As a consequence of the Lorentz transformations, time and space transform into each other when changing reference frame. This calls for a unified description: Minkowski spacetime.

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Is there a proof that space expanding produces observers at all points that see what we see?

I know that galaxies are moving away from us, and so can see that it's intuitive that if space was expanding, then the astronomical observations from Earth would be the same as at all other points in ...
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325 views

Commutation relations in QFT and the principle of locality

My question is, given two space-time points $x^{\mu}$ and $y^{\mu}$, if the events that occur at these points are simultaneous, i.e. $x^{0}=y^{0}$, are the two events necessarily space-like separated? ...
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151 views

Lorentz transformation paradox

I got to solve a simple exercise about special relativity when I kinda came to the conclusion it doesn't stroke with my intuition. The homework-problem The problem was about two people Sam and ...
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1k views

Regarding time dilation and particle entanglement

I have a question regarding time dilation and particle entanglement. As I have read a few forums and questions here, I am aware both aspects do not contradict each other. Still, a question that I am ...
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How do Doppler Effect and Time Dilation differ?

Above, I have drawn a diagram showing Doppler Effect (here we are using space-time but in a non-relativistic sense. Time and distance are the same for A and B). Edit: I am adding a relativistic ...
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92 views

How to motivate the importance of the spacetime interval

The spacetime interval is a rather important thing in Special Relativity. It allows us to define the separation between any two events as spacelike, timelike or lightlike and more importantly, the ...
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Does gravitational redshift imply gravitation time dilation?

The EEP is used to justify that if an observer on the ground shoots a beam of light towards a tower, then when the light reaches the tower, it will be red shifted. This is because of what happens in ...
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7k views

Do we live in a world with 4 or more dimension?

A NOVA show have told the audience that we are live in 3 dimensional world, the world we lived in is compose by 3 element: the energy, matter, space. By the time Einstein have invented the 4-...
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How could spacetime become discretised at the Planck scale?

I didn't have much luck getting a response to this question before so I have tried to reword and expand it a little: In early 2010 I attended this inaugural lecture by string theorist- Prof. ...
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136 views

How do we choose how to discretise spacetime in loop quantum gravity?

In LQG we choose a two-complex (or other) on which to discretise GR before quantising. I'm a little uncertain about the nature of this choice. Is the two-complex an a priori property of the universe (...
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106 views

Since space expands (and can theoretically contract) faster than light, does that mean that in a big crunch information could travel FTL?

Layperson here. In a theoretical big crunch with space contracting faster than the speed of light, would information be travelling faster than speed of light? Because the points A and B themselves ...
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260 views

What does the Higgs boson have to do with the uncertainty principle and quantum oscillations?

I was looking in New Scientist the other day when I saw something to do with the Higgs boson, energy levels, entropy, space/time, quantum oscillations and many other things. It was in a feature to do ...
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228 views

Why is $S^1\times\mathbb{R}^{n-1}$ the topology of $AdS_n$?

Anti-de Sitter $AdS_n$ may be defined by the quadric $$-(x^0)^2-(x^1)^2+\vec{x}^2=-\alpha^2\tag{1}$$ embedded in ${\mathbb{R}^{2,n-1}}$, where I write ${\vec{x}^2}$ as the squared norm ${|\vec{x}|^2}$ ...
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136 views

Which causal structures are absent from any “nice” patch of Minkowski space?

Which "causal separation structures" (or "interval structures") can not be found among the events in "any nice patch ($P$) of Minkowski space"?, where "causal separation structure" ($s$) should be ...
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623 views

Why does the homogeneity of the universe require inflation?

They say inflation must have occured because the universe is very homogeneous. Otherwise, how could one part of the universe reach the same temperature as another when the distance between the parts ...
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1k views

Space-like Killing vector of Robertson-Walker metric?

