What is Space-time: Definition and 417 Discussions
In physics, spacetime is any mathematical model which fuses the three dimensions of space and the one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why different observers perceive differently where and when events occur.
Until the 20th century, it was assumed that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. The famous physicist Albert Einstein helped develop the idea of space-time as part of his theory of relativity. Prior to his pioneering work, scientists had two separate theories to explain physical phenomena: Isaac Newton's laws of physics described the motion of massive objects, while James Clerk Maxwell's electromagnetic models explained the properties of light. However, in 1905, Albert Einstein based a work on special relativity on two postulates:
The laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference)
The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.The logical consequence of taking these postulates together is the inseparable joining together of the four dimensions—hitherto assumed as independent—of space and time. Many counterintuitive consequences emerge: in addition to being independent of the motion of the light source, the speed of light is constant regardless of the frame of reference in which it is measured; the distances and even temporal ordering of pairs of events change when measured in different inertial frames of reference (this is the relativity of simultaneity); and the linear additivity of velocities no longer holds true.
Einstein framed his theory in terms of kinematics (the study of moving bodies). His theory was an advance over Lorentz's 1904 theory of electromagnetic phenomena and Poincaré's electrodynamic theory. Although these theories included equations identical to those that Einstein introduced (i.e., the Lorentz transformation), they were essentially ad hoc models proposed to explain the results of various experiments—including the famous Michelson–Morley interferometer experiment—that were extremely difficult to fit into existing paradigms.
In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zürich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the formal definition of the spacetime interval. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded.Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed how mass and energy curve flat spacetime into a pseudo-Riemannian manifold.
A few yesrs ago now I read a First Course in String Theory.
In that book strings were part of normal space-time plus for consitency some extra dimensions. Spin 2 partices natually emerged and so did GR.
I didnt think anything of it at the time (pun intended), but I recently saw a...
people say that gravity is not a force, that it's rather a distortion of space-time
so objets that go to a gravitational center are actually just moving through space in linear direction
but there is a problem in this theory
shouldn't objects go to the center in constant speed? why are they...
The context is the so called warp drive.
In pop-sci articles I've seen the claim that the speed of light limit only applies to objects in space but not the space-time itself, thus claiming that the expansion and contraction of space by a warp drive has no speed limit.
On the other side, I've...
Hello everybody. I have been having a lingering question about the State of the Universe. As humans, we view the Universe's expanse as historical from the vantage point of Earth. For example, 10,000 light years away would have occurred 10,000 years ago. On that same logic, looking at Earth from...
Modern physics describes matter by real numbers. This means that an absolutely accurate description of any particle requires an infinite amount of information.
Intuitively, it seems that this should not be so, and the model of the Conway's Game of Life looks more close to reality. In this...
Is the twin paradox settled by saying that any non-straight path between two events (points) in space-time has less proper time that a straight path between the two events? So the twin in the frame which has a longer trajectory between the two pints(curved) will have less elapsed time?
I need your help. I've just begun learning about space time diagrams. Below is my doubt:An event is shown as a point on a spacetime diagram
Another frame has coordinates of space and time as:
##\begin{aligned} c t^{\prime} &=(\cosh \theta)(c t)-(\sinh \theta) x \\ x^{\prime} &=(-\sinh \theta)(c...
I am trying to replicate the space time plot (the 2nd plot with Proper distance vs Time) as in this thread: space-time
I wrote everything in python using the astropy cosmology package.
Everything went smooth, but I am stuck at plotting the light path on the 'purple path', as per the above...
I have tried to draw a simplified diagram depicting the original Michelson experiment. I am only looking at the paths from the beam splitter to the mirrors at the end of the arms and back,
Below, you can see the following: A space-time diagram with two space axes (x andy) and one time axis...
I am confused by the concept of space-time in special relativity, I have 3 spatial dimensions and 1 time dimensions. In Newtonian physics don't I also have 3 spatial dimensions and 1 time dimension? Then why call it space time in special relativity and not in Newtonian physics?
I have a 2D space-time PDE and I want to solve it numerically over the time axis. The time initial field is already known with respect to space, i.e., the spatial distribution is already known at time `t = 0`. I solved the same PDF in Mathematica and got a solution. I tried to solve it...
