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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Does the current acceleration of universe imply that our universe is open?

Does the current acceleration of universe imply that our universe is open? If the universe is closed, from the Friedmann's equation, the acceleration of universe wouldn't be possible, would it be? (Of ...
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783 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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124 views

Can special relativity be derived from the invariance of the interval?

As far as I know, the classical approach to special relativity is to take Einstein's postulates as the starting point of the logical sequence, then to derive the Lorentz transformations from them, and ...
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136 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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102 views

Charged versus rotating black holes as different kinds of wormholes

I've heard that a maximally extended charged black hole can be a traversable wormhole to the same universe whereas a maximally extended uncharged rotating black hole can only be a wormhole to ...
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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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1k views

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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807 views

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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549 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 time dilation at the earth's center

I would like to know what happens with time dilation (relative to surface) at earth's center . There is a way to calculate it? Is time going faster at center of earth? I've made other questions ...
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219 views

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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432 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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645 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 ...
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189 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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630 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 $x^{\mu}=(t,r, \theta, \phi)$: $$ ...
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214 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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315 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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96 views

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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208 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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994 views

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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248 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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146 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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401 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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746 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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352 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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578 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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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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229 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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1answer
661 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 $n$ ...
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137 views

Real, non-constant scalar field with special properties in class of 4-dimensional spacetimes

David Deutsch (Oxford University) asked the following question which I think is an interesting one: In what class of 4-dimensional spacetimes does there exist a real, non-constant scalar field φ with ...
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123 views

Does time have a minimum 'speed'?

Sorry if this is an ignorant question, but I've been having some trouble grasping some concepts related to time dilation. So far, my understanding of the concept says that if I am in a certain frame ...
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290 views

Is there proof gravity bends space or is it just the most convenient explanation?

I have read this sentence in an article: The theory [of general relativity] holds that gravity is geometry: particles are deflected when they pass near a massive object not because they feel a ...
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187 views

Is acceleration caused by curvature or space or time or both?

I'm trying to get a hold of the idea of gravity in general relativity and spacetime. I've seen plenty of demonstrations of the rubber mat analogy to describe gravity and spacetime curvature. Is this ...
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286 views

Why doesn't the number of space dimensions equal the number of time dimensions?

It seems as though symmetry is a driving force behind theoretical physics. With symmetry in mind, should we expect that the number of time dimensions should be the same as the number of spatial ...
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885 views

Does time dilation correct for the Doppler effect?

Knowing that a body in motion experiences time dilation, "also" knowing when two objects travel at a great speed away from one an other, both observers experience the others clock as moving slower ...
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Could fast vibrations cause us to travel forward in time

Assuming it's possible to vibrate a human at near light speed without harming him, would a few minutes of this from his point of view be much longer from a stationary observer's point of view? In ...
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Proof that Energy Momentum Tensor of Scalar Field Theory satisfies Weak Energy Condition

It's a question on Sean Carroll's Spacetime and Geometry, where we are supposed to prove that the energy momentum tensor of scalar field theory satisfies Weak Energy Condition (WEC). The energy ...
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Can space and time separately be curved?

How can I imagine curved time, if it is not a part of four dimensional spacetime? Similarly for space. What are the measurable, observable consequences of these two phenomena in a laboratory or in ...
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How can we justify dropping the absolute time hypothesis?

In some approaches to Special Relativity the theory is motivated talking about the Michelson-Morley experiment and how this relates to the postulate that the speed of light is the same in every ...
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231 views

Is the concept of space-time curvature a recursive one? [duplicate]

A way some people explain (or try to explain) how gravity works is using space-time curvature: an object with high mass distorts the surrounding space-time plane like a bowling ball distorts a sheet ...
4
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1answer
218 views

How does Spacetime Curvature increase the velocity of particles falling towards the earth?

Two particles fall side by side, towards the earth. The horizontal distance between them is 10m. As they advance nearer and nearer to the earth's surface, the horizontal distance decreases, from 10m ...
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157 views

Curvature of spacetime: pincushion distortion?

This may be an elementary question, but if gravity causes a curvature in spacetime, then why isn't everything distorted when looking down on earth, or up at the moon? Shouldn't there be a pincushion ...
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876 views

How much time has passed for Voyager I since it left the Earth, 34 years ago?

34 years have passed since Voyager I took off and it's just crossing the solar system, being approximately at 16.4 light-hours away. How much time have passed for itself, though?
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438 views

Could metric expansion create holes, or cavities in the fabric of spacetime?

Is it possible for metric expansion to create holes, or cavities in the fabric of spacetime? According to the Schwarzschild metric, the metric expansion of space around a black hole goes to infinity ...
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How should one interpret the de Sitter slicings?

When 'constructing' the usual de Sitter space in $\mathcal{M^5}$ by invoking the contraint $-X^{2}_{0} +X^{2}_{1} +X^{2}_{2} +X^{2}_{3} + X^{2}_{4} = \alpha^2$ we quickly see that we end up with a ...
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452 views

Physically what does warping (of space-time) mean?

So there's general relativity and Einstein's field equations that tell us "mass(or equivalently energy) warps space-time, and the warping tells mass how to move", but I'm still having trouble ...
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What are the photon/electron consequences of matter in a gravitational time dilation?

So I saw the movie Interstellar, and it got me thinking. I won't even mention all the plot holes, but I wanted to ask about a planet orbiting a black hole. I always thought you had to travel near the ...