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.
The Wikipedia section below says that gravity is the earliest to appear out of the fundamental interactions, but wasn't high energy in every area already curving its local spacetime surroundings?
https://en.m.wikipedia.org/wiki/Chronology_of_the_universe#The_very_early_universe
Reading this PDF from Professor Richard Conn Henry, I am confused by the multiplication by c on page 2.
x, y and z are metres. t has units seconds. So I would think, "We can't subtract seconds from metres , we can't subtract dt from dx."
To sidestep that, Einstein multiplied dt by c. c has...
Based on the current understanding of general relativity, it is possible that curving spacetime in the back of a spacecraft would allow for faster-than-light travel. In general relativity, the curvature of spacetime is determined by the universe's distribution of matter and energy. If a...
After trying to kinda get a picture of the field of play in quantum physics according to the standard model, a question came up. I tried to formulate the known bosons each as a particle transferring some property.
1. Photons transfer electric charge: the electromagnetic force gives attraction...
Can there be worldlines that are neither timelike, nor null, nor spacelike? They can
Are there curves in spacetime that are neither timelike, nor null, nor spacelike? Why?
Exercise:
My solutions:
For events to be simultaneous, the invariant interval must be bigger than zero (spacelike). I got $$I = -c^2 \Delta t^2 + \Delta x^2 + \Delta y^2 + \Delta z^2 = -(0-1)^2 + (0-2)^2 + (0-0)^2 + (0-0)^2 = -1 + 4 = 3 >0$$. Which is indeed greater than zero, to find the...
Are there non-smooth metrics for spacetime (that don't involve singularities)?
I found this statement in a discussion about the application of local Lorentz symmetry in spacetime metrics:
Lorentz invariance holds locally in GR, but you're right that it no longer applies globally when gravity...
Pseudo-Riemannian manifolds (such as spacetime) are locally Minkowskian and this is very important for relativity since even in a highly curved spacetime, one could locally approximate the spacetime into a flat minkowski one.
However, this would be an approximation. Perhaps this is a naive...
I was reading a discussion where some physicists participated* where the topic of Lorentz invariance violations occurring in cosmology is mentioned.
There, they mention that we can imagine a Lorentz-violating solution to the cosmological equations. What do they mean by that? Can anyone specify...
I have heard that some types of inhomogeneties and topological defects (like cosmic strings) in cosmology have been proposed to be able to break fundamental symmetries of nature such as the Poincaré, Lorentz, diffeomorphism CPT, spatial/time translational...etc symmetries... However, I have not...
Perhaps this is a stupid question but, if Lorentz symmetry and time translational symmetry are not global in an expanding universe, wouldn't that mean that is possible that other Hubble spheres outside our observable universe could have other symmetries or an absence of the Lorentz symmetry? I...
I was discussing this paper with a couple of physicists colleagues of mine (https://arxiv.org/abs/2011.12970)
In the paper, the authors describe "spacetimes without symmetries". When I mentioned that, one of my friends said that no spacetime predicted or included in the theory of relativity...
In the context of the Theory of Relativity are there any spacetimes or metrics with a complete absence of symmetries?
I mean, consider a type of space or metric where no symmetries would hold (at least not exactly, but approximately). A space or metric where the Poincaré invariance (including...
Why do the Cauchy Stress Tensor & the Energy Momentum Tensor have the same SI units? Shouldn't adding time as a dimension changes the Energy Momentum Tensor's units?
Did Einstein start with the Cauchy Tensor when he started working on the right hand side of the field equations of GR?
If so, What...
Einstein showed (via general relativity) that spacetime is curved by mass, mass moves in relation to this curvature, and that gravitation arises as secondary effect. Why then are we looking for quantum gravity as some sort of mass<->mass interaction?
Aren't the fundamental interactions better...
I was reading this paper (*Green's functions for gravitational waves in FRW spacetimes:* [https://arxiv.org/abs/gr-qc/9309025](https://arxiv.org/abs/gr-qc/9309025)) and I had a specific question about one statement in the paper that I would like to ask:
At page 6, the author says that...
This is a very basic question, and I am not sure I have the answer.
A photon goes from point A to point B, only 1 meter distance apart from each other. A spacetime diagram would show a line connecting points A and B at a 45 degree angle. This can be a right triangle with equal sides, with...
By following article a magnetic field can produce a least a minimum distortion in spacetime.
If we have a inertia disk spinning 50% inside of a strong closed magnetic field may we suppose that we will create an unbalanced in the angular disc moment producing a propulsion without mass variation...
Hi, there. I am currently reading the paper, Gravitational Faraday rotation induced by a Kerr black hole (https://doi.org/10.1103/PhysRevD.38.472). After Eq. (2.4), it reads that
The paper does not provide the derivation of the equations and no related reference is listed. Also, ##k^i## is not...
With one spatial dimension ## x ##, the spacetime interval between two events ## A ## and ## B ## is
## \Delta s= \sqrt{(ct_{B}-ct_{A})^{2}-(x_{B}-x_{A})^{2}} ##
I have a technical question: on the plane of the graph (x,y=ct), the ordinary distance between 2 points ## A ## and ## B ## is
##...
I was reading a paper by J.M.C Montanus which was published in <low quality journal reference removed> in which he claims under AEST the new gravitational dynamics and electrodynamics are reformulated in close correspondence with classical physics, and subsequently leads to the correct...
