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62

I'm not a quantum cosmologist, but I am an early-universe cosmologist, so I can give you my opinion after having read this paper. The article claims that Bohmian trajectories is a valid replacement for geodesics. This was claimed in the very beginning of the paper and not much is offered in the way of defense for this assumption. That's not to say that it's ...


26

While this work certainly investigates an interesting point, I think simply replacing geodesics in GR with similarly looking quantum trajectories does not solve the issues here. Finding the Friedmann equations while assuming large-scale homogeneity and isotropy is no surprise to me. There are a number of people working on so-called Big-Bounce Cosmologies. ...


15

Firstly, the Equivalence Principle reduces to the statement that in a freefall frame, the spacetime manifold is locally exactly as it is for special relativity (see my answer here for a fuller explanation of why this is so). So you can swiftly reduce your question to "Why does Minkowski spacetime have a nontrivial, non-Euclidean signature?". Since we're ...


8

There are a number of models for the universe over the years. The Big Bang as you show it in the figure has become the "standard model" for the creation of the observed universe as we know it because it fits observations, i.e. data, using known theories and behaviors from elementary particle theories. This model has been evolving as data are added in our ...


7

From the little I've read, it seems that spacetime is Lorentzian. Unfortunately, the need for a metric that isn't positive-definite escapes my understanding. Could someone explain the reasoning? The short answer: - because of the attractiveness of the geometrical language and because of the Lorentz transformations, which do not preserve any positive ...


6

I think it might help to think about the spacetime interval $\text{d}s^2$ as a measure of movement in spacetime relative to the speed of light. Let's say that you want to move from a point $p=(0,0,0,0)$ to another point $p'=(t,x,0,0)$. The quantity $\text{d}s^2 = c^2\text{d}t^2-\text{d}x^2$ is then: Positive if $x<ct$, which means that you traversed the ...


5

No, it's not possible. The other galaxies we see are to radically different. Additionally, if we are the surface volume of hyperspace, then the universe should be closed. Our best estimates and observations indicate it's flat. Let me address both of these in more detail. As for the other galaxies. First of all, there's the Andromeda galaxy. That is a galaxy ...


4

If you had empty space and then matter expanded from a point in it, then some of the matter would be in the center, seeing everything moving away from it. Some of it would be near the edge and see darkness filling half their world. We see matter moving away, and it seems unlikely that we just happen to be so close to a center of the universe. So we look ...


4

"The way I see it, space, true "space" is literally nothing" Most physicists and I believe many philosophers would disagree. The notion of "Nothing" is impenetrable logically: "nothing" has neither any properties nor relationships with anything else that can be reasoned about. The best you could do would be to assert that "nothing" is somewhat like the ...


3

Your argument is incorrect: The curvature of a spatial slice is coordinate-independent. What is true is that in general relativity, there is a priori no preferred spatial slicing. For example, de Sitter spacetime (a universe dominated by cosmological constant) can be sliced into positively curved, negatively curved or flat spaces. When we say that our ...


3

By the term black hole we normally mean one of four spacetime geometries, the Schwarzschild, Reissner–Nordström, Kerr or Kerr-Newman metrics. The universe is (we believe) approximately described by the Friedmann–Lemaître–Robertson–Walker metric, and it is not a black hole. The Big Bang is not the same as the singularity at the centre of a black hole. For ...


3

Yeah, you've not yet adapted. That's OK. Let me take you through it. In this conventional world of classical physics we have separate notions of distance and time, with the idea that either two events happen at the same time and therefore have an objective distance between them, or two events happen at different times and therefore have an objective time ...


2

Let's separate out some definitions: metric(1): Given a set $X$, a function $d : X \times X \to \mathbb{R}$ such that the following axioms hold for all $x,y,z \in X$: $d(x,y) \geq 0$, $d(x,y) = 0 \Leftrightarrow x = y$, $d(x,y) = d(y,x)$, and $d(x,z) \leq d(x,y) + d(y,z)$. pseudo-metric(1): Given a set $X$, a function $d : X \times X \to \mathbb{R}$ ...


2

There are models where the extra dimensions don't need to be curled up. The main issue with extra dimensions is, 'why don't the particles/fields we interact with travel in those directions?' We have extremely good limits on standard model particles (electrons, photons) travelling in extra dimensions. However, it is possible to imagine a string inspired ...


