Special relativity Definition and 1000 Threads

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.

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  1. S

    Infinitesimal coordinate transformation of the metric

    I kinda know how to do this problem, it is just that I hit a sign problem. If I take the partial derivative of the coordinate transformation with respect to ##x'^\mu##, I get writing it first in the inverse form, ##x^\alpha = x'^\alpha - \epsilon^\alpha## ##\frac{\partial x^\alpha}{\partial...
  2. cianfa72

    I Speed of Light in Vacuum in Non-Inertial Frame

    Hi, I read various threads in PF about the concept of invariant speed and the speed of light in vacuum that in our universe happens to be the same as the 'invariant speed'. My doubt is about the speed of the light in vacuum as measured from a non-inertial frame (basically in the context of SR...
  3. LawH

    B Energy, Mass, Speed of Light: Can We Reach It?

    Hello everyone! Let's say that you were to attempt to go as fast as possible on a spaceship with the mass of an average car in an absolute perfect vacuum. What I am wondering is, that if you were to reach a certain speed, and stop applying energy to this imagined spaceship, would the spaceship...
  4. Bob Enyart

    I Do We Need ESC in Earth's Atmosphere?

    Einstein's synchrony convention (ESC) defines the one-way speed of light as equal to the roundtrip speed IN A VACUUM, at least, the discussions and papers I read on it (even Einstein's 1905 paper) always seem to set the context as in space (a near vacuum) or in a (theoretical) vacuum. I'm...
  5. M

    I Where is Contraction Point in Special Relativity?

    Generally speaking, when a simple contraction occurs there is a contraction point. Length contraction in special relativity appears to be a simple contraction, and hence there should be a contraction point. Where is this contraction point located?
  6. M

    I Special Relativity & No Special Inertial Frame of Reference

    As per special theory of relativity, no inertial reference frame is special! If a spaceship is moving at 100 m/s, no one can conduct an experiment to determine whether it is moving at 100 m/s or the rest of the universe is moving to the opposite direction at -100 m/s, if I understand the...
  7. S

    Antisymmetry of the electromagnetic field tensor

    I am trying to answer exercise 5 but I am not sure I understand what the hint is implying, differentiate with respect to ##p_\alpha## and ##p_\beta##, I have done this but nothing is clicking. Also, what is the relevance of the hint "the constraint ##p^\alpha p_\alpha = m^2c^2## can be ignored...
  8. K

    I Special Relativity: Constant Speeds or More Complex GRT?

    I'm reading the online version of a book that says Rindler observer comes right into my mind when I read this. So I think the book is wrong. What do you all think? On a second guess, perhaps the author takes the view that SR is only for constant speeds in the same sense that one could say that...
  9. S

    Contracting one index of a metric with the inverse metric

    Since ##\nu## is contracted, we form the scalar product of the metric and inverse metric, ##g_{\mu\nu}g^{\nu\lambda} = (\vec{e_\mu} \cdot \vec{e_\nu}) \cdot (\vec{e^\nu} \cdot \vec{e^\lambda}) = \vec{e_\mu} \cdot (\vec{e_\nu} \cdot \vec{e^\nu}) \cdot \vec{e^\lambda} = \delta^\lambda_\mu## I...
  10. LeeHilliard

    B Time & Special Relativity: Is Time Object-Specific?

    If time slows as an object increases velocity wouldn't that indicate that time is object specific? And if the speed of light is a constant and does not change regardless of the velocity of an object wouldn't that indicate that time used to measure the speed of light changes? The video I have...
  11. T

    A shot in the dark -- Need help understanding Special Relativity

    first off hi all. Just joined, i was looking for someone to help me understand time dilation and spatial contraction in relativity. its not homework just something i was watching, very good btw, but left me with some contradictory information as i see it. if anyone with any level of expertise at...
  12. KipIngram

    I Struggling with a special relativity "paradox"

    Ok, I hope someone can help me see how to sort this out. Alice has a full-frame (no rolling shutter) video camera that records exactly 30 frames per second. It's mounted to a telescope looking far out into space. Bob is out there in space with a digital clock that reads out to the millisecond...
  13. S

    I Transformation of the contravariant and covariant components of a tensor

    I have read many GR books and many posts regarding the title of this post, but despite that, I still feel the need to clarify some things. Based on my understanding, the contravariant component of a vector transforms as, ##A'^\mu = [L]^\mu~ _\nu A^\nu## the covariant component of a vector...
  14. BadgerBadger92