I am familiar with the concept of the curvature of space-time. I imagine that space-time can also expand. If this is possible then objects far from our view may appear to accelerate. No force required they are traveling through space that is changing in curvature or expanding. Is this a...
One of the paradoxical principles in Quantum Physics is the principle of quantum superposition, since in quantum theory we are not really talking about the superposition of waves or oscillations, but about the superposition of states.
A classic example demonstrating the phenomenon of quantum...
What is the relationship between the electromagnetic field and space-time? I am basically assuming that space-time is one big gravitational field.
Is there a relationship between space-time and the field (I presume) created by the strong force (however negligible it may be at any significant...
If a Black Hole is spinning (perhaps they all do) I have heard it distorts the 'fabric' of Space-time in the vicinity. What is the 'friction' component which allows the distortion?
In a few days, I will be hosting a Zoom-based meetup in which I will be explaining the Twin Paradox (time dilatation) and the Pole-in-a-Barn paradox (Lorentz contraction). To this end, I will need to make graphics of space-time diagrams like those in Wheeler's book Spacetime Physics. Can anyone...
Formally, this means that all timelike lines in Minkowski space are mapped onto helical lines of an infinite cylinder. Can it be argued that in such a modified space-time, classical physics inevitably turns into quantum physics?
I am following a lecture note on the QFT.
But am a little confused about some parts related to the vacuum bubbles.
We define the Feynman propagator, ##D_{F}(x-y)##, as giving the amplitude for a particle emitted at ##x## to propagate to ##y## (where it can be measured).
After following the...
Is there a general method to determine what geometry some line element is describing? I realize that you can tell whether a space is flat or not (by diagonalising the matrix, rescaling etc), but given some arbitrary line element, how does one determine the shape of the space?
Thanks
Hi, there. I am reading An Introduction to Quantum Field Theory by Peskin and Schroeder. I am confused about some equations in section 2.4 The Klein-Gordon Field in Space-Time. It computes the Heisenberg equations of ##\phi \left ( x \right )## and ##\pi \left ( x \right)## as (in page 25)
##...
I'm working through Ray d'Inverno's book "Introducing Einstein's Relativity" and I've got to the section that introduces Penrose diagrams. The first example is just Minkowski space-time. The construction goes from Schwarzschild coordinates ##t## and ##r##, to define null coordinates ##v = t +...
I was having a discussion with someone, regarding whether Time Travel was possible. The opposing individual argued that people are composed of matter that is simply woven into the fabric of space-time, therefore, rendering us unable to travel through time. I wasn't sure if he was right because I...
I think that if we plot an inertial frame in the XY axis separated 90º, the photon, which has a velocity of c, should be put on one of the branches of the light cone. The questions are:
Which branch, left or right one?
Which position along the branch, if I don't know the distance it has...
Be the red point this spacecraft , the purple line the world line with slope = 2 and the green point a photon thrown towards the Earth from the spacecraft , would this spacetime diagram ok? (distance would be 1.2 billion km, and the time, 1000 times of shown, but scale is badly displayed, even...
I've managed to thoroughly confuse myself. Before Minkowski came along and combined 3-dimensional Euclidian space and time into Minkowski spacetime, I was under the impression that we only dealt with three dimensions and that time was just a universal parameter. Thorne and Blandford write...
Googling "emergent spacetime" I get lots of articles which offer various conjectures about what that may be; an overview for example is given in http://guava.physics.uiuc.edu/~nigel/courses/569/Essays_Spring2018/Files/gupta.pdf. However, although I understand that emergent spacetime is not yet a...
Hi, I'm looking at QHE notes D.Tong and wondering how he gets from equation 5.46 to 5.48 ( http://www.damtp.cam.ac.uk/user/tong/qhe/five.pdf )
##S_{CS}=\frac{k}{4\pi}\int d^3 x \epsilon^{\mu \nu \rho} tr(a_{\mu}\partial_{\nu}a_{\rho} -\frac{2i}{3}a_{\mu}a_{\nu}a_{\rho})##.
manifold ## \bf{R}...
There is the famous experiment of measuring the "movement" of a star close to the sun during an eclipse. The stars position is determined before the disc of the sun moves just under it and than the position is again measured when the sun moves just "under" the star. The star will have appeared...
