What is Special relativity: Definition and 1000 Discussions
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.
So from particle 1 scattering in all directions with equal probability in the CM frame, I believe that that means probability of finding particle 1 in an angular range ##d\theta## is just ##\frac{d \theta}{2 \pi}##. Let P(E') be the probability density of E', so from the probability of finding...
I'm having a discussion with a friend/family member about a paper by Radwan Kassir in which he calculates the distance traveled by a muon (atmosphere thickness) in a non-standard way that shows the atmosphere thickness in the muons frame (L') is γ times the atmosphere thickness in the Earth...
In the left point of view the bar is approaching at 0.8c and the other space ship at something very near c (Einsteins velocity addition rule). To reach the left ship the other ship has to bridge double the distance of the bar with less than double the speed of the bar. Therefore they meet right...
Hi, starting from a recent thread, I'd like to discuss a point related to the Lorentz transformation of EM Faraday tensor field between inertial reference frame.
As explained in this video at minute 11:20, in the Lab inertial frame there is only a magnetic field B in the region surrounding the...
In the context of SR we know time dilation is basically the rate of change of moving clock's proper time w.r.t. the inertial frame coordinate time. It does mean that in principle the "tick events" of moving clock are compared against the time measurement of clocks Einstein's synchronizated in...
When scientists measured the position of Mercury in the 18th century, they interpreted the results assuming a Euclidean background, because they did not know general relativity. So they measured r and φ in fuction of time attributing to these coordinates an Euclidean meaning, that is, assuming...
How should I approach this problem? My first thought was to subtract the velocity of the second proton from the velocity of proton going upwards. However, the velocity vectors are perpendicular to each other, therefore I cannot use the SR velocity addition formula.
Hi, I was thinking about the following.
Suppose we have a geometric mathematical model of spacetime such that there exists a global map ##(t,x_1,x_2,x_3)## in which the metric tensor is in the form $$ds^2 = c^2dt^2 - (dx_1)^2 + (dx_2)^2 + (dx_3)^2$$ i.e. the metric is in Minkowski form...
I am a long-retired physics lecturer, with the bulk of my lecturing focused on quantum and relativity. I am still active in research. I have completely lost contact with the challenge of explaining this stuff to students, and was curious to see how these challenges are met on this forum, not...
I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they said, and I quote,
This part feels too abrupt for me and I am looking for a more elaborated explanation.
Here is a link to that chapter.
I was going through Spacetime Physics by Taylor and Wheeler and came to a point where they showed a proof of Invariance of Spacetime Interval. You can find the proof Here and Here is the second part of that proof.
They used an apparatus that flies straight "up" 3 meters to a mirror. There it...
I cannot get the following out of my head. Suppose this situation. Three frames, with varying velocities, simultaneously intersect their origins at the same time and place, making this point and time x0=0 and t0=0. These frames... let's call them observers. These observers have an agreed upon...
TL;DR Summary: Solving a problem regarding a train going past a station using length contraction and the Lorentzian transformation.
I'll dive straight in. I encountered a problem where there is a train travelling at 0.6c going past a station, length 500 m when measured by an observer at rest...
I'm doing special relativity in undergrad and I have the following problem:
Let a particle of mass M travelling at speed ##\beta = 1/2## (##\gamma = 2/\sqrt 3 \ \ c=1##) decay in to two photons: ##A \rightarrow 1+2##
1) Calculate energy and moment of the photons in the reference frame of the...
I am reading Wald's General Relativity and just did problem 2.8(b). The result I get is ##\omega^2(x'^2+y'^2)-1## as the coefficient for ##dt^2##, and I am wondering about the physical significance of when ##x'^2+y'^2=\frac{1}{\omega^2}##, what would this mean?
Mads
This semester, I'm taking a class on Observational Astronomy which requires us to perform observations for a final project over the course of roughly a month (mid-March to Mid-april, although it could be a bit longer or shorter). As we get to choose the project, I'd like to take this opportunity...
Hello
I have not posted here for a while, but just wanted to post this puzzle I devised. Was posted on Reddit, but no takers. I think the solution is interesting.
