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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If photons don't “experience” time, how do they account for their gradual change in wavelength?

It is often said that photons do not experience time. From what I've read, this is because that when travelling at the speed of light, space is contracted to infinity, so while there is no time to ...
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What spacelike, timelike and lightlike really mean?

Suppose we have two events $(x_1,y_1,z_1,t_1)$ and $(x_2,y_2,z_2,t_2)$, then we can define $$\Delta s^2 = -(c\Delta t)^2 + \Delta x^2 + \Delta y^2 + \Delta z^2$$ which is called the spacetime ...
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Is space infinitely divisible?

As a child I remember hearing the popular paradox presented by Zeno proposing that Achilles could never catch a tortoise in a race since he would have to traverse the infinite space between himself ...
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What are the linear maps which preserve the time-like cone?

I'm looking at the set of time-like vectors: $\mathcal{T}_+ = \{ x \in \mathbb{R}^4 \mbox{ s.t. } x^T \eta x \geq 0 \:, x^0\geq 0\} $, where $\eta = \mbox{diag}(1, -1, -1, -1)$. I want to be able to ...
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682 views

How can I vizualize and understand curved spaces in general relativity?

I'm taking a basic physics class and the teacher described space with a special table that has curves and black holes etc. He would throw a metal ball down onto it and the class would watch it circle ...
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Why should one expect closed timelike curves to be impossible in quantum gravity?

From the Wikipedia article, it seems that physicists tend to view closed timelike curves as an undesirable attribute of a solution to the Einstein Field Equations. Hawking formulated the Chronology ...
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264 views

Plausible explanations for 3 local space dimensions

Every now and then I see accounts of models that claim to explain why we experience only 3 space dimensions (locally, i.e. within cosmic horizons and outside black hole horizons). One such of course ...
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265 views

Is a spinor in some sense connected to space?

Spinors transform under the representation of $SL(2,\mathbb{C})$ which is the double cover of the Lorentz group $SO(1,3)$ - or in the non-relativistic case under $SU(2)$, the double cover of $SO(3)$. ...
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358 views

Our Universe Can't be Looped? [duplicate]

With reference to the Twin-Paradox (I am new with this), now information of who has actually aged comes from the fact that one of the twins felt some acceleration. So if universe was like a loop, and ...
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Does the “Andromeda Paradox” (Rietdijk–Putnam-Penrose) imply a completely deterministic universe?

Wikipedia article: http://en.wikipedia.org/wiki/Rietdijk–Putnam_argument Abstract of 1966 Rietdijk paper: A proof is given that there does not exist an event, that is not already in the past for ...
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106 views

Hamilton operator in absence of causal order?

I hope, this question isn't too broad or vague. In a recent paper, Ognyan Oreshkov et al. worked out a theory of quantum correlations in absence of any causal order, dropping the assumptions of a ...
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Does (it make sense to say that ) the universe has a center?

I was reading this page: http://www.guardian.co.uk/science/2011/oct/23/brian-cox-jeff-forshaw-answers and I found this sentence by Brian Cox: That seems to imply that everything is flying away ...
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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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4answers
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If gravity is a bend in Space-time then what is magnetism?

Einstein postulated that gravity bends the geometry of space-time then what does magnetism do in to the geometry of space-time, or is there even a correlation between space-time geometry and ...
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2answers
4k views

What is imaginary time? [duplicate]

I am not professional physicist; but I am curious about Stephen Hawking's "imaginary time". It would be better to elaborate exactly what it is. I am not confused because of the word "imaginary" but I ...
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3answers
517 views

Do objects with mass “suck in” spacetime?

I don't really understand the general theory of relativity (GTR) really deeply, but according to my understanding, the GTR say that gravitation is caused by the curvature of spacetime by objects with ...
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3answers
769 views

Why do clocks measure arc-length?

Apologies in advance for the long question. My understanding is that in GR, massive observers move along timelike curves $x^\mu(\lambda)$, and if an observer moves from point $x^\mu(\lambda_a)$ to ...
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Is it possible to stop time? [duplicate]

Assuming the spacetime principle, if the space is modified the time does too. So if the velocity in the space is increase, does the time slow down? What happens if the speed is the speed of light, ...
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How do I derive the Lorentz contraction from the invariant interval?

Reviewing some basic special relativity, and I stumbled upon this problem: From the definition of the proper time: $$c^2d\tau^2=c^2dt^2-dx^2$$ I was able to derive the time dilation formula by using ...
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What does it mean for objects to follow the curvature of space?

In science documentaries that touch on general relativity, it is often said that gravitational pull isn't an actual a pull (as described by classical physics), but rather one body travelling in a ...
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Alternate layman's metaphors for illustrating curved space-time

The metaphor of a surface (typically a pool table or a trampoline) distorted by a massive object is commonly used as a metaphor for illustrating gravitationally induced space-time curvature. But as ...
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6answers
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If space is “expanding” in itself - why then is there redshift?

The "kid's" way of understanding the expanding universe is that: "space" is totally "ordinary", and all the galaxies are expanding through it (like an explosion). Of course, that's wrong. The usual ...
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555 views

Can we show that time is orthogonal to space?

