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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Empty Space - Could we exist without it? [closed]

I have been giving empty space much thought. I imagined reaching the edge of the Universe and thought of 2 scenarios(focusing on 1): There is no more empty space 1.1 Would space extend with me if ...
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5answers
103 views

Does spacetime have a “preferred” speed/metric? [duplicate]

I read recently that spacetime has a preferred speed, c, and that all observers would agree on the speed of anything moving at c. In particular, there is nothing unique about light when talking about ...
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2answers
405 views

Curvature gravity and a falling apple? [duplicate]

I know very little of physics after Einstein. I am aware of that Einstein's gravity theory says that the existence of matters creates curvature of a space-time, so that our Earth orbits our Sun. I ...
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4answers
252 views

Is light amplitude spatial?

In diagrams I often see light waves depicted as little sine waves that travel through space. And often when describing polarizers, the explainer will angle their hand to show the angle of ...
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6answers
854 views

Mass without Matter?

My cursory studies of general relativity had introduced me to the concept of how gravity is associated with the warping of spacetime and that the presence of matter in space warps space and this ...
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3answers
153 views

How do we expect distance measurements to compare inside and outside the event horizon of a black hole?

I've read that as one approaches the event horizon of a black hole, time is dilated relative to time measured farther away from the event horizon (clocks tick slower near the event horizon). I've ...
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3answers
149 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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1answer
221 views

Does a spacetime manifold have the structure of a metric space?

My first introduction to spacetime physics was Wheeler and Taylor's book Spacetime Physics. This book gave me an appreciation for how important the spacetime interval was for giving the distortions to ...
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1answer
152 views

General relativity: is curvature of spacetime really required or just a convenient representation?

I'm not really far into the general theory of relativity but already have an important question: are there formulations that can do without spacetime curvature and describe the general theory of ...
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2answers
104 views

Is a non-accelerating object far from a gravity source moving at the speed of light through time?

I'm trying to understand the Minkowski spacetime better. If an object is not undergoing acceleration, and is far from any large mass, does it travel maximally "fast" through time? Can we calculate a '...
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2answers
870 views

Curvature of spacetime as a real thing?

I get the curvature tensor in General Relativity, it is “just” math. Does space-time REALLY curves as a tangible thing, or is Einstein proposing a mathematical abstraction? More naively, please allow,...
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2answers
1k views

Spacetime geometry around two black holes

For space-time geometry we all know images like he one below. But if I were to take a neutron star and put it right next to but not touching a black hole what effect would that have on the geometry of ...
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1answer
53 views

Expanding possibilities

How does the nature of space-time and how we are able to interact within it relate to the expansion of space? If Space expansion ceased to be a constant would a body of mass still be able to change it'...
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2answers
440 views

Is space stretched with no limits by a black hole?

Some depictions of black holes show space being warped into a singularity, with no end, e.g. as pictured below. Moreover, in Cosmos, Neil Tyson speculates with the possibility that Black Holes contain ...
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2answers
134 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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1answer
87 views

How do we presently understand time?

How do we presently understand time? Can a second be related directly to physical phenomena? What is a second really? Why are we sure that time is linear?
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1answer
387 views

Time coordinate inside black hole horizon [duplicate]

I am new to physics and was trying to learn more especially about general relativity. The Schwarzschild metric, changes the sign of the time and radial parts of the metric once we cross the event ...
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1answer
194 views

Are a black hole really connecting 2 parallel universe?

What is beyond the point of singularity in a black hole and universe expands in all the 3 $x$, $y$ and $z$ axis? So how can one thing be on top of another when we don't know where the end point of ...
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3answers
818 views

How does a rotating object cause frame dragging?

Frame dragging is a consequence of general relativity. But I don't really understand it. Of course I can find metaphors like the "honey metaphor" where stirring a honey can move the specks even if ...
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2answers
93 views

What logic did Newton give in support of using relative spatial measurements? [closed]

The crux of space-time is that it is one thing to have abstract concepts of absolute space & time,and it is other thing to describe the actual motion of an object in terms of measured changes of ...
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1answer
580 views

If space warps distort moving objects' trajectories, does it mean that static objects are immune to gravity? [closed]

If gravity is just space distortion, which affects trajectories of moving objects, then a static object (not moving, thus no trajectory) will not suffer any type of accelerating force from gravity? ...
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1answer
416 views

What is dimension and how many types of dimensions are there in the universe?

What is dimension and how many types of dimensions are there in the universe? I mean how many total dimensions are there? I have only heard about 2d and 3d. Other than these two, are there any other ...
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0answers
55 views

Is measurement of energy also relative? [duplicate]

From SR we know that the measurement of space and time are relative to the specific reference frame of the observer. What about measuring energy content? When an object is accelerated to a near ...
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1answer
204 views

Solving relative velocity without Lorentz transform [closed]

A train with proper length $L$ moves at speed $\frac{5c}{13}$ with respect to the ground. A ball is thrown from the back of the train to the front. The speed of the ball with respect to the train ...
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2answers
434 views

Complex numbers in quantum mechanics and in special relativity

Is there a physical relation between the use of complex numbers for the wavefunction in (non-relativistic) quantum mechanics and in special relativity (as formulated in the setting of Minkowski space)?...
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1answer
127 views

Spacetime Metrics and Quantifying Length of a Spacetime Curve

On page 247 in Gravitation by Misner, Thorne, and Wheeler, they state: "No metric means no way to quantify length; nevertheless, parallel transport gives a way to compare length!" Three questions: ...
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2answers
187 views

Can other fundamental forces bend spacetime?