The Puzzle
You are flying around in space and you see your friend Steve chilling in an inertial frame in his own spaceship and you...
Hi all,
I've been going over some special relativity as it's a topic I never really studied during my younger years and wanted to get to grips with it, especially since it's such a fundamental part of our understanding of the cosmos.
I was reading about Einsteins train lightning thought...
Common interpretation is that time slows down at lower potential. I wonder if people are simply saying for the time interval between two events at lower potential, it's smaller than what would be measured at greater potential ##d \tau < d t##. i.e. Clock at lower potential shows a time interval...
Quite simple question. There are two planets A and B, they are 4 light years apart measured by tom on planet A. Say both A and B remain stationary. Mary flys 0.8c to tom on planet A. When she passes planet B she should see Tom or planet A 2.4 light years away, am I correct? What about tom now...
I'm currently studying the covariant formulation of electromagnetism for a research project I'm doing and I'm a bit a stuck on how to perform the 3+1 split of the Electromagnetic Field Tensor and Maxwell's Equations.
I understand that a 3+1 split of a four-vector consists of separating the...
I'd like to perform an experiment that will build intuition for Special Relativity in the real world. While I do believe that it occurs in the real world, I'd like to be able to prove it for myself, and I feel that such an experiment would help others on this forum as well. Is there an...
As far as I know, something like relativistic mass is just a concept, just a trick, there is nothing like the relativistic mass. When I move faster, I have higher kinetic energy, but my mass is still the same as if I was at rest. Kinetic and potential energies do not increase object's mass.
A...
In https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_University_Physics_(OpenStax)/University_Physics_III_-_Optics_and_Modern_Physics_(OpenStax)/05%3A__Relativity/5.06%3A_The_Lorentz_Transformation
First, the equation (5.6.7) apparently has a typo: the x' should not be in the...
Since energy is conserved and the particle is initially at rest, we can determine that ##E(0) = m_0 c^2##, so
$$
m_0 c^2 = \sqrt{ c^2 p^2 + m_0^2 c^4 } + \alpha x.
$$
Squaring this eqation gives
$$
m_0^2 c^4 = \alpha^2 x^2 + c^2 p^2 + m_0^2 c^4 + 2 \alpha x \sqrt{ c^2 p^2 + m_0^2 c^4 }...
Let me preface this by saying that I do not claim to dismantle relativity.
That said, in reading the Feynman I came across an ideal experiment that is not entirely clear to me. The context is the usual two spacecraft moving at relatively constant speed. With the reasoning I give below Feynman...
In a previous post, I investigated a wrong way to synchronize clocks in a single inertial reference frame.
Here is a correct way
An alternative would be
A few observations
1) These methods all place clocks at specific locations and synchronize them using signals (namely, light). This is a...
I'm going to go step-by-step through the reasoning. If there is any mistake, then it is a true mistake because I am trying to make each statement that follows as accurate as I can.
Unambiguous time scale in a single frame of reference.
Consider that we have two inertial frames of reference, 1...
I have always had certain difficulties in correctly understanding the theory of special relativity; I often apply it to certain situations and they fall apart...
Imagine there is a rectangular object placed with its long sides parallel to the ground and its short sides perpendicular to it...
So I've often heard that when GR is applied to the entire observable universe to calculate its curvature, we get a value of zero, meaning that the entire universe is flat. I've got 2 problems with this.
The first is that I thought GR was a local theory i.e. it only applies locally. Trying to...
I have a question about the concept of length contraction.
The black line from (0, 0) to (1, 0) represents a meter stick in my stationary frame, call it frame A. The blue axes represent my coordinate system with coordinates x and t.
The green axes represent the coordinate system of a moving...
Susskind's book "Special Relativity and Classical Field Theory" derived the Lorentz transformations
$$x'=(x-vt)\frac{1}{\sqrt{1-v^2}}$$
$$t'=(t-vx)\frac{1}{\sqrt{1-v^2}}$$
$$x=(x'+vt')\frac{1}{\sqrt{1-v^2}}$$
$$t=(t+vx')\frac{1}{\sqrt{1-v^2}}$$
While redoing the calculations, I reached a...
