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. A

    B Solving Special Relativity Equation: Rail Car Thought Experiment

    I know that c is the same in all reference frames. I am trying to understand the rail car thought experiment. I've got it down pretty well except for one part - the difference between an observer moving toward a light source versus an observer moving away from a light source at the same...
  2. J

    B Is Special Relativity Universally Accepted?

    Hi pf, When I was taught about SR, I was told it was one of the most successful theories in science and has been verified over and over again. However, I have been watching some videos online and wanted some guidance. I initially came across this: <link deleted> This guy claims to have a PhD...
  3. M

    B Double-Slit Experiment: Exploring SR's Impact on Time

    Special Relativity dictates that if there is relative motion between two objects; their relative experience of time will change and this is measurable at velocities approaching 'c'. Within the context of the Double-slit Experiment (with detection): When a given quantum-duality is detected by a...
  4. K

    Relative velocities in special relativity

    Homework Statement Two spaceships fly toward a space station as shown in the figure. Relative to the station, spaceship A has speed 0.8c. Relative to the station, what speed is required of spaceship B such that its pilot sees A and the station approach B at the same speed? (a) 0.40c (b) 0.50c...
  5. joneall

    B Order of events and cause and effect

    I'm reading "Bang!", by Brian May, Patrick Moore and Chris Lintott. On page 40, they say: "So one [observer] may believe A preceded B by a minute, and another that A and B were simultaneous, it is impossible for any observer to see B preceding A. Hence cause and effect are preserved..." But in...
  6. S

    Forward light-cones and special relativity

    Homework Statement How can we tell that quantum effects do not propagate along forward light-cones that represent two separate events? How do light-cones demonstrate this notion of quantum effects? Homework EquationsThe Attempt at a Solution We don't know which events occur first given...
  7. R

    I Solving Integration by Parts for Relativistic Kinetic Energy

    Hi, I've been following a derivation of relativistic kinetic energy. I've seen other ways to get the end result but I'm interested in finding out where I've gone wrong here: I'm struggling with integrating by parts. The author goes from...
  8. D

    I Special Relativity: Kinetic Energy Expansion and Contradictions

    When expanding Kinetic energy as T=mc2-m0c2 where m0=rest mass and m=m0/sqrt(1-β2) the first term correction is coming out to be -p4/8m03c2 but taking T=E-m0c2 where E=sqrt(c^2p^2+m02c4) the correction is coming to be 3p^4/8m03c2 is there any contradiction?
  9. M

    I Velocity difference not preserved in special relativity

    Consider single line motion. If an observer sees two objects, and one is seen moving say 50 m/s faster than the other, will all other observers measure the same velocity difference? The answer seems to be 'No' from the velocity addition formula of special relativity? Thus same velocity...
  10. S

    I Velocity addition and conservation of the energy

    Hello everyone, For some time I'm a little bit confused about (at the first view) a very simple question, which is about the conversation of the energy of moving objects (in terms of special relativity). As an example let's talk about firearms. If the mass of the gun M1 is infinitely higher...
  11. L

    Electric dipole EM field using Lorentz Transformation

    Homework Statement An electric dipole instantaneously at rest at the origin in the frame K' has potentials \Phi'=\mathbf{p}\cdot\mathbf{r}'/r'^3 and \mathbf{A}'=0 (and thus only an electric field). The frame K' moves with uniform velocity \mathbf{v}=\vec{\beta }c in the frame K. Show that in...
  12. J

    B Special Relativity & Relativistic Mass

    Hi, If a particle is within 2 m/s of the speed of light (like at CERN) and then more energy is transferred to the particle, where does this energy go? Some sources I have read talk about relativistic mass getting bigger and approaching infinity as a particle approaches 'c'. However, this source...
  13. Santilopez10

    I Help with special relativity mathematics

    I am having a hard time trying to understand this transformation from lorentz:https://imgur.com/a/WYWMO (You should ignore the spanish part and just focus on the math). I can’t understand well why they turn into what you can see in the second picture, when taking really small values of x...
  14. ISamson

    B Can Time Dilation Affect the Mechanical Functioning of a Clock in Orbit?

    Hello. I want to clear a doubt on Special Relativity, time dilation and clocks. If we get an accurate clock and make it orbit the, for example, Earth very, very fast, will the actual mechanical clock lag behind from the accurate clocks on Earth? The thing in this question is about the actual...
  15. D

    Time Dilation and Length Contraction Problem

    Homework Statement Anna and Bob are both born just as Anna's spaceship passes Earth at 0.9c. According to Bob on Earth, Planet Z is a fixed 30 ly away. As Anna passes Planet Z on her continuing outward journey, what will be (a) Bob's age according to Bob, (b) Bob's age according to Anna, (c)...
  16. R

    B Visual Effects of Light Travel: Analyzing "Journey to Edge of Universe

    Hi, Can someone please anlayse the visual effects for light travel in the documentary 'Journey to edge of the universe' Especially around the 43:12 and the 1:02:20 mark. Can you also tell me if it is or is not an accurate depiction of what we should be seeing theoretically?
  17. F

    I Demonstration of time dilation

    I try to find the formula of dilation of time between a reference frame (R') moving at a speed v and a fixed observer in (R). For this, I take the example that we often find as a demo : that of a train in which a light beam is emitted vertically (in the train): this vertical trajectory in the...
  18. W

    I Answer: Understanding the Effect of Gravity on Falling Objects

    You are launched upward inside a railway coach in a horizontal position with respect to the surface of Earth, as shown in the figure. After the launch, but while the coach is still rising, you release two ball bearings at opposite ends of the train and at rest with respect to the train. a)...
  19. P

    B Time Dilation: Moving Rocket 0.5c vs Accelerating Rocket 0.5c

    A non-moving observer is looking at two different rockets in space. One rocket is moving at a steady velocity of 0.5c, and the other rocket is currently moving in 0.5c but has steadily accelerated from 0.3c and will continue accelerating until it gets to 0.7c. Assuming that there is no...
  20. S

    B Volumes and Hyper Volumes Related Special Relativity

    How can volumes and hypervolumes be related to Einstein's theory of special relativity and to quantum mechanics? Also, can volumes and hypervolumes of objects be used for modeling how different scenarios can change over time? Oh yeah, and hi my name is Sasha Jaffarove!
  21. T

    Acceleration in special relativity

    Homework Statement Homework EquationsThe Attempt at a Solution it is known that ##a_0 ##is the proper acceleration ## a= \frac{a_0}{\gamma^3} ## hence integrating it gets ## v = \frac{a_0t}{\sqrt{1 + (\frac{a_0 t}{c})^2}} ## but this is in terms of t how to make it in terms of t'
  22. D

    I Velocity Addition Formula: u_y > c?

    If a frame S' moves with velocity v in x direction wrt S, and you have v = 0.5c, u_x' = -0.9c and u_y' = 0.9c then it seems you find that u_y = 1.417c, greater than c. The relevant formula is: u_y = u_y'/(gamma * [1+v u_x' / c^2]) Apologies for formatting. Details: