In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates:
The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration).
The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or observer.
This topic assumes special relativity only, so no gravity is involved. I wanted to know how a superluminal thing would appear to an observer, and two of the 'things' I thought of were a moiré pattern and the red dot projected by a laser pointer. The former can be discussed, but this post will...
I have a quick question about the Galilean transform. If I have Alice running and Bob stationary. The Galilean transform will tell me the position of Alice from Bob's stationary position. Also if I have Alice's position which is moving it will tell me Bob's stationary position.
If I want Bob...
@PeroK sent me here based on a discussion starting at https://www.physicsforums.com/threads/some-ideas-on-interstellar-space-travel.1006562/post-6550265.
Summary:
Someone claimed that an accelerated observer's clock (observer at 1g from Earth to halfway to Alpha Centauri, then -1g the rest of...
I'm struggling to wrap my head around the twin paradox in special relativity especially when dealing with multiple vectors.
In my thought experiment say I have a set of twins. Both set out in opposite directions and intend to sling shot around two different black holes(luckily equidistant from...
While deriving Lorentz transformation equations, my professor assumes the following:
As ##\beta \rightarrow 1,##
$$-c^2t^2 + x^2 = k$$
approaches 0. That is, ##-c^2t^2 + x^2 = 0.## But the equation of the hyperbola is preserved in all inertial frames of reference. Why would ##-c^2t^2 + x^2##...
We know that both momentum and position can not be known precisely simultaneously. The more precisely momentum is known means position is more uncertain. In fact, as I understand quantum mechanics, position probability never extends to 0% anywhere in the universe (except at infinity) for any...
I recently trying to learn General Relativity by first scraping the surface on ScienceClic's general relativity playlist, and then I stumbled upon a video where it said that we actually move through spacetime on a constant speed of c, and then I remember about time dilation because how speed on...
Hi, I´m trying to solve a special relativity problem, and I think I need some help. There are two inertial frames of reference, ##O## and ##O'##, the last one moving with relative velocity ##v## in the ##x## direction. There's a rod with length ##L'## fixed to frame ##O'##, such that front end...
> A particle of mass M at rest decays into two particles of masses m1 and m2 travelling in opposite directions at velocity v1 and v2 respectively. Express v2 in terms of v1, m1, m2, and M.
Since both objects are from a single object that's why I took relativistic mass of both objects are same...
Summary:: Special relativity and Lorentz Transformations - I got this problem from a first-semester course at university. I have been struggling for a few days and decided to get some help.
A rocket sets out from x = x' = 0 at t = t' = 0 and moves with speed u in the negative x'-direction, as...
I am reading pretty much everywhere that LET (Lorentz Ether Theory, or call it Neo-Lorentzian Relativity, or whatever theory that involves a preferred undetectable frame with some yet unknown properties that make all the moving objects with respect to this frame length contact and time dilate)...
I am new here, so pardon my ignorance.
First of all, I am aware of the impossibility to distinguish experimentally between SR (Special Relativity) and LET (Lorentz Ether Theory). I know there is a PF policy article on LET and the Block Universe.
I must admit though that LET is more appealing...
If a person was rotating on a verticle axis from head to toe like the earth or quasar. If nothing can go faster than light, from the person's perspective looking at the stars traveling across the night sky, if you increase the rotation of the earth, stars further than a certain critical distance...
Hello everyone,
I have a hard time to conceptualize the case of a moving black hole.
We know from SR that time slows down for moving objects; but time dilation at the event horizon is already equal (tends) to zero. It seems that it can create some sort of conflict for the black hole movement...
Hello everyone. I have just complete an experiment calculating the speed of a muon. I got it to 2.6E8 m/s, however I know that they are created at close to speed of light to be able to get down to earths surface in their short lifespan. This speed could not have been its initial speed, as it...
Some introduction books on Lagrangian and Hamiltonian mechanics use classical mechanics as the theoretical framework, and when it come to special relativity it goes back to the basics and force language again. I would like to ask for some recommendations on good books that introduces Lagrangian...
I'd like to get some help on checking my understanding of special relativity, specifically I'm trying to clarify the idea of coordinates. Any comment is really appreciated!
The spacetime is an affine space ##M^4##, which is associated with a 4 dimensional real vector space ##\mathbb{R}^4##...
Why is time = ct and not t in special relativity?
I just started reading the book I was recommended. Maybe I missed it but as stated in the title why is time = ct and not t in special relativity?
I understand they want distance/space = time. Just how do they go about doing that...
Hello everyone, Im preparing to write an exam project in college about special relativity, however i am missing the critical experiment to prove that it is true. I thought about using the life time of muons, but i dont have a scintillator to detect them, so unless a standard geiger counter works...
I recently had a discussion with my brother, about what it means to "move through time". His opinion is, that physicists cannot take this literally. His opinion is, that time is just an expression for change that takes place at different rates for different observers depending on their speed...
I drew the Minkowski diagram, but I'm not sure if this is correct.
From what I drew the angle between x and ct ##\approx 0##
then the event is "inside" the light ray and will eventually reach A.
I want to learn special relativity.I have read a tiny bit of 2nd edition of Spacetime Physics: Introduction to Special Relativity and am liking it. Is it a good book? I also want problems to solve. I tried Special Relativity: For the Enthusiastic Beginner but found it to difficult. Does anyone...
I have seen the "Hafele-Keating with the plane as reference frame?" thread (https://www.physicsforums.com/threads/hafele-keating-with-the-plane-as-reference-frame.767913/ ), but the replies do not seem to explain (to me anyway) what when taking a plane as a reference frame, balances the slowing...
I'm reading a book called "Reality is not what it seems: the journey to quantum gravity" by Carlo Rovelli and I'm struggling to understand this diagram that is part of the chapter about special relativity.
https://i.stack.imgur.com/JgBDJ.jpg
Before this image Rovelli writes:
"It's not...
While I am working through proving the homework statement, I encountered a problem. The problem is as follows:
From the energy equation above, one can see that the minimum value of ##p## is ##m_T##. However, how does one explain why when ##p=m_T##, ##\sqrt{m^2_B+m^2_T}>m_A##?
According to this link here https://en.wikipedia.org/wiki/Relativistic_mechanics#Force , we can inverse the relation of force in terms of velocity and acceleration:
$$
\mathbf{F} = \frac{m\gamma^3}{c^2}(\mathbf{v} \cdot \mathbf{a})\mathbf{v} + m\gamma\mathbf{a}
$$
to get:
$$
\mathbf{a} =...
If there is a spaceship traveling at 0.999c, the time to reach a star 100 lyr away would be approx 100 yr (assuming no accel and decel). But on the spaceship, It would be 100 yr * sqrt(1-0.999^2) = 4.5yr.
Why do we take 100 yr as the time seen on Earth and not the time on the spaceship?
Summary:: Require confirmation regarding answers to a question posed by the book "Basic Relativity" by Richard A. Mould.
Here is a problem which I encountered while going through Basic Relativity by Richard A. Mould-
I'd like to receive a confirmation regarding the answers I've come up with to...
I came across an interesting question in the Hartle's textbook, "An Introduction to Eisntein's General Relativity". The question is as follows:
Explain why a photograph of an object moving uniformly with a speed approaching the speed of light, parallel to the plane of the film appears not...
Hi All,
I've been doing some reading on the above but having some problems understanding certain parts of it (maybe it's wrong from Wikipedia!) To simplify it for me I will first pose a simple scenario where we are not factoring in speed yet, then go from there.
Say we have two planets A and B...
[Moderator's note: Spin-off posts from previous thread have been included in this new thread. Also, the OP's re-post of the scenario for discussion has been moved to this top post for clarity.]
Yes.
Physically, scales measure a force (and indirectly the energy) in their frame. Consider the...
Hi,
I've a doubt about the application of the principle of relativity as follows.
Assume as principle of relativity the following statement: It is impossible by any experiment performed inside a "closed" laboratory to say whether we are moving at constant velocity or staying at rest.
Consider...
Velocity is a 4-vector which has 3 space dimensions and 1 time dimension. It's space parts will be directed at the 3 space directions and time parts will be directed at the time dimension (But it is inverse. So, will it point at the inverse direction?). How can someone Visualize it? How they...
Why momenergy has magnitude equal to the mass?
> The mom-energy of a particle is a 4-vector: Its magnitude is proportional to its mass, it points in the direction of the particle's spacetime displacement, and it is reckoned using the proper time for that displacement. How are these properties...