I am following the book "Special Relativity and Classical Field Theory: The Theoretical Minimum" by Susskind.
I want to go through a sequence of ideas to try to understand simultaneity.
We have a rest frame A and a moving frame B along the x-axis.
Let the coordinates be ##x## and ##t## in...
Hey,
What is meant by Coulomb gauge not being Lorenz invariant?
The Coulomb gauge is just a constraint on \mathbf{A} and \phi and thus it is independent of inertial frame.
I posted the question in the wrong section. This question is in the context of QFT. The notes says:
A disadvantage of...
In the mental experiment of special relativity (which has been experimentally proven anyway), in which it is shown that for the traveler on the spaceship, time passes more slowly because the clock (the tick-tock of light beams) goes slower... What is the correlation between the traveler's...
For quite a while I thought that time dilation was the effect of bodies moving close to the speed of light dilates the passage of time.
I also have read about red shift, which seems to be the same thing, though I’m sure they are totally different.
I learned in special relativity (the time...
[Moderator's note: Thread moved to relativity forum as it is not a specific homework problem but a general question about SR.]
Homework Statement: While studying relativity, a question arose for me about time intervals measured by stationary and moving observers. In particular, one of the...
Let's assume Dark Flow is real.
If so can't we measure it based on 2 atomic clocks.
Dark Flow occurs presumely in a southerly direction.
One atomic clock must start at the time the earth's rotation begins to bring the first atomic clock in a slightly southerly direction, (due to the earth's 23.4...
Hi all,
Recently I've tried to wrap my head around a common explanation of magnetic fields that you see online, especially among science educators like veritasium or minute physics.
The setup is as follows: there is a wire, composed of the same number of negative charges (electrons) and...
I considered example of time dilation with light clock. I have a question about measuring time in reference frame with clock.
If we know that clock move from A to B in the reference frame with clock then what time of motion is measured in this reference frame? (In non-moving reference frame...
If we have an observer that is accelerating in one direction (perhaps a rocket ship accelerating towards the sun), would its reference frame be identical to an observer at the same point that is not accelerating, but has the same instantaneous velocity? In other words, is an accelerating...
Here is a screenshot from Einstein's 1905 ELECTRODYNAMICS OF MOVING BODIES:My understanding is that here Einstein says that the rod, the 2 observers and the 2 clocks are in the moving system, one observer & clock at each end of the rod. From their point of view they are not moving. They can very...
Full disclosure: I have asked this question on stackexchange too, but I think I didn't frame my question properly there, which probably led to misunderstandings and complicated answers. Plus some comments there led me to refine the question a bit so I hope it's in a good state now.
I am new to...
I was reading Einstein's Simple Derivation of the Lorentz Transformation which is Appendix I in his book Relativity: the Special & the General Theory. (Online copies can be found at Bartleby's and the Gutenberg Project websites.) I came across an interesting but confusing result by using the...
The ship left Earth at a speed of 0.5c . When the distance between the ship and Earth was 0.25 light year, a terrorist was caught on Earth who said that he had planted a bomb at the time of departure and activated it for 10 months. At that moment, a warning signal was sent from Earth.
The...
I'd like to understand how to obtain equation (2) below.
**My question is how to obtain (2)?**
**Here is my attempt to answer this question (which runs into an obstacle)**
Suppose we have a telescope on earth with air inside the tube (instead of water) and around the telescope.
Consider...
Recollections of a late Spring semester's lesson describing the derivation of Lorentz's Transformation often solicit many unanswered questions. The textbook used has been secured; however, it is unknown. Whether, that secondary school instructor provided the premises used for the derivation from...
A large disk rotates at uniform angular speed ##\Omega## in an inertial frame ##S##. Two observers, ##O_1## and ##O_2##, ride on the disk at radial distances ##r_1## and ##r_2##, respectively, from the center (not necessarily on the same radial line). They carry clocks, ##C_1## and ##C_2##...