Metric Tensor | The Curvature of Space

According to general relativity, we live in a four dimensional universe. Three dimensional space plus one dimensional time, known as spacetime. Human beings are 3D creatures, but are we able to perceive a four dimensional spacetime from a 3 dimensional perspective? Today, we are going to answer this question, and unveil the true nature of curvature in our universe. All in 8 minutes.

[@AlexWatson117]

I love your channel Pls make some videos explaining quantum mechanics too

[@michaelkahn8744]

The problem of modern physics is they're trying to explain everything with particle physics and the physics is being cornered more and more to the dead end. The interaction between mass and space must be explained with quantum mechanics. But that doesn't mean gravity is the QM phenomena. That's because gravity is not a force. Gravity is just a joint effect of the expansion of the Universe and the curvature of spacetime. Details are given below. Alternative Explanation of Dark Matter and Dark Energy - Newly proposed model of Universe can explain both of Dark Matter and Dark Energy Einstein’s theory of General Relativity states that spacetime is curved by the presence of mass. This curvature influences the motion other objects with mass and gives rise to gravitation. Thus, gravity is a result of geometric features in spacetime. However, we also observe gravitational effects - curvature of spacetime - in areas without any detectable mass. This has given rise to the concept of dark matter, which is matter that does not interact in any detectable way with normal matter, except through gravity. So, there is some large quantity of dark matter scattered throughout the universe, which curves spacetime and causes gravitational effects just like normal matter, but we cannot see or detect it with any known method. An alternative theory to the identity of dark matter is proposed - it is not matter at all, but rather an intrinsic curvature of spacetime. In other words, spacetime is not naturally flat. Even in the absence of matter, we observe some inherent curvature of spacetime. So, the question is now - why is spacetime naturally curved? Why is it not flat in the absence of mass? The universe is 4-dimensional, with 3 spatial dimensions and one dimension in time. Rather than consider time as a linear dimension, we can consider it as a radial one. Therefore, rather than describing the universe with a Cartesian coordinate system, we describe it with a 4-dimensional spherical coordinate system - 3 angular coordinates, φ1, φ2, φ3, and one radial coordinate in time, t. We live on the 3-dimensional surface of a 4-dimensional bubble which is expanding radially in time. Thus, the Big Bang represents t=0, the beginning of time. The crucial point is that the expansion of the universe is not homogeneous in all directions. The expansion rate at one point on the bubble’s surface may differ slightly from another point near it. The universe is only roughly spherical in 4 dimensions, the same way that the Earth is only roughly spherical in 3 dimensions. The same way we observe local mountains and valleys on the surface of Earth, we observe local “mountains” and “valleys” on the surface of the universe bubble. The inhomogeneity of the expansion of the universe has given rise to natural curvature of spacetime. This natural curvature causes the phenomenon of “dark matter”. “Valleys” in spacetime pull matter in, similarly to the warping of spacetime of massive objects. So “dark matter” is really “valleys” in spacetime that are expanding slower than the regions surrounding it. These valleys tend to pull matter in and create planets, stars, and galaxies - regions of space with higher-than-average densities of mass. Conversely, “mountains” in spacetime will repel matter away, an “anti-gravitational” effect, which gives rise to cosmic voids in space where we observe no matter. Each point on the surface of the universe bubble traces out a time arrow in 4-dimensional space, perpendicular to the surface. These time arrows are not parallel to each other since the universe is not flat. This causes points to have nonzero relative velocity away from each other. It is generally accepted that the universe is expanding faster than observable energy can explain, and this is expansion is believe to be still accelerating. The “missing” energy required to explain these observations has given rise to the theory of dark energy. The time dilation caused by non-parallel time arrows can be proposed as an explanation for dark energy. Alternatively, dark energy is real energy coming from potential energy gradients caused by non-parallel time arrows. As a sanity check, we can calculate the expansion rate of the universe based on the universe bubble model. Since the radius of the universe bubble is expanding at the speed of light in the time direction, it increases at 1 light second per second. Therefore, the “circumference” of the 3-dimensional surface increases by 2π light seconds per second, or about 1.88*10^6 km/s. This expansion is distributed equally across the 3-dimensional surface, so the actual observed expansion rate is proportional to the distance from the observer. At present, the age of the universe is estimated to be 13.8 billion years, so the radius of the universe bubble is 13.8 billion light years, or about 4233 megaparsecs (3.26 million light years to 1 Mpc). Thus, we can calculate the expansion rate of the universe, per megaparsec from the observer, as: Expansion rate = ((d(circumference))/dt)/radiusofuniverse=(1.88*〖10〗^6 km⁄s)/(2π*4233Mpc)=(1.88*〖10〗^6 km⁄s)/26598Mpc=70.82(km⁄s)/Mpc The popularly accepted empirical expansion rate is 73.5 + 2.5 km/s/Mpc, so our calculated value is close. There may be some additional source of expansion (or observed red shift) to make up for the discrepancy. For example, if two adjacent points have some gravitational gradient due to non-parallel time arrows, then light passing through these points will be red-shifted. - Cited from www.academia.edu/82481487/Title_Alternative_Explanation_of_Dark_Matter_and_Dark_Energy

