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.

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  1. L

    Relativistic Dynamics Problem - Reference Frames

    Homework Statement Two images are attached. The first image details the problem. The second image has an x',y' coordinate system depiction of the problem. Homework Equations The total energy of a particle is defined as E = mc^2, with m = γ*m_0. The Attempt at a Solution If the x', y'...
  2. zehkari

    Relativistic momentum of two photons from a decay

    Homework Statement Homework Equations (1) E2 = p2c2 + m02c4 (2) E = γm0c2 (3) E = Eγ1 - Eγ2 (4) p = E / c (5) E = hf (6) λ = c / f The Attempt at a Solution a) Using eqn (1), rearranged p = (E - m0c2) / c , I obtained 2.9 MeV c-1. Not sure if I have the right answer here as I...
  3. M

    B Special Relativity & Acceleration: Unequal Inertial Frames

    Given that one or both inertial frames must have been subject to acceleration at some point; resulting in an imbalance of application between the two inertial frames, why does the consequential effect of general relativity not feature in calculations. Surely, as such, neither observer's...
  4. S

    I Escape Velocity: Newtonian vs Relativistic

    Hi, Do we obtain the same escape velocity equation: Ve = sqrt(2GM/r) using both Newtonian and Relativistic approach?
  5. J

    B Basic Lorentz transformation derivation

    The Lorentz transformations are mathematically simple. I had always imagined they could be easily derived. I however just found out from another PF thread that this is not so. Their originators Lorentz and Poincaré simply stated them without derivation. And the "proofs" I have seen to date have...
  6. N

    I Motion of Null, Timelike & Spacelike Particles

    For a null particle, ds^2 = 0, Timelike, ds^2 >0, spacelike, ds^2 < 0, how would you characterize the motion of each particle?
  7. N

    Best books for special relativity?

    Hello everyone, I'm studying physics as an undergraduate and I'm currently taking the course special relativity. But sadly I'm not too big a fan of the book we are using for the course. So I was wondering what are the best books you know of regarding special relativity for undergraduates.
  8. P

    B Math-Based Time Dilation Paper: Seeking Suggestions

    I'm writing a mathematical paper on time dilation. Does anyone have any suggestions on how to incorporate math into the topic? I'm considering applying a Loedel diagram. The emphasis needs to be on the math, and not the physical aspects, though they can be introduced through the use of math. The...
  9. lomidrevo

    SR: magnitude of a particle's 3-momentum

    Homework Statement We observe an experimentalist moving by with 4-velocity ##u^\mu## and a particle zipping by with 4-momentum ##p^\mu##. Show that magnitude of the particle's 3-momentum as seen by the experimentalist is given by $$ |\vec p| = \left [ (p \cdot u)^2 + (p \cdot p)^2 \right ]...
  10. CDL

    Einstein Velocity Addition for a Moving Charge in a Wire

    Homework Statement I am reading through Griffiths' Electrodynamics, and I have come to the scenario in the Relativity chapter where in an inertial reference frame ##S##, we have a wire, with positive charges (linear density ##\lambda##) moving to the right at speed ##v##, and negative charges...
  11. zox00

    I Deriving Lorentz from time dilation and length contraction

    Is it possible to derive the Lorentz transformation from time dilation and length contraction? If so, how should I start? I know how to derive it while considering 4 scenarios finding values of A, B,D,E in x'=Ax+Bt t'=Dx+Et and the transformation is: x'=(x-vt)/sqrt(1-v^2/c^2)...
  12. A

    I Visual effect in special relativity

    I have an exercise: A distant camera snaps a photograph of a speeding bullet (speed v) with length b in its rest frame. Behind the bullet and parallel to its path is a meter stick, at rest with respect to the camera. The direction to the camera is an angle $\alpha$ from the direction of the...
  13. F

    I Get Relation from Stress-Energy Tensor Def.

    Starting from the following definition of stress-energy tensor for a perfect fluid in special relativity : $${\displaystyle T^{\mu \nu }=\left(\rho+{\frac {p}{c^{2}}}\right)\,v^{\mu }v^{\nu }-p\,\eta ^{\mu \nu }\,}\quad(1)$$ with ##v^{\nu}=\dfrac{\text{d}x^{\nu}}{\text{d}\tau}## and...
  14. Jonathan Stanley

    B Special Relativity Self-Contradiction?

    From his original thesis, Einstein said light speed is always constant (c). There is very clear evidence for this. Every ray of light moves in the “stationary coordinate system” with the same velocity c, the velocity being independent of the condition whether this ray of light is emitted by a...
  15. J

    Should I use time dilation or length contraction?