    I Special Relativity vs Lorentz Transformation: Difference Explained

    What is the difference between special relativity and the Lorentz transformation? Aren't they basically the same thing? Also, I was wondering what about matter makes spacetime curve?
  15. S

    I Electric Field Directly Ahead of or Behind a Moving Charge

    Since it is stated that ##E'_x = E_x##, I am going to set a special case where ##z' = z = 0##, ##E_x## in (5.10) reduces to, ##E_x = \frac{1}{4 \pi \epsilon_0}\frac{Q}{x^2}## However, ##E'_x## in (5.13) reduces to, ##E'_x = \frac{1}{4 \pi \epsilon_0}\frac{Q}{\gamma^2 x'^2}## There is an...
  16. Athenian

    [SR] - Test Particle inside the Sun's Gravitational Field - Part 4

    So, here's an attempted solution: With ##r_{min}##, $$r_{min} = \frac{1}{B + \frac{\beta}{\alpha^2}}$$ With ##r_{max}##, I get: $$r_{max} = \frac{1}{B - \frac{\beta}{\alpha^2}}$$ or $$r_{max} = \frac{1}{\frac{\beta}{\alpha^2}}$$ Other than this, I and the team have absolutely no idea on how...
  17. S

    How Does the Relativistic Rocket Equation Describe Velocity?

    Show that, according to relativistic physics, the final velocity ##v## of a rocket accelerated by its rocket motor in empty space is given by ##\frac{M_i}{M} = \Big ( \frac{c+v}{c-v} \Big) ^ \frac{c}{2 v_{ex}}## where ##M_i## is the initial mass of the rocket at launch (including the fuel)...
  18. Athenian

    [SR] - Test Particle inside the Sun's Gravitational Field - Part 3

    Below, I have already solved - I assume - correctly for question 1. Question 2, I am nearing to what I believe is the solution. Question 3, I simply have no idea where I should begin considering that it is interconnected with question 2. With that said, below is the lengthy and somewhat tedious...
  19. LukasMont

    I Special Relativity Controversy: Solving the Paradox

    Hey guys, My question is a bit confusing: When we observe a train moving close to the speed of light, passing by the platform, according to the frame of reference in the platform, the clocks in the train are ticking slower than the clocks in the platform itself. According to the frame of...
  20. W

    I Getting Used to Killing Vector Fields: Explained

    I'm struggling to get the hang of killing vectors. I ran across a statement that said energy in special relativity with respect to a time translation Killing field ##\xi^{a}## is: $$E = -P_a\xi^{a}$$ What exactly does that mean? Can someone clarify to me?
  21. Athenian

    [SR] - Test Particle inside the Sun's Gravitational Field - Part 2

    To begin with, I posted this thread ahead of time simply because I thought it may provide me some insight on how to solve for another problem that I have previously posted here: https://www.physicsforums.com/threads/special-relativity-test-particle-inside-suns-gravitational-field.983171/unread...
  22. Athenian

    [Special Relativity] Test Particle Inside the Sun's Gravitational Field

    Below is an attempted solution based off of another user's work on StackExchange: Source: [https://physics.stackexchange.com/questions/525169/special-relativity-test-particle-inside-the-suns-gravitational-field/525212#525212] To begin with, I will be using the following equation mentioned in...
  23. S

    How Do Four-Vectors with Orthogonal Dot Products Determine Each Other's Nature?

    Two four-vectors have the property that ##A^\mu B_\mu = 0## (a) Suppose ##A^\mu A_\mu > 0##. Show that ##B^\mu B_\mu \leq 0## (b) Suppose ##A^\mu A_\mu = 0##. Show that ##B^\mu## is either proportional to ##A^\mu## (that is, ##B^\mu = k A^\mu##) or else ##B^\mu B_\mu < 0##. Part (a) is...
  24. P

    Particle decaying into two daughter particles - special relativity

    Right, so I thought I'd done this correctly but clearly not because my velocity is greater than the speed of light, where have I gone wrong? P = (M, 0, 0, 0) p1 = (E1, p1x, p1y, p1z) p2 = (E2, p2x, p2y, p2z) P = p1 + p2 p2 = P - p1 square each side to get (p2)2 = P2 - 2Pp1 + p12 therefore (m2)2...
  25. P

    A moving pi-meson decaying into 2 photons - finding their energy

    I've tried using gammamc^{2} = E1 + E2 but how do i find gamma?? If i try to use the kinetic energy then I just get gammamv^2 = 1gev but i don't know v? very confused
  26. A

    I Does p=mc Apply To Photons? | A.P. French's Special Relativity

    In A.P. French's Special Relativity, the author said the following, As I understand, photons are massless, so I don't think the last equation above applies to photons, but then, when deriving it, he used an equation proper to photons (##E=pc##). So in which context is ##m=p/c## valid?
  27. B

    Special relativity problems — More details below

    [Note from mentor: this was originally posted in a non-homework forum, so it lacks the homework template.] Summary:: Special relativity problems. More details below The formula for speed for special relativity is V = (u-v) / (1-u*v) / (c^2) Here the book...
  28. R

    Collisions in special relativity

    Happy new year, I got very far in this question. I attempted to use conservation of energy first. Ei=(Pfc)^2+mec^2 Where pf is the initial momentum of the photons Ef=(γmec^2)+(pf'c)^2 Then used conservation of momentum Pf=γmvcos(Θ) Pf'=-γmvsin(Θ). After that I added Pf and Pf'. and used...
  29. Saptarshi Sarkar

    I Speed of Light in Inertial Ref Frames: Photon Perspective

    According to the 2nd postulate of Special Relativity, speed of light in vacuum is the same in all inertial reference frames. If I take a beam of photons and see the other photons in the beam from a frame of reference of a single photon, do they look stationary or moving at the speed of light...
  30. N

    B Development of Special Relativity

    I'm interested in the history of thought that led to the discovery of special relativity. Of all the equations in special relativity, e.g. the equation for the invariant interval, the equation for gamma, the Lorentz transformation equations, the equation for velocity addition, etc., which one...
  31. L

    I Momentum and energy calculation in special relativity

    ## \ \ \ \ \ ##In ##K##，System ##M## is composed of a spring ## N ## and four particles ## P, Q, A and B ##. The ends of spring ## N ## are fixedly connected with particles ## P and Q ## respectively. Particle ## A ## is adjacent to particle ## P ##, and particle ## B ## is adjacent to particle...
  32. bos3yed651

    I Exploring Special Relativity: A Pickle in Lorentz Theory

    This is my first thread. I hope I do it right. I just started reading the book Special Relativity by W.Rindler. And as I was reading it, I stumbled upon a pickle. So in Lorentz theory, it says, supposedly we could measure the original to-and-fro time T2 directly with a clock, and suppose we...
  33. K

    I Bohmian mechanics and special relativity

    [Moderator's note: Thread spun off from previous thread due to topic change.] Thanks! I am working on understanding why non-local effects violate the special theory of relativity. I am not there yet, but maybe when I finally get there I will leave the BM train.
  34. Athenian

    I Lorentz Boosts: Finding Speed, Coordinates & Rotation w/ Matrix Multiply

    Recently, I've been studying about Lorentz boosts and found out that two perpendicular Lorentz boosts equal to a rotation after a boost. Below is an example matrix multiplication of this happening: $$ \left( \begin{array}{cccc} \frac{2}{\sqrt{3}} & 0 & -\frac{1}{\sqrt{3}} & 0 \\ 0 & 1 & 0 & 0...
  35. L

    A Solved: Velocity of Isolated System in Different Inertial Sys.

    A problem of an isolated system's velocity in different inertial systems, in special relativity ##\ \ \ \ \ ## In the inertial reference frame ##K##, the velocity of each component of an isolated system in ## x## direction is zero at a certain time. ##\ \ \ \ \ ## The inertial reference frame...
  36. Athenian

    [Special Relativity] Lorentz Transformation and Boosts

    [BEGINNGING NOTICE] Before I begin showing my attempted solution, I would just like to quickly mention that this is a "repost" of the same question I had around a week ago. While I would usually use the "reply" function on the same thread, I believe that thread is getting pretty messy (sometimes...
  37. Athenian

    [Special Relativity] - Finding Angle θ as Measured in Frame S

    Below is the attempted solution after researching the contents available on Introduction to Electrodynamics by Griffith. To begin with, I defined the rod as having a length of ##l'## at rest in frame ##S'##. Thus, in frame ##S'##, the height of the rod is ##l' sin(\theta ')## and its horizontal...
  38. Athenian

    [Special Relativity] Scalar Invariant under a Lorentz-transformation

    "My" Attempted Solution To begin, please note that a lot - if not all - of the "solution" is largely based off of @eranreches's solution from the following website: https://physics.stackexchange.com/questions/369352/scalar-invariance-under-lorentz-transformation. With that said, below is my...
  39. U

    How Can We Generalize the Lorentz Transformation to Two Dimensions?

