate that space time is more of a fluid medium and gravity itself is more of a phenomena where this space time fluid "flow" is being interrupted by mass/energy? I mean, gravity still doesnt technically exist in the conventional form as a force itself but yeah
Oh my god. I was thinking the exact same thing. Or are we?
I was thinking, if we are to take a sealed tank of water (or whatever fluid) into a vacuum, add a ball inside that tank of water, make that ball spin, maybe, the reaction of the water to the spinning ball inside it will show how spacetime reacts to the mass (say, earth) in it. I mean, I don't know if that even makes sense, but that is how I understand einstein's idea of gravity. The space (fluid) around us pushes us to the big mass that caused disturbance in it.
Paulo Villacorte I was thinking about this and, from my very limited understanding, I realize that we are not taking into account a 4D or even 5D universe. What we may perceive as a 3D fluid like properties of this structure may actually be something completely different. For example, length and time dilation and the physical shape of the universe being affected by mass counteract what we were thinking on the matter.
DaTurdburglar I suppose that curvature in spacetime causes the presence of mass. Mass in its ultimate form is nothing as you deep dive into the quantum world and you just see a while lot of nothingness as you navigate deep in an object. So the ultimate smallest unit of mass is just nothing. Then wat explains the presence of mass when its ultimate unit is nothing? It is the deformation of spacetime that creates mass.
At 5:25 how can we say the lengths (s) aren't the same is a bad thing since the x and t values will differ?? Any help please? :)
so we experiense time becos we are moving through space...is that correct?
since everything is relative then what this curve is relative to ? we do everything in spacetime then what does it mean by spacetime itself curve with respect to ?may be i am not able to fully explain my query...but please answer if you could get my question
Not everything is relative.
But why does the apple fall??what illusion causes it to accelerate from rest to straight downwards till it reaches the ground???
Make the earth invisible compare throwing an apple in space to that of earth & presto ...you have curved space...simple logic
is that why i cant go back in time...everything inflate….everything changes? what if i could go back to that point in Space maybe 10 yrs ago...would that bring me back to a time 10 year ago if i could travel instantly like a pair of entangled particle?…..
Love this....I find this engaging, ¿weird que no?
0:55 no shit dude :v
also, great video as always, greetings from Argentina (?
Does this mean gravity is not a force?
I ran out of space (no pun intended). Dark-M/E serves as a cushion gradually pushed by the bent space-time in "large mass areas" , in which while Black-Holes and their gravity will nullify the effects.
/Crackpot Alert*
A railroad track is curved. A railroad car will follow that curve no matter what velocity. That is true curvature.
With spacetime, the curvature is dependent upon the velocity of the object and their relative masses, it is variable. That is a mathematical curvature.
Just because you were taught it doesn't make it true.
Plz dr physics explain it in Mathematical terms .
True or ??
Dark Matter Ques , Galactical data shows That , The Galaxy don't follow The Law of kepler , newton and Einstein 's Orbital motion .and its graph is not as predicted , instead it's Linear . !!!!!!!And it said to be because of Darkmatters .So am asking?
why , it is not because of Gravitational Time dilation or , relative time differences between two regions of spacetime in galaxys !!!!, May be it would be our wrong observation of orbital motion !!! Because Einstein has Said , Gravity Slowdown Theflow of Time , relative to Less gravitational Area .
So .... May be it is the reasons , That's why we observing linear graph instead , predected Curve on graph !!!!
1:40 into this video DrPhysicsA quotes Einstein and says, "there's no experiment than can tell you whether you're accelerating through space, or on the ground". Yet in a previous video he talks about "tidal forces".
So I have to disagree. You would not experience these tidal forces in a spaceship accelerating at 1 g. If you had a sensitive enough "gravitometer" you would predict tidal forces but observe "none" in a spaceship accelerating at 1g.
Consider that this gravitometer is one you've calibrated yourself outside this "box" (or spaceship). If you can't reproduce these tidal forces like you did in a lab (at 1g), then you could easily conclude that the ship is accelerating.
- Mike drop
At the beginning of the big bang how can all the matter expand while there are gravity in that single point, or does gravity not even exist then?