I created a model of spacetime based on an extension I added to the principle of relativity. I then derived the coordinate transformations which preserve the speed of light in all frames, which are different from the Lorentz transformation. I worked out the formulae for energy and momentum, and...
In describing the spacetime around a massive, spherical object, one would use the Schwarzschild Metric. What metric would instead be used to describe the spacetime around multiple massive bodies? Say, for example, you want to calculate the Gravitational Time Dilation experienced by a rocket ship...
Are there any kind of observed and experimentally verified processes or mechanisms where photon emission occurs and which are directly cause by spacetime expansion in some way?
Sean Carroll has an article (https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/) where he explains that matter can gain energy from spacetime expansion.
At the end of the article, he says: In general relativity spacetime can give energy to matter, or absorb it from...
Greetings. I registered to this forum because of a particular issue regarding Gravity. I'm no astrophysicist or mathematician, i searched to find an answer, but the terminology and equations are a little much for me. I feel the best direct way is to ask people with the right expertise.
It is...
While not having a professional physics background I was still interested in knowing more about special and general relativity. Therefore I was trying to find out where the space time interval was coming from in relation to the speed of light. Of course this is the first point to start I...
About a year ago, I heard Leonard Susskind discussing how entangled black holes could create spacetime. As I was listening to Prof. Susskind describe the mechanisms for creating entangled black holes, and how these black holes might create their own spacetime, it occurred to me that if we were...
Suppose you have the following situation:
We have a spacetime that is asymptotically flat. At some position A which is in the region that is approximately flat, an observer sends out a photon (for simplicity, as I presume that any calculations involved here become easier if we consider a...
Here is a simple scenario where Object A and Object B cross past each other on an x-axis (for simplicity sake, let's just assume that they somehow passed each other on one spatial dimension). As they cross past each other, a photon gets released in the positive direction, and then gets absorbed...
Hi,
The quote below has been taken from this article, https://math.ucr.edu/home/baez/einstein/node2.html, which I came across.
The quote doesn't make any sense to me, especially the part in boldface. Could you please help me with it?
This topic has been discussed in the past on this forum, however there is one point that seems to be unclear.
One example of the setup is the following:
The universe is at a stage where all the matter is concentrated in a single black hole, except two spacecraft s A and B that orbit it far...
I cannot find the paper that is referenced here
https://www.nist.gov/publications/why-minkowski-spacetime-non-euclidean
Why Is Minkowski Spacetime Non-Euclidean?
Author(s)
J M. Cronkhite
I have looked here https://aapt.scitation.org/action/doSearch?SeriesKey=ajp&AllField=Cronkhite&ConceptID=...
I have read that non-inertial frames are those, where time is not orthogonal on space. Does it just mean that the speed of light is not isotropic there or does it mean anything else? How can I picture more easily this concept (for space orthogonality I just imagine perpendicularity of one axis...
I have some questions about the space of the rectangle shown in the spacetime diagram. The red and blue lines are world lines of objects at rest with each other.
1) Does the rectangle have an area? (if no please go to question 3)
2) Is the rectangle a 2d Euclidean space? (if no please go to...
On my diagram, a person is traveling in a spaceship to the right in red, which is displayed as a Minkowski diagram . At the origin (0,0) the person traveling travels by a stationary person. And the 2 blue lines are the worldlines of two blue stationary rocks.
But when I try to figure out what...
We derive the most basic laws of physics from several fundamental symmetries (those from Noether's theorems, gauge symmetries, Lorentz symmetry...). But are there any types of spacetime where no symmetries, no matter how fundamental, would be valid? Any special metric, geometry or shape?
I understand the mechanism of defining the curvature of a 2D manifold via triangle. But I don't understand how this works in 3D. Meanwhile, Lawrence Krauss mentioned in his book A Universe from Nothing it does.
How does this work in 3D?
This is my first post so I apologize if i am in error anywhere. I recently had a thought that I have had trouble confirming. Based on the following assumptions.
1.) As you accelerate an object near the speed of light it’s mass increases exponentially.
2.) Mass warps space time.
3.) Spacetime...
Some physicists prefer to explain the problem of conservation of energy in General Relativity by considering the gravitational potential energy of the universe that would cancel all the other energies and therefore the energy in the universe would be conserved this way.
However, many other...
I am stuck deriving the gauge field produced in curved spacetime for a complex scalar field. If the underlying spacetime changes, I would assume it would change the normal Lagrangian and the gauge field in the same way, so at first guess I would say the gauge field remains unchanged. If there...
Hi,
although there is a lot of discussion here in PF, I'd like to ask for a clarification about the definition of 'spatial x direction' in the context of flat or curved spacetime.
Consider a set of free-falling gyroscopes (zero proper acceleration) passing through an event A with different...
Gamma is a Minkowski spacetime diagram generator. I probably started this project in August and have been working on it almost full-time since. It will be a free, open-source application.
The program can draw all the usual things: axes, grids events, and worldlines, etc.
It's easy to create...
i do not know if the question about entangled particles has found mainstream answers;
Suppose that pairs of maximally entangled particles are shared by Bob and Alice in a time independant gravitational field. Bob measures the spin in the direction of far fixed stars. There is a direction in...
Hi,
reading Carrol chapter 5 (More Geometry), he claims that a maximal symmetric space such as Minkowski spacetime has got ##4(4+1)/2 = 10## indipendent Killing Vector Fields (KVFs). Indeed we can just count the isometries of such spacetime in terms of translations (4) and rotations (6).
By...