I was wondering what makes gravity so special that it bends spacetime? and if it is part of the four-fundamental forces, why or why cant the other forces bend the time space continuum?
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2answers
628 views

Visualizing GR spacetime distortion in 1+1D spacetime instead of 2D space

Usually spacetime distortion due to mass in GR is visualized as a rubber sheet distorted under some massive object, like this: source or as shown in this link. But what has always bothered me is ...
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0answers
144 views

Kleppner derivation of Lorentz transformation

I am reading Kleppner.(Lorentz transformations) He said,we take the most general transformation relating the coordinates of a given event in the two systems to be of the form $$x'=Ax +Bt, y'=y, z'=z, ...
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2answers
2k views

Visualizing gravity in 3D

We've all seen the depiction of gravity bending space downwards, and so attracting objects into the dent it creates, cf. e.g. this and this Phys.SE posts. That's intuitive and makes a lot of sense, ...
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1answer
151 views

Can two distinct events occur at precisely the same moment in time?

I am writing a simulation and am having difficulty resolving the order in which two distinct forces occur. The simulation will give different results if the forces are applied to the state in ...
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1answer
122 views

A Theory of Almost Everything? [closed]

Before I present this theory, I ask that you take the time to read this disclaimer. I do not claim to have an excellent knowledge of physics, it is actually rather limited. Therefore, I am not ...
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0answers
104 views

Is time depending on the observer in string theory?

I heard that in the theory of relativity the time of an action is depending on the observer. But in string theory, is the time also depending on the observer? Are strings acting according to the ...
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3answers
681 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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3answers
75 views

Space time curvature bends back

If our perception of space-time curvature is gravitation and Reduced Gravity Plane can reach weightlessness on some point of its trajectory, doesn't that mean that when Reduced Gravity plane reaches ...
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1answer
324 views

Is imaginary time a fifth dimension? [duplicate]

I've read that by introducing the concept of imaginary time, the dimension of time can be treated like a spatial dimension mathematically. Assuming, without imaginary time, one considers the universe ...
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2answers
977 views

Does spacetime have a “mass” value? or What is “Spacetime” made out of?

When measuring the MASS within the Universe, does "space" or "spacetime" have a value? I only ask, because when speaking of expansion, space is expanding. Could it be possible, to reverse the process,...
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0answers
109 views

Alternate theories of space and time [closed]

Do mainstream theories in physics make implicit assumptions about the nature of space and time? In particular, are there any theories which implicitly assume that space and time are continuous, or is ...
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0answers
36 views

Does a body curve spacetime at higher velocities? [duplicate]

Suppose we have two objects where the distance over time decreases. Now, as I understand it, general relativity says that we can observe the Universe from the perspective of both objects an get a ...
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1answer
721 views

Gravity is curved geometry: A fact of nature or model-dependent interpretation?

We are regularly taught in high-schools and universities that, according to General Relativity (GR), gravity is nothing but a manifestation of space-time curvature (which, in its turn, is caused by ...
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2answers
81 views

What are the end points in the action integral of field theory?

In the mechanics of particles when we apply the principle of the least action the two end points are two spatial coordinates. Therefore, if we consider the variation of the action with respect to the ...
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3answers
178 views

Infinite Universe and Big Bang

A common view now in the physics community is that the Universe is infinite in extent (which makes Hubble sphere an infinitely small part of the Universe). On the other hand, there is the Big Bang ...
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1answer
228 views

What happens to black holes if/when the universe “ends”

I've heard several ideas about what happens to the universe when it dies, and they range from infinite expansion and heat death, to a "big crunch". In the event that something like a "big crunch" ...
5
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2answers
418 views

Spacetime diagram of a collapse of a rotating star

There is a well-known "standard" spacetime diagram (Kruskal and Penrose) for the collapse of a spherically symmetric star to a Schwarzschild black hole (for example here, or here in EF), which stands ...
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1answer
88 views

What it would look like to observe people with a different time flows?

As I learned, that the bigger gravity source you are influenced by the more slow time ticks for you, the farther away you are from a gravity source the faster times ticks. So Imagine two different ...
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1answer
73 views

Why is $\mathbb{R}^1$ different than Euclidean space $\mathbb{E}^1$? Roger Penrose road to reality

In Roger's book, the following is stated: (I'm paraphrasing because my book is in spanish) "We consider time as part of a space, namely $\mathbb{E}^1$, instead of it just being a copy of the line $\...
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1answer
59 views

Convergent series in the real world with equal time for each term

A few months ago someone was explaining a philosophical principle in Aikido (a martial art) which involved a convergent series. The analogy he used was that, say you have a pool, and each day the pool ...
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0answers
133 views

Visualizing bending of Spacetime around a heavy object

The commonly used example of viewing bent SpaceTime around a heavy object such as the Sun is the Trampoline. However, this image is limited as it shows only the bending below the Sun. What about the ...
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2answers
74 views

Gravitational force of several massive bodies, from the viewpoint of general relativity

According to Wald's GR, "absolute gravitation force has no meaning". The text goes on to describe two cases: one where a gravitational force can be defined, and one in which it cannot. I'd like to ...
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Do three spacelike separated events on the same lightcone satisfy the triangle inequality?

If three events are (pairwise) spacelike related to each other then their interval ratios do not necessarily satisfy the triangle inequality. (For example, consider the case that two of the three ...