In the book "Kinetic theory in the expanding Universe" (J. Bernstein, 1988, Camb. Univ. Press), it was stated that "for nonstationary Robertson-Walker matrixes [sic] there is no spacelike ...
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234 views

Closed timelike curves in the region beyond the ring singularity in the maximal Kerr spacetime

The region beyond the ring singularity in the maximal Kerr spacetime is described as having closed timeline curves. Why and/or how is the question. Now if you look a Kruskal-Szkeres Diagram (or a ...
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788 views

The nature of time, according to quantum field theory

I will try my best to ask the question that best fits something I have been pondering on for a few days. Are virtual particles really constantly popping in and out of existence? Or are they ...
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137 views

If spacetime is discrete: what would space expansion mean? [closed]

How is space expansion explained in physical theories where spacetime is quantized? Discrete spacetime is claimed in some candidate theories of quantum gravity like loop quantum gravity and algebraic ...
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4k views

Is time quantized? Is there a fundamental time unit that cannot be divided? [duplicate]

Is the present just a sharp line between the past and the future with no time at all, or is the present a short frozen unit of time? Could time be quantized into a fundamental units? Like Planck ...
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135 views

Gravitational waves in other dimensions

I know this question is purely speculative, as we don't know if more dimensions do exist and also we do not know if gravity is indeed stronger in other dimensions (if they were to exist). But, one of ...
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Example of space-like intervals in spacetime

From wikipedia: When a space-like interval separates two events, not enough time passes between their occurrences for there to exist a causal relationship crossing the spatial distance ...
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If something is not moving in space, is it moving on the time axis at the speed of light? [duplicate]

I heard this theory yesterday: If something is not moving in space, then it is moving on the time axis at the speed of light. I realize that in essence there is no object which can be considered as "...
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Nature of spacetime 4-vector and tangent space?

An entry level confusion about spacetime. I understand that a 4-vector describes a point or event in spacetime. But I've also read (Bertschinger, 1999) that re spacetime "we are discussing tangent ...
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568 views

Why time is considered a dimension?

Why is time considered to be a dimension? And the other 7 (except the 3 dimensions of space, and the dimension of time) dimensions that string theory suggests, why can't they be realized?
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Gravitational self-interaction

Today, someone asked me why "the warped space-time warps itself" (he read it in Kip Thorne's: The Science of Interstellar). I guess this is related to the gravitational self-interaction. But I don't ...
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691 views

A sees B's clock running slow and B sees A's clock running slow? [duplicate]

This paradox is very common it seems, in which A sees B's clock running slow and B sees A's clock running slow. Here is the question a little more concretely. Let's say B flies by A's spaceship. If B'...
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434 views

Age of the universe and the singularity at the Big Bang

Using the standard model of cosmology we calculate the Hubble time to obtain an estimate of the age of the universe. This model assumes a beginning of time in the past. But that point is a true ...
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124 views

Visualizing gravity

When you see graphics trying to help people visualize what gravity in Einstein's relativity "looks" like it will often be a mostly two-dimensional plane with a concave warp where a massive object is ...
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193 views

Distance in General relativity

I read a few lines about general relativity and one of the first equations is the one defining the eigentime of a time - like curve. But observers should also be able to measure length, right? So is ...
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631 views

Why do people put exponentials there

In his book, Sean Carroll, says p. 194 chapter 5: To impose spherical symmetry, we begin b writing the metric of Minkowski space in polar coordinates $x^{\mu}=(t,r, \theta, \phi)$: $$ ds^2=-dt^2+...
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230 views

4-vectors in special relativity and spacetime interval

In one of my vector mechanics lectures, the lecturer said the the space time interval was the dot product of the four position vector. But then he proceeded to show it was this: $s^2$ = $\Delta r^2$ - ...
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317 views

How does relativity explain gravity, without assuming gravity [duplicate]

I have seen the "objects pull down on space-time" explanations, but they assume a "pull down" force themselves. Could anyone explain the space-time explanation without assuming gravity in the first ...
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199 views

If an astronaut had stationed in International Space Station for the duration of mission, 17 years, would he be older?