It's easy to show that the time we measure is "in a different direction" from the space directions we measure. However, it's not immediately obvious to me that these directions are orthogonal. How do ...
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4answers
773 views

Hamiltonian and the space-time structure

I'm reading Arnold's "Mathematical Methods of Classical Mechanics" but I failed to find rigorous development for the allowed forms of Hamiltonian. Space-time structure dictates the form of ...
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678 views

Getting back out of an Alcubierre warp bubble

Does the theory on paper provide a way for hypothetical travelers to get back out of the bubble that has gotten them close to their distant destination by compressing all the space in front of them ...
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693 views

The Big Bang in an infinite universe

If the universe is spatially infinite (and assuming, if it makes a difference, that we don't have eternal inflation), what actually happened 13.7 billion years ago? Was the energy density infinite (or ...
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1answer
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Is the universe finite and discrete?

Is the universe finite, both in the sense of being a closed spacetime manifold, as viewed from the macro level, but also in the sense of being fully discrete and finite in all of its intricate quantum ...
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209 views

Equilibrium for a rope hanging in a Schwarzschild spacetime

Update: Trimok and MBN helped me solve most of my confusion. However, there is still an extra term $-(2/r)T$ in the final result. Brown doesn't write this term, and it seems physically wrong. Update ...
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292 views

How warped spacetime bends trajectories of light and moving objects?

I fail to see why the light follows something like the blue line and not the green line on the attached image. Figure 1 - light bends around warped spacetime Afaik. something similar happens ...
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177 views

What coordinate system is used to describe planets positions in the universe?

How are planets positions described in the space and in respect to what? For example is Sun the origo and right now at this moment Earth has [coord_X, coord_Y, coord_Z]? or maybe [lng, lat]? ...
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6answers
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Does vacuum (empty space) exist? [closed]

Added: 5 times down vote for now! Down voter is this religion or physics, please try to explain your decision. I'm confused about this. In physics we know for a vacuum, but I think that there is a ...
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903 views

Can special relativity distort the relative order in which events occur?

Pretend you are throwing darts at a dart board. You throw dart $d_1$ at time $t_1$. After you throw your first dart, you throw your second dart $d_2$ at time $t_2$. Given that $t_2 > t_1$ in a ...
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Does the existence of “gravitational waves” (assuming they exist) imply that time exists as a 4th dimension in the universe? [closed]

I'm new to thinking about special and general relativity and I have no formal training as a physicist. However, I've been doing a bit of thinking about spacetime recently. I was wondering if ...
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7answers
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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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2answers
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What does “foliation” mean in the context of a “foliation of spacetime?”

I've seen foliation used in the context of "foliation of spacetime" here and elsewhere in papers and such. Generally defined in reference to a "sequence of spatial hypersurfaces." But I don't know ...
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247 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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Measuring the speed of light and defining the metre - absolute or relative?

If the metre is now defined as the distance light travels in vacuum in 1⁄299,792,458th of a second and the speed of light is accepted to be ...
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4answers
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ALL “forces” as manifestations of properties of space-time

I apologize if this seems like a quack question, but I need some insights by those who know much more than me in Physics. Anyway, the gravitational "force" (not really a force) is a manifestation of ...
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Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon?

Does String theory say that spacetime is not fundamental but should be considered an emergent phenomenon? If so, can quantum mechanics describe the universe at high energies where there is no ...
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3answers
402 views

Is my grandmother alive for some alien who is located on some place and is moving with some speed?

(I am science fiction writer. I had a goal in my novel to argue that time travel to past will not be available even in future. I asked here how to argue that. I collected answers and analyzed them and ...
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4answers
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Why does string theory require 9 dimensions of space and one dimension of time?

String theorists say that there are many more dimensions out there, but they are too small to be detected. However, I do not understand why there are ten dimensions and not just any other number? ...
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187 views

What manifold is spacetime?

In General Relativity, spacetime is a $4$-dimensional manifold with one Lorentzian metric tensor defined on it. In the Special Relativity case what manifold is spacetime is quite clear: it is ...
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582 views

Do clocks really measure time?

Each time I listen to this quote from The man from Earth, I'm absolutely intrigued: Dan: Time... you can't see it, you can hear it, you can't weigh it, you can't... measure it in a laboratory. It ...
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344 views

What really is Spacetime?

What is a good definition on Space, Time and the most specific topic "Spacetime"? Because someone told me that spacetime is the foundation of the entire universe? And also, Is it possible to create ...
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2answers
344 views

Sewing together flat spacetime pieces = flat spacetime?

I'm trying to imagine the geometry "operations" here: Angular deficit and Conical spacetime of cosmic string If we sew flat spacetime pieces together, what is the requirement for the sewing to not ...
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1answer
365 views

How is it that distortions in space can be measured as distances? [duplicate]

Imagine yourself and anything you're able to perceive to be drawn onto a rubber band. Any means of determining distances would be affected by the stretching/contracting of the rubber band. The ...
6
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3answers
486 views

“Warp-drive” thought experiment

Why wouldn't this "warp-drive" work? Assuming we can build a flywheel that can survive near light speed and have an onboard power storage or beamed energy that can spin it up to that speed and back ...
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180 views

Does expanding space cost energy?

Does the cosmic inflation reduce the energy density (inversely) proportional to the volume, or does the inflation "cost" energy? Is space itself "something" created at the expense of energy?
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1answer
243 views

A Game Of The Number Of Space-Time Dimensions

Holger Bech Nielsen, one of the founders of string theory, has apparently just played some sort of game between different potential dimensions for space-time and reached the conclusion that D4 wins in ...
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1answer
184 views

If a fundamental theory exibits e.g. a mirror symmetry, in what sense it the underlying geometry real?

Are the more recently discovered symmetries in string theory such that the theories based on mirroring geometries are absolutely the same from an observable point of view? I have mirror symmetry ...