    1. Homework Statement [/B] This is a problem that was in my Physics HW. Two powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially ## 2.52 × 10^{12} ## m apart as measured by Liz, an Earth observer, as shown in Figure P1.59. Both...
  16. E

    B Momentum in special relativity

    Although I thought that I understand special relativity enough, I cannot now clearly answer on the following question: What is the most direct derivation, why momentum in special relativity is ##p=\gamma m v##, where ##v## is velocity of the rocket? Let us assume that Lorentz equations are...
  17. Jazzyrohan

    I Einstein's Equivalence Principle: Freely Falling Local Frames

    Einstein's equivalence principle states that: The sets of inertial frames in the real world that correspond to (portions of) the ideal set of inertial frames discussed in special relativity consist of freely falling local frames. In other words,can we say that since all the local frames are in...
  18. P

    SR - Time dilation, space-time diagram, and radio signals

    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 =...
  19. F

    Show that a matrix is a Lorentz transformation

    Homework Statement Given the matrix $$ \Omega = \begin{pmatrix} 0 & -\psi & 0 & 0 \\ -\psi & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix}$$ show that ## e^{\Omega}## is a Lorentz transformation along the x-axis with ## \beta = tanh(\psi)## Homework Equations During the lesson we...
  20. J

    What are Joe Bigler's interests and background in physics?

    Hello, I graduated from Penn State in 1986 with a B.S. in Physics and a minor in Electrical Engineering. My interests are in Special and General Relativity. I also very interested in finding ways to teach and explain physics to the general public. Joe Bigler
  21. P

    Relative velocity in special relativity

    Homework Statement Imagine we are observing two aeroplaes from the ground and let their velocities be ##\mathbf{u}## and ##\mathbf{v}## respectively. Assume that the first plane has radar equipment permitting a measurement of the speed of the other plane relative to itself. The velocity so...
  22. Jazzyrohan

    I No Ultimate Speed: Exploring Relativistic Effects

    Would there have been any relativistic effects if there was no ultimate speed?
  23. R

    When Will We Arrive? Calculating Time Differences in Special Relativity

    Homework Statement : You are the first astronaut aboard a ship to travel to Alpha Centauri. Coincidentally, a scientist working on an outer space station post is one of your former classmate. Your ship, with your former classmate onboard, leaves the space station traveling at constant velocity...
  24. Jazzyrohan

    I Time Dilation Explained: Feynman Lectures 15-4

    Feynman Lectures 15-4 Transformation of time first para http://www.feynmanlectures.caltech.edu/I_15.html How is it possible that the moving clock slows down and also shows more time elapsed to the man outside?
  25. Jazzyrohan

    I What is the physical cause behind time dilation?

    Time dilation can be shown mathematically but what is the physical phenomenon due to which it occurs?
  26. V

    B Special relativity - frame of reference

    This must be a basic question. :) Bob and Alice have the same age. So in special relativity Bob leaves Alice and travels at very high speed and when it returns is younger than Alice. Bob's time is dilated and his space is contracted from Alice frame of reference. But now, if I take Bob's frame...
  27. C

    I Derivation of Rindler Metric and How It Resolves the Twin Paradox

    From what I have read the twin paradox can be resolved with the Rindler metric and without the need to bring in general relativity. Special relativity will suffice. But how does the Rindler metric get derived in the context of a constant accelerating reference frame. I haven't seen anything in...
  28. S

    B Using SR & Curved Coordinates for Time Calculation

    Someone told me that I don't need the whole mechanics of GR to be able to calculate the proper time in an accelerated frame of reference. I can just use SR but with curved coordinates and then integrate for time. But he didn't give me a reference where I could find the formula to do this. How do...
  29. P

    Classically communicate information faster then light?

    Where in this though-experiment do I get it wrong? Even though no mass can travel faster then c, maybe information can? And I'm not talking about quantum entanglement etc. Consider a pipe, filled with balls that are very tightly arranged. If I push the outermost ball on one side of the pipe...
  30. M

    B Help with constant acceleration under special relativity

    Hi, I am trying to wrap my brain around special relativity equations but I'm struggling with the math. I am a computer programmer comfortable with the algebra and but never studied calculus or physics. Say I am already traveling at velocity "v" where "v" is approaching the speed of light. I...
  31. 4

    I Measuring Time with Mirrors: Exploring Special Relativity

    Special relativity is replete with examples of turning mirrors into clocks. Place two mirrors across from one another, bounce light between them, and measure the time. But as I thought about this, when a photon hits the mirror, it is absorbed by an electron which moves to a higher energy...
  32. N

    I Exploring the Paradox of Relative Truth in Special Relativity

    As I understand it with an orthodox interpretation of Special Relativity, if in flat space there was a velocity difference between two inertial frames of reference, then observers in either could calculate the clocks in the other to be going slower. And it could be said that both views are...
  33. Q

    I Difference Between T_{a}^{b} & T^{a}_{b}: (1,1) Tensors

    What is the difference between ##{T{_{a}}^{b}}## and ##{T{^{a}}_{b}}## ? Both are (1,1) tensors that eat a vector and a dual to produce a scalar. I understand I could act on one with the metric to raise and lower indecies to arrive at the other but is there a geometric difference between the...
  34. B

    I Differential equation from derivative of time dilation

    Hi all! I was messing around with the equation for time dilation. What I wanted to do was see how the time of a moving observer ##t'## changed with respect to the time of a stationary observer ##t##. So I differentiated the equation for time dilation ##t'## with respect to ##t##: $$\frac {dt'}...
  35. maajdl