2

I just want to point out that the dimensionality of spacetime is a bit of a fluid concept in string theory. Superstring theory can only be formulated in 10 dimensions, but it can be shown to be dual to an 11-dimensional theory called M-theory. It has also been conjectured to be dual to a 12-dimensional theory known as F-theory, although whether or not this ...


2

If you just look at a space-time diagram without any particles (or observers), there is really no physical difference. However, if there are particles, there can't exist both spacelike and timelike particles. Otherwise, paradoxes such as tachyonic antitelephone rise, in which information can be sent into past. So as an observer, it is simple to determine ...


2

One can apply the underlying principle of relativity -- that all reference frames are valid and agree on the speed of light -- to expanding space, but one has to be careful. In particular, special relativity assumes reference frames are these global things that cover all of space and time. Picture a uniform grid clocks and rulers stretching as far as the ...


2

Sometimes the word universe is just used colloquially and can just refer to everything on some side of a horizon (an event horizon, a causality horizon, etc.) But when used precisely, I'm sure different definitions are used in different fields. For instance, in mathematical general relativity, you assume that your universe is a connected four dimensional ...


2

If the question is asking whether there is a definition that encapsulates our universe, then I believe the answer is No. This is because encapsulating a "space" into a formal system requires defining bounds. However, we don't know the bounds of our own universe--let alone what bounds might be possible for any universe. We can only describe what we can ...


2

We are not entirely sure what OP's question (v4) is asking, but here are some comments: I) The Dirac belt trick demonstrates that the Lie group $SO(3)$ of 3D rotations is doubly connected, $$ \pi_1(SO(3))~=~\mathbb{Z}_2. $$ II) As for the title question Are spinors somehow connected to spacetime? one answer could be: Yes, in the sense that the mere ...


2

According to inflation, strictly speaking, space is still being created. I find this idea very interesting. Also, the idea of space as being an empty void to be filled is out of date. Space is full of fields, even when there are no particles present.


1

The Clifford algebra $\mathrm{Cl}(\mathbb{R}^{1,3})$ is the algebra generated by endowing the vectors in $\mathbb{R}^{1,3}$ with a free algebra multiplication and then imposing the constraint given by $v \circ v = \eta^{\mu\nu}v_\mu v_\nu$ with $\eta$ as the Minkowski metric on $\mathbb{R}^{1,3}$. Any Clifford algebra has a natural connection to the ...


1

You ask the question of whether the title for the Wikipedia article should be "Curved Spacetime" instead of "Curved Space". The answer is a resounding no, leave it as is. The article itself covers strictly the mathematics of any curved space and is not specific to physics contexts. As is, the usage of "Space" does not mean purely spatial and not temporal ...


1

You're exactly right. What you've discovered, is the cosmological horizon, the distance beyond which we can no longer have any causal contact with distant galaxies. The fact that galaxies that are out of causal contact with each other in fact appear to be so uniformly distributed in density and temperature is considered a major problem in cosmology, the ...


1

The problem of including time as an operator rather than a parameter in Quantum Mechanics is what led to the development of Quantum Field Theory. I.e., the position operator was demoted to a parameter rather than promoting time to an operator. The two uncertainty principles you quote are entirely different. The first (position/momentum) principle is the ...


1

I believe you know about the three dimensional Euclidean space which in general represented by $x, y$ and $z$ coordinates. Euclidean space has the important property of being flat. Now, you can think of the Minkowski space as a four dimensional space which is flat! The fourth coordinate is generally chosen to be time $t$, so people call it not "space" but ...


1

Is it legitimate to speak of distant red-shift galaxies as experiencing time more slowly in relation to our experience of time? No, it is not, since they are not moving relative to the hubble flow, which means that they are sitting on their comoving coordiantes and are therefore at rest relative to the CMB, just like we are (peculiar velocities ...


1

First, just a clarifying point: the fact that more of the universe becomes observable over time has to do with the finite speed of light, not the expansion of the universe (which is indeed happening at an accelerated rate). And of course it is best to consider the universe as a whole. Even though we can't see the dark side of the moon, we still know ...


1

"Universe" can have several meanings. Some describe the visible universe (small u), others describe the whole Universe (capital U), whatever that might be. That we can described the "visible" universe, perhaps implies a visible and non-visible universe.


1

No. You seem to be implying that the fact that the world-line of the satellite looks curvy, is what is meant by "curvature of space-time". No, that's wrong. The world-line of the satellite looks curvy in the picture, yes. But, it should be clear that you can have a curvy-looking world-line without gravity. Anything that orbits anything for any ...



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