Today the NASA International Space Station started the 100000 orbit after 17 years in the space. I just wonder if there were a team of astronauts which were in the Lab for all the duration of last 17 ...
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Aside from experimental evidence, is there any reason to model space as Euclidean?

Obviously experiment is the end-all-be-all of any science, but I'm curious if there's any a priori reason to model space as Euclidean three-space (from a pre-relativity viewpoint, of course; I'm ...
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216 views

Difficulty in understading a part of the book “A Brief History of Time”?

Sorry if the question is not upto the standard of the site but i really can't understand what the following para says. I am reading the book "A Brief History of Time" by Stephen Hawking and in the ...
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The order of seeing event in different spacetimes

Assume this question: Three events A, B, C are seen by observer O to occur in the order ABC. Another observer O$^\prime$ sees the events to occur in the order CBA. Is it possible that a third ...
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127 views

Conservation of Energy vs Expansion of Space

My question pertains to a possible inconsistency between the first law of thermodynamics and the general expansion of space itself. First, the knowns: Space itself has, and continues to expand - ...
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256 views

Why are orbits around black holes stable?

Black hole theory involves space (or space-time), itself, being sucked into the black-hole, with the event horizon marking the point at which space/space-time is moving faster than the speed of light. ...
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150 views

Is a metric tensor field the same thing as $ds² = -dt² + dx²+ dy² + dz²$?

I am having trouble understanding the nature of the metric tensor field on spacetime manifolds. In particular, a Riemannian manifold $(M,g)$ is defined as a real smooth manifold $M$ equipped with an ...
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408 views

What Does it Mean for an Extra Dimension to Have Size?

Recently I watched this presentation by Brian Greene on string theory. In it he describes how the reason we don't observe the extra dimensions required by string theory could be because they are very ...
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770 views

The inner workings of the Olbers paradox

A long time ago I was told that the universe is finite. The provided "proof" (or reasoning), known as Olbers' paradox, was that on infinite universe there would be an infinite number of stars, and ...
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378 views

Behavior of black holes in higher- and lower-dimensional space-times

The behavior of black holes in 3+1 dimensional space-time as our own is rather well known: formation, event-horizon size, mass, spin, radiation etc. However, my question is what would black holes ...
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How energy curves spacetime?

We know through General Relativity (GR) that matter curves spacetime (ST) like a "ball curves a trampoline" but then how energy curves spacetime? Is it just like matter curvature of ST?
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Are the principles of space-time homogeneity and Isotropy independent of one another?

Einstein in deriving the Lorentz transformations, used the principles of space-time homogeneity and Isotropy. Does space-time isotropy follow from space-time homogeneity or are they completely ...
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174 views

Is time an observable in Relativistic Quantum Mechanics?

Relativistic Quantum Mechanic is based, as far as I know, in the Dirac Equation. Now, the Schrödinger equation, in the abstract state space takes the form: $$i\hbar \dfrac{d|\psi(t)\rangle}{dt}=H|\...
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597 views

Could a finite amount of space in the universe exist without time? [closed]

Is it possible that a finite amount of space in the universe exists without time? Namely, that it is possible for us to find an element of space that has no time (everything happened at one point and ...
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140 views

Is the surface of a heavy sphere bigger than $4 \pi r^2$ due to general relativity?

I am unfortunately not familiar with the mathematics behind general relativity. However, on a heavy planet (say a sphere) gravity will bend space-time in a way that an object initially in rest, will ...
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237 views

How far can something travel in a straight line?

Suppose you have an object some distance from you and moving at a velocity different to the Hubble velocity you'd expect at that point. How does the motion of this object change with time? Does it ...
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673 views

Questions about angular momentum and 3-dimensional(3D) space?

Q1: As we know, in classical mechanics(CM), according to Noether's theorem, there is always one conserved quantity corresponding to one particular symmetry. Now consider a classical system in a $n$ ...