Hey dear physics community :)
I ask myself what exactly happens to forces between materia when the materia hits near lightspeed.
I know, that for an objective bystander watching lets say elon in his rocket with 99,99999% the speed of light, that the time goes slower, the mass of the rocket...
Assumptions
1. General Relativity is the modern and most complete widely accepted theory of gravitation, formulated in a background independent, geometric way.
2. General Relativity is formulated in a manner consistent with Special Relativity and I could imagine that it might be possible to...
The information I have are the following:
##p^\mu=(E, p, 0, 0)##
##p'^\mu=(E', p'\cos\beta, -p'\sin\beta,0)##
##k^\mu=\tilde{E}(1, \cos\alpha, \sin\alpha, 0)##
Where:
##E=\sqrt{M^2+p^2}##
##E'=\sqrt{m^2+p'^2}##
Using the conservation of the four-momentum
##p^\mu=p'^\mu+k^\mu##...
Consider an observer on Earth (Neglect any effect of gravity). Call him A. Let 2 rockets be moving in opposite direction along x-axis (x-axis coincides with the x-axis of A) with uniform velocities. Call them B and C. At t=0, in A's frame, the rockets are separated by length ##l## . Let ##V_a##...
First I wrote in ##S'##, by using Gauss theorem
$$
\int_{\Sigma} \underline E' \cdot \hat n d\Sigma = \frac Q {\varepsilon_0} \rightarrow E'(r)2\pi rH=\frac{\lambda'H}{\varepsilon_0}
$$
$$
\underline E'(\underline r)=\frac{\lambda'}{2\pi\varepsilon_0r}\hat r
$$
Its components are...
Homework Statement:: This isn't a homework but more of a conceptual question.
Relevant Equations:: Proper time, ##\tau##
Simply put, the proper time between two events as observed in an unprimed frame is calculated along the timelike worldline between the two events. This implies that the...
As widely separated particles within a large enclosed space are differently affected by the nonuniform gravitational field of Earth, to use the Newtonian way of speaking, two particles released side by side are both attracted toward the center of Earth, so they move closer together as measured...
In Minkowski spacetime, calculate ##P^{\gamma}_{\alpha}U^{\beta}\partial_{\beta}U^{\alpha}##.
I had calculated previously that ##P^{\gamma}_{\alpha}=\delta^{\gamma}_{\alpha}+U_{\alpha}U^{\gamma}##
When I subsitute it back into the expression...
Hi,
I'm a 15-year-old highschool student and I was wondering what textbook you guys recommend for Special- and General Relativity. I'm familiar with the concept of the Metric Tensor and Christoffel Symbols, but I wanted a good textbook where I can really learn derive it all and gain a deeper...
Deriving time dilation was easy:
Imagine two events in frame O' at the same location.
##ds^2 = -c^2 dt'^2##
The same viewed in O frame is:
##ds^2 = dx^2+dy^2 + dz^2 - c^2 dt^2##
##\Rightarrow dx^2+dy^2 + dz^2 - c^2 dt^2 = -c^2 dt'^2##
##\Rightarrow (\frac{dx}{dt})^2+(\frac{dy}{dt})^2+...
I was trying to show that the field transformation equations do hold when considering electric and magnetic fields as 4-vectors. To start off, I obtained the temporal and spatial components of ##E^{\alpha}## and ##B^{\alpha}##. The expressions are obtained from the following equations...
Why aren’t all the SR effects cumulative like Time Dilation? Why should the Space dimensional effect become null when v—>0 while the Time dimension does not revert back to the 2 frames being in sync if Space and Time are treated on an equal footing. Clearly, Space and Time are not treated on an...
Hello,
here on PF I've seen many threads about the concepts of 'reference frame' and 'coordinate system'.
In the context of SR my 'envision' about the concept of 'frame of reference' is basically the 'rods & clocks latticework' as introduced in the book Spacetime physics (Taylor, Wheeler)...
Good day. I have read many books, forums, and articles, and watched many youtube videos, all in an effort to understand special relativity and time dilation. Or rather, more precisely, trying to find a valid explanation that does not result in contradictions and paradoxes, and if it does, one...
Special Relativity tells us - the faster things travel their time is slower relative to a stationary observer.
Do massless particles, like photons travelling at the speed of light, experience zero time and in their frame of reference travel "instantaneously".