    I Any database of results for the Michelson-Morley Experiment

    Hello, I would be interested in a collection of experimental data for the Michelson-Morley Experiment . I would like to see if there would be many data available, and if a statistical analysis could be of some fun. Would you know some compilation of data? Thanks, Michel
  36. S

    I C Speed, Gravitational Time Dilation & 4-Velocity

    Hi 1-)If an object's total velocity through space-time(four-velocity)is c, for example even we stand still we move with velocity c (through time) and if mass slows down time, can we say mass also increase our velocity in space? 2-) Is Four-velocity magnitude constant in General Relativity...
  37. RealKiller69

    Special relativity and Lorentz factor problem

    Homework Statement There are 2 particles(1,2) separated ∆x=L moving with the same velocity u_x in frame of reference S , there's an other reference S' moving at v . I have to calculate ∆x'. GAMMA(LORENTZ'S FACTOR) Homework EquationsThe Attempt at a Solution I have done x1=0 when t=0 So for...
  38. Philip Dhingra

    I Feedback Requested: Special Relativity Simplified by Phil

    I took a stab at simplifying Special Relativity, but I want to be 100% sure I'm not butchering physics in the process. Anybody care to weigh in on that? Here is a draft of my Medium article: https://medium.com/@philipkd/special-relativity-explained-with-a-deck-of-cards-f99bfd873bd5 Thanks, - Phil
  39. M

    I SR Time Dilation in Rigid Structure Clocks

    Special relativity says that all clocks will show same time dilation, irrespective of clock mechanism. But Time period of a clock is a formula that must continue to hold even if time dilates. Let us look at a tuning fork clock. Here time period depends on the dimensions of the vibrating...
  40. K

    I Consequences of light moving in a medium

    I'm reading Special Relativity by TM Helliwell and in it he describes the second postulate and the fact that moving with respect to air changes the speed of sound, and that because light doesn't need a medium it's speed is constant. I remember my physics teacher saying that light itself(EM...
  41. P

    B Layman's Question about Special Relativity

    I'm just an undergraduate with a layman's interest in Physics. With regards to special relativity, I think I grasp the concept that the laws of physics are the same for all observes in uniform motion relative to one another. So if I am standing still and a spaceship zooms past me at 80% the...
  42. P

    I Understanding the Relationship Between Energy and Momentum in Special Relativity

    In Special Relativity, we have the four vector, (E/c, px, py, pz). However, isn't the first term just `p` given that `E=pc` for a photon? Why is it an energy-momentum four vector when the first term isn't really energy but momentum?
  43. Cocoleia

    Momentum dealing with decay, special relativity

    Homework Statement A particle A (mother particle) with a mass of mA decays to two particles B and C (daughter particles) with mass values of respectively mB and mC. Calculate momentum of the two daughter particles, pB and pC. (at first the mother particle is at rest) Homework Equations The...
  44. alejandromeira

    Special Relativity Exercise (A.P. French)

    I just solved an exercise in the special relativity book of A.P. French. I would like you to tell me if the answer is correct. Yes I suposse is a very easy exersice. I hope you can help me, because I really like learn relativity and cosmology, but I have not had teachers of this, and I am...
  45. dRic2

    Electromagnetism and special relativity

    Hi I just saw this video . Here it's said that that electromagnetic force is just a consequence of special relativity, but I don't get the explanation. According to the video the electromagnetic force is generated by relative motion of charges, so it is essentially an electric force. It doesn't...
  46. Felipe Prado

    I Fizeau's Exp: TRANSFORMING VELOCITIES to Explain

    In 1851 Fizeau made a famous experiment which corroborated de Fresnel's drag coefficient of the luminiferous ether. In the experiment two light beams traveled through a tube of moving water (at 7cm per second), one moving against the water flow (let's called it beam A), and one for the water...
  47. N

    I Does a blueshift change the energy of a photon?

    The energy of a photon depends on its wavelength, so theoretically when it is blueshifted it should have more energy right? Then what if a spaceship with a solar panel on the front is traveling towards the sun at relativistic speeds. An incoming photon undergoes a blueshift from the observer on...
  48. BookWei

    I Solving Boundary Conditions in 4D Spacetime Volume

    Hi, my classmate asks me an interesting question: For a finite 4D volume in spacetime, its boundary is a 3D close surface. If the 4D volume is a 4D rectangular, the boundary consists of eight 3D surfaces. The boundary condition is specified on these eight 3D surface. Please explain the physical...
  49. G

    Time Dilation for Moving Rectangle with Clocks at its Corner

    Homework Statement A rectangular structure carries clocks at its four corners. The clocks are synchronized in the structure’s rest frame, in which it has length L =4ft and width W = 3ft. In our laboratory frame the rectangle is moving in the positive x direction at speed v = 0.8c. As the clock...
  50. Jan Nebec

    B Is it Possible to Know Which Object is Moving? Special Theory of Relativity

    The Special Theory of Relativity is based on two principles. The first one is, that if you have two objects, then it is not possible to tell which object is moving, and which object is standing still. So someone moving in a spaceship relative to observer, can't say who is actually moving and who...
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