Can the effects of gravity possibly extend through time? Is there a natural law that forbids this?
Could this be a possible explanation for dark matter?
So I understand that mass creates curvature in space-time. But what I struggle with is how nothing has a shape. I picture the space around say a planet, but how does the space (nothing) actual have form? Does anyone have a good intuitive explanation for that?
Given that the expansion takes place "in nothing".
Given that all space-time exists all of the time. (past/present/future)
If the ultimate fate of the Universe is that it collapses back in upon itself.
Shouldn't a singularity of space-time occur instantaneously?
After all, all time existed...
Please see attached illustration (from Discover September 2004. Einstein 100 years special issue).
Is it correct that one key to Einstein's thinking is to analyze a spnning disk. That "Since the rim of the disk travels faster than the center of the disk, the theory of relativity states that the...
https://arxiv.org/pdf/1812.06239.pdf
In this paper,the authors use ricci flow to construct Lifshitz spaces. But it is known that ricci flow is limited by Riemannian manifold, which has a positive metric. but in this paper the author use ricci flow in a lorentz manifold, whose signature...
Summary: Mathematical and Physical queries in regards to Electromagnetic Fields and their manipulation of Space-Time.
I recently started looking into Einstein's Field Equations, to get a better understanding of how mass distorts and curves the plane of Space-Time, however from doing this I...
I'm confused by this question, from minimal coupling shouldn't the answer simply be ## \nabla^a \nabla_a F_{bc} = 0 ##? Any help would be appreciated.
EDIT: I should also point out ##F_{ab}## is the EM tensor.
Greetings: I watched several videos describing so-called "empty space" as being permeated with fields (electron field, quark field, etc.). Is it possible that it is actually these fields that curve about large masses and that the trajectory of light and matter curve because they follow the...
First off, this is just an assumption. My knowledge of the field is extremely limited and I beg you to come and correct my mistakes, so I can learn.
So, I guess we all know how that space-time fabric is bended by gravity. When a star dies, all of the atoms are brought extremely close...
I just read through a paper on a \mathbb{Z} _ 3 graded Algebra. In this instance we are talking about color Dirac spinors in space-time. It looks like the author is talking about \left ( SU(3) \otimes L^4 \otimes \mathbb{Z}_2 \otimes \mathbb{Z} _2 \right ) \otimes \mathbb{Z} _3. ( SU(3) is...
I was talking to a graduate physics student about the issue of energy conservation in an expanding universe. I paraphrased the argument against energy conservation as follows -
Suppose we have a photon in outer space that is very far from earth. The universe is expanding (by this I meant that in...
Homework Statement
P.S.: I'm not sure if it is allowed to ask multi-part questions.
Two equally old sisters Alice and Barbara leave Earth simultaneously in opposite directions. The following velocities and distances have been measured in the Earth system. Alice travels with a speed of ##v_A =...
In an ideal world with uniform gravity field, what does its space-time curvature look like? Is it non-zero? If not, how a free particle would be accelerated with the point view of space-time curvature?
By uniform gravity field, I mean a gravity field with same value, same direction everywhere...
When you put a mass on a trampoline it causes the trampoline to V. If you put another similar or same sized mass on the same trampoline at a great enough distance, will the curve on the trampoline/space-time look like a W or a U ?
If you can get the curves on a trampoline/space-time to look...
I'm interested in all movies with themes or genres about us being visited by visitors
who operate outside the limits of our space-time continuum yet have the ability to cross
over into our reality. Try to imagine the guys of Dark City but operating outside time.
Have you seen any movies or tv...
Besides the Feynman lectures on gravitation, I'm looking for modern and complete treatments of the topic of classical gravitation as a field theory in flat space time. Any suggestion?
Hi all,
I understand the mathematics behind special relativity pretty well, but I only have a bare conceptual understanding of general relativity. My understanding is that energy, momentum and stress (as described in the energy-stress tensor) are what contribute to space-time curvature and...
I wonder if someone would field a beginner's muse I had: If gravity is just an illusion of the curvature of space caused by mass, does not the matter within that space follow the curve? and what is the granularity of that curvature? Does the curvature exist in the space between the nucleus and...