[@mariocesarsousa]

Thsnks. Great vídeo ☝️

[@MN-MNMN]

Keep up the good work

[@Epoch11]

I would still love to know how curved SpaceTime causes acceleration. Why does an objects speed increase rather than just uniformly moving in a particular direction?

[@FVLMEN]

That's what I would ask myself years ago before I abandoned the lunatic idea of general relativity. They liken it to a warped rubber sheet but the only reason marbles roll towards a bowling ball on a rubber sheet IS because of gravity. A rubber sheet analogy would not work without the force of which they're trying to analogize with the rubber sheet. It's paradoxical. The mere rubber sheet being distorted is not the cause for marbles pocketing into a bowling ball, so why would they posit the earth's mass curving space itself is why apples fall?

[@ExistenceUniversity]

Squished and stretch spacetime changes time to travel through a unit length

[@satabdikakati5759]

Want more videos

[@Semper_Fish]

"curved space time" is so magical that it shows no observable curve at large bodies of water to match earth curve calculator.

[@everythingisalllies2141]

Space isn't "curved" . That would just be your math geometry you are getting confused with actual space. I have a 1 meter straight plank of wood here, now I can locate any spot on it using Euclidean coordinate system, a grid of straight lines if you like. its easy. OR I COULD locate any spot anywhere on that plank, using a SPHERICAL system of coordinates, or a new system that has octagons as the base shape. Pont is, even if I choose to use Radius and Angles, a Polar or a Spherical system, I still have a FLAT STRAIGHT PLANK OF WOOD. And likewise if Einstein, for no justifiable reason, decides to use his math Metric tensors, that wont make "Space" or my wooden Plank curved.

[@trainjumper]

It is true that the nature of space is independent of what coordinate system we impose on it. However the fact that certain observations (i.e. time dilation, gravitational lensing) cannot be trivially explained without use of such a coordinate system, can be used to form decent arguments toward space itself having intrinsic curvature.

[@ExistenceUniversity]

Light travels in straight lines and yet travels in curves around large masses, see Eddington Experiment. Sorry space curves and light proves it.

[@ramesh_rm]

Stress energy tensor

[@every1665]

All explanations I have ever known essentially claim that "as space is curved, travelling in a straight line is really a curved line". Doesn't explain anything.

[@Bizija123]

Straight line for you, but geometrically it's curved.

[@every1665]

@@Bizija123 Is a straight line even possible (apart from theoretically)? Or is there no way of knowing when it's straight?

[@Bizija123]

@@every1665 i think that's just relative to the topology or surface. In a 2D euclidean system, there is such a thing as a perfectly straight line because two parallel lines will never intersect, but on a spherical surface, there is no such thing as a straight line as two initially parallel lines will eventually intersect. That being said, spacetime's topology and coordinate system changes in the presence of a gravitational mass.

[@every1665]

@@Bizija123 Thanks for explaining that.

[@stevenswapp4768]

Suh fear ickull Spherical SFear

[@cosmicwakes6443]

Ricci tensor.

[@franceleeparis37]

To the average person, this theory is not only bizarre but highly unlikely.. for every dip there has to be something above it, for every peak there has to be something around it.. but ‘space’ is everywhere so the peaks and dips in space do not exist.. otherwise light, which travels in a straight line would be transiting through nothingness.. you can thank me later…🙂

[@ExistenceUniversity]

You are 250 years too late for that debate. Light exists because spacetime has properties, and that spacetime curves and light follows that curve as straight lines.

[@RobertoCarlos-tn1iq]

just straight out tell people that you don't speak english and that the video uses a computer-generated voice.

[@phally8442]

Let find out more easy ways to understand. Because I am not good in mathematics. Thank.