    Summary: The problem is to generalize the Lorentz transformation to two dimensions. Relevant Equations Lorentz Transformation along the positive x-axis: $$ \begin{pmatrix} \bar{x^0} \\ \bar{x^1} \\ \bar{x^2} \\ \bar{x^3} \\ \end{pmatrix} = \begin{pmatrix} \gamma & -\gamma \beta & 0 & 0 \\...
  40. M

    Special Relativity question using Lorentz Transformation time dilation

    with distance between planets as 4x10^8m measured by you on the ship My attempt: t' = γ(t - ux/c^2) γ = 5/3 u = 0.8c t = 0.9s x = 4x10^8m answer is: -0.278 Therefore not possible My question is what if we traveled rightwards, from p2 to p1, would the answer change? Should my above information...
  41. Athenian

    [University Special Relativity] Lorentz Transformation and Boosts

    Unfortunately, I am not entirely confident of the above equations being able to do the trick and ultimately solve for the question. However, my guess is that using the equation written above for "boost", I could perhaps use ##v## and insert it into the ##x##-direction part of the matrix...
  42. Athenian

    Traveling to Planet X in 23 Years: An SR Challenge

    Homework Statement: Problem: The planet X is far 48 light-years from Earth. Suppose that we want to travel from Earth to planet X in a time no more than 23 years, as reckoned by clocks aboard our spaceship. At what constant speed would we have to travel? How long would the trip take as reckoned...
  43. A

    Lorentz transformation of 4-acceleration

    I have been getting back to studying physics after a long break and decided to go through the problems in Rindler. But there is something I don't quite understand in this problem. To first answer the second part, Exercise II(12), I wrote $$\frac{du_2}{dt} = \frac{du_2}{du_2^\prime}...
  44. dsilvas

    Solving the Mystery: Exploring E << m Condition for Carbon 12 Ions

    Clarification: The statement in the title is actually from the solution to the homework question, as given by the textbook (you can see the whole thing below under "Textbook solution"). The solution doesn't explain everything, which is where my confusion comes from. Usually in my classes we...
  45. Demystifier

    I Special relativity vs Lorentz invariance

    The Lorentz covariance of Maxwell equations was known before Einstein formulated special relativity. So what exactly special relativity brought new with respect to mere Lorentz covariance? Is special relativity just an interpretation of Lorentz invariance, in a sense in which Copenhagen...
  46. M

    Global Positioning System / Clocks in Space

    I'm a bit lost at how to exactly start this exercise... As far as I understand we need to first determine ##d\tau_E## and ##d\tau_S##. First question: Since we can neglect the Earth's movement, can I also neglect the movement of the satellite with respect to the far away observer? If so, I...
  47. M

    How Does Acceleration Transform in Special Relativity?

    I'm struggling in the details of this exercise. Let ##S'## be the reference frame where the acceleration of the spaceship is constant, in which case we have ##u'(t')= a' t'## (since we assume no acceleration at the beginning). The rest frame of the rocket ##S## is connected to ##S'## via a...
  48. alexmahone

    Prove that “leading clocks lag”

    Homework Statement: A spaceship has two clocks: one in the front and one at the back. The clocks are synchronized in the spaceship's frame of reference. The spaceship zooms past the Earth's surface at a relativistic speed. Prove that in the Earth's frame of reference, the clock at the front...
  49. M

    I Special Relativity: 2-D Collisions for Alice & Bob

    Alice and Bob are initially in the same inertial frame. There are 2 point test masses m1 and m2. Initially m1 is at the origin and m2 is on the positive x-axis. At time zero, m1 is instantaneously accelerated to velocity Vx in the positive x-direction. After some time, m1 collides with m2...
  50. M

    I Accel. in Spec. Relativity in 2-Dims: Point Test Mass

    Let m be a point test mass. Initially m has velocity Vy in the poisitive y-direction, and zero velocity in the x-direction. At time zero, m is accelerated in the positive x-direction. In the limit as the time goes to infinity, the velecity in the positive x-direction goes to the speed of...
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