Oners82 please explain
Oners82 thanks
If one could say that gravity that we feel here on earth would be same situation as in an accelerated elevator, couldn't we also say that we've been accelerating for the past 4.5 billions years? If so, by now, wouldn't we have a huge velocity with respect to some observer ?
Indeed, which is why stars/galaxies on the edge of the expansion of the universe will eventually move so fast they'll break the light speed barrier and their light will never reach our telescopes.
Fantastic
Thanks a lot ,
At 5:16 isn't it ok to say the lengths are different since t and x values have changed? Or have I missed something? Urgent help needed please.
+Spell456 The curve DrPhysicsA draw at 4:52 is a _hyperbolic_ distances obeying the formula X^2 - Y^2 = C^2, where C is a constant. The dots he made on the curve are time points. The lines he draw to the curve are time lines of simultaneous time. The curve itself represent the _constant_ hyperbolic distance C (s^2 = (ct)^2 - x^2 in DrPhysicsA's notation) from origo over all time points in space. Therefore all the straight time lines he draw are of the same distance s. Take note that the axis marked t is not time - but time times c (ct), which is a distance. Also notice that s, unlike x, is not a distance in ordinary space with x/y axis but a space-time distance from origo to a point on the curve in _space-time_ - which per definition is a constant distance.
If you were to draw such space-time curve in an ordinary x-y diagram, it would be a circle with the radius C, which could be thought about as a motion in space under constant acceleration but at a constant, radial, distance.
Another way to think about it is to think about a hovering craft at a fixed height C above the surface in a gravitational field. In order to hover at the height C you will need to accelerate constantly to compensate the acceleration from the gravitational field. If you do that your position in space time will create the very same curved space-time diagram. You are now in a situation where you are under constant accelerate but your position x,y.z in space and as well your time flow t is constant so it follows that your space-time distance s also must be constant for all time points - even though you are accelerated!
jomen112 Thank you very much, I understand now.
Gravity is the bent space time done in the presence of a mass according to general theory of relativity. Only impressive math skills you have to have. Tensors, derivatives, fields. Imagine a rubber sheet the Sun a cannon ball and the Earth like a marble rotating around it. There is not an attraction force per say like Newton thought although is very intuitive, but rather the Earth moves on curved space-time geodetic lines that Sun bends. It’s like it always chasing a valley.
Does anyone know of any good theories that try to explain why mass curves(warps) spacetime?
A wizard did it.
If we think about the trampoline model at 6:00 we have our weight stretching the fabric of the trampoline
In this analogy the fabric of the trampoline is like spacetime
This implies that each bit of space is connected to each other bit of space
It's said that the trampoline model isn't as accurate as this image: 64.media.tumblr.com/659da12fac7582bf5c47f4efbb2152d9/tumblr_o5ee0gLt591s5nl47o1_500.gifv by 1ucasvb
here we see a ball compressing the space around it like a penis becoming floppy
Let's imagine that we are directly above a gigantic penis looking down on it. What do we see? Just the tip
We see the circular head of the penis. The "glans" if you will.
In the penis analogy, erections stretch the penis like an elastic band & when the blood leaves the penis, elastic forces pull the penis back down to it's original size. Thus we can imagine our planet, Earth attached to each bit of space with an elastic band, pulling on each bit of space bringing them inwards like a giant space penis.
HOW does mass curve space-time? And is this saying that gravity isn't actually a *force*?
+standingunder If space-time is curved it means it contains energy, and if there is energy in space-time it curves space-time. In Einsteins general theory, gravity is not a force but a property (curvature) of space-time itself. Mass tells space-time how to curve. In turn the curvature of space-time tells the masses show to move in space-time.
+standingunder Yes, it's saying gravity is not a force. Objects are coming near each other due to them travelling through space. But we thought they were moving in the first place because of gravity. It seems to me they move through space and if they try to occupy the same position they are stuck to each other and that's how we're stuck to the earth. Now the question is. Why are we all moving, maybe even why does light move?
I don't actually get what "time" is in physics, is there any precised definition and mathematical structure of time.
Time actually as we know it is..... 1 second = 9,192, 631,770 cycles of the standard Cs-133 transition
So, in motion, the number of cycles is less than the actual according to special relativity, is that correct? Motion effects the transition of atom,doesn't it?