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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Deriving formula for time dilation

Last week in class we derived the formula for time dilation using light clocks and got $$t=\gamma t_0\quad \gamma=\left(1+\left(\frac vc\right)^2\right)^{-1/2}$$ So far so good. However, after class I ...
18
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7answers
2k views

What grounds the difference between space and time?

We experience space and time very differently. From the point of view of physics, what fundamentally grounds this difference? Dimensionality (the fact that there are three spatial dimensions but only ...
2
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1answer
62 views

Spacetime Diagrams

Suppose an observer $\mathcal{O}$ uses the coordinates $t$, $x$, and that another observer $\mathcal{O}'$, with coordinates $t'$, $x'$, is moving with velocity $\mathbb{v}$ in the $x$ ...
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6answers
2k views

Experimental evidence of a fourth spatial dimension?

As human beings, we observe the world in which we live in three dimensions. However, it is certainly theoretically possible that more dimensions exist. Is there any direct or indirect evidence ...
2
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1answer
118 views

If Space is continuous, why can't we go below Planck Length?

I am not talking about any other attributes of particles, vacuum etc ruling out Uncertainty Principle thing. If talking about pure Space (which is continuous, not discrete, cf. e.g. this Phys.SE ...
6
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4answers
769 views

How to measure the curvature of the space-time?

I know G.R. change our vision of space and time as a unique surface than can bend. We can associate the curvature of the space-time as the gravity created by the mass of planets, stars... But how can ...
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0answers
34 views

Quantized spacetime structure? [duplicate]

Is quantized spacetime more like a chessboard or a matrix of lights? I have heard two analogies, the light bulb one appears to allow for movement whilst the chess piece one seems to violate zenos ...
3
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6answers
4k views

How does velocity cause time dilation?

I've been trying to learn about the speed of light and time dilation, but I'm at an impasse. The presented facts say that if I travel around the solar system at 50% the speed of light and then come ...
10
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1answer
410 views

Can masses move in 2+1 gravity?

I would like to understand basic concepts of the general relativity in 2+1 spacetime. As far as I know, GR predicts that such a spacetime is flat everywhere except for the point masses which create ...
2
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2answers
136 views

What is the meaning of space-time curvature?

What is the difference between the Space-time curvature and Space curvature?
3
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1answer
178 views

Proper time along path in Minkowski Space

Consider the path $x^\mu(u)$ in Minkowski space; such that: $$t = \frac{a}{c} \sinh(u) , \quad x = a \cosh(u) ,\quad y = 0 ,\quad z = 0 $$ where $a$ is a positive constant and $u$ is a parameter ...
1
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1answer
56 views

Is cosmic background radiation absolute [duplicate]

Now that we don't have permeating Ether anymore, why don't we consider the omnipresent Cosmic background radiation in place of it? and measure Speeds with respect to the CMBR? In that way an object ...
4
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0answers
220 views

Nature of Microscopic space-time

I am going through the introductory chapter's of Schwinger's Source theory. He writes, It [Source Theory] is a phenomenological theory, designed to describe the observed particles. No speculations ...
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1answer
117 views

Time Reversal in a Black Hole

I had a lively discussion with a person about black holes recently, and was making the point about gravitational acceleration in GR being paralleled by speed in SR. One thing that I know people talk ...
10
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1answer
367 views

Causal and Global structure of Penrose Diagrams

What kind of global and causal structures does a Penrose diagram reveal? How do I see (using a Penrose diagram) that two different spacetimes have a similar global and causal structure? Also, I ...
0
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1answer
52 views

Speed=mass=time? [closed]

I was wondering why objects gain mass with speed? How can we measure speed if there is no truly stationary point to measure from? And if an object comes to a stand still will it loose its mass? ...
0
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1answer
378 views

When are we now? Time coordinate system [closed]

The Second and the metre are well defined. We have those units available. Of course units are meant to express measurement, tools to compare with precision, and interchange that information ...
3
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2answers
283 views

Restriction of a Lagrangian

I'm wondering if anyone could help me with the following questions. Let $M$ be the Minkowski spacetime, given $f\in C^{\infty}(M) ; f(m)=x^{0}(m)$, with $\{x^{\mu}\}$ being a global Cartesian ...
0
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0answers
62 views

Does non-matter energy curve spacetime? [duplicate]

I know that matter (mass) curves spacetime, but do other forms of energy do the same? I.e. is matter the only form of energy that curves spacetime?
4
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3answers
91 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 ...
23
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2answers
3k views

Does the Planck scale imply that spacetime is discrete?

On a quantum scale the smallest unit is the Planck scale, which is a discrete measure. There several question that come to mind: Does that mean that particles can only live in a discrete grid-like ...
6
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1answer
124 views

Could dark energy make a large black hole less black?

Theoretically, if a black hole grew to a huge scale such that the effect of dark energy was large, could the black hole become 'normal' space again (i.e. no horizon or singularity)? What I'm trying ...
4
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6answers
1k views

Surely space-time Curvature does not explain gravity, it just describe its effects?

In special relativity co-moving objects see the other's 4-velocity as being only temporal. When they move relative to each other they see the other's 4-velocity has rotated so that it points less in ...
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1answer
59 views

Internal and spacetime symmetries?

I am trying to understand Wiki's explanation about correlation. Part of this article talks about internal and spacetime symteries: If the probability distribution has any target space symmetries, ...
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3answers
624 views

Whats left at the center of the Universe after Big bang?

If you consider big bang. According to that What's left at the center of universe where the Big bang occured?
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1answer
35 views

Taking signal travel time into account in Special Relativity

I am having problems taking the time it takes for a light signal from an event to reach an observer into account: For instance, if we have two observers $A$ and $B$ who synchronize their clocks when ...
0
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2answers
131 views

How does “space” expand? [duplicate]

According to Big Bang theory and The Red shift theory "space" is "expanding". Keeping this notion of "space" as physically something in and of itself(space -time did not exist before The Big Bang); ...
4
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1answer
91 views

Does inflation predict a multiverse?

Does inflation necessarily predict a multiverse? Or is it the case that "It all depends on the properties of the initial field responsible for inflation, about which we can only speculate"?
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6answers
2k views

Is 3+1 spacetime as privileged as is claimed?

I've often heard the argument that having 3 spatial dimensions is very special. Such arguments are invariably based on certain assumptions that do not appear to be justifiable at all, at least to me. ...
0
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1answer
69 views

How does someone move space?

I've heard that we've known components of the universe appear to be flying apart faster than $c$, and that this can happen because the space containing these materials are also moving apart. How does ...
0
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4answers
156 views

Time Dilation at zero velocity (and zero gravity)

From what I've learned, the more an object travels closer and closer to the speed of light, the more time will slow down for that object.. at least from an outside perspective.. It was shown that ...
16
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2answers
1k views

Inflation and the Meaning of Time

I'm not quite sure how to ask this so that it can be answered in layman's terms, but I have lately seen, in several places, that with cosmological inflation, there was a point where the universe ...
3
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0answers
246 views

Is it mathematically possible or topologically allowable for cutouts, or cavities, to exist in a 3-manifold?

A few weeks back, I posted a related question, Could metric expansion create holes, or cavities in the fabric of spacetime?, asking if metric stretching could create cutouts in the spacetime manifold. ...
2
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2answers
321 views

Is it possible for dark matter to somehow turn into regular matter?

Is it possible for dark matter to create the regular matter that we, the stars, and the galaxies are made of? The reason I'm asking this is because I have a hard time imagining how something can ...
2
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1answer
86 views

Where do our 4 macroscopic spacetime dimensions reside in multidimensional models of the universe?

In models such as M-theory with 7 'higher dimensions' plus the 4 macroscopic spacetime dimensions, where do our 4 macroscopic spacetime dimensions reside ordinally? My reason for asking is TV shows ...
0
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2answers
94 views

Infinitely many points of space-time?

Please can someone provided me with academic literature (Journals/Books, titles & links) which discuss the current view on space time i.e. that there is not Infinitely many points of space-time?
4
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3answers
209 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 ...
15
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9answers
3k views

Is the flow of time regular?

Is the flow of time regular? How would we come to know if the our galaxy along with everything in it stops for a while(may be a century) w.r.t to the galaxies far beyond our reach. Is there a way to ...
1
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2answers
68 views

What are the factors affecting the spacetime curvature?

Large masses in space as stars and planets cause a curvature in the spacetime fabric. What are the factors that affect this curvature? Is it only mass? And can we conclude these factors using Tensors? ...
0
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2answers
41 views

Theoretical Physics Notation (Hamilton-Jacobi in the Relativistic Domain)

I am having trouble understanding how to solve some theoretical physics problems I have come across. Specifically how to convert the Hamilton-Jacobi equation: $$(\partial_\mu S+e A_\mu)^2=m^2$$ From ...
-1
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1answer
150 views

Can we have a static point in the universe? [closed]

Big bang theory states that the universe began from a single point (which we may consider as a central frame of reference for the objects in the Universe). In 1929, Edwin Hubble confirmed that the ...
1
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0answers
32 views

antimatter moving back in time [duplicate]

This just blew my mind away! I was watching a video about imagining the fourth dimension and the narrator said that little line. Can some people elaborate on this. Also please keep it simple not ...
5
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5answers
902 views

Naive visualization of space-time curvature

With only a limited knowledge of general relativity, I usually explain space-time curvature (to myself and others) thus: "If you throw a ball, it will move along a parabola. Initially its vertical ...
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0answers
41 views

Space time curvature due to electric charge or magnetic charges [duplicate]

since we know that gravitational force is nothing but a curvature in space-time. I have a similar analogous for the electric or magnetic charges. Similarity is that both electromagnetic and ...
55
votes
4answers
6k views

Why would spacetime curvature cause gravity?

It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" ...
1
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2answers
171 views

A question about multiverse

I have a question that I would like to ask here since I'm not an expert or any near to that. Actually I just came up with this question when I was watching The fabric of cosmos. I couldn't find where ...
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3answers
144 views

Questions about spacetime curvature and gravity

These are some further important queries regarding the question here Why would spacetime curvature cause gravity? Q1. Explain the statement “Everything in spacetime moves at the speed of light”. Is ...
0
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0answers
29 views

Velocity in a pseudo-Riemannian manifold

Suppose we have a pseudo-Riemannian manifold (modeled by $\mathbb R^{p,q}$) with signature $$(\underbrace{+,+,\cdots,+}_p,\underbrace{-,-,\cdots,-}_q)$$ Meaning we have $q$ spacelike dimensions and ...
3
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1answer
105 views

Is it possible that the universe in its entirety is discrete rather than continuous? [duplicate]

Since electric charge is comprised of discrete units and and mass is formed by discrete units is it possible that space-time itself is discrete as well?
0
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4answers
728 views

The real meaning of time dilation

Is this true or false: If A and B have clocks and are traveling at relative velocity to each other, then to B it APPEARS that A's clock moving slower, but A sees his own clock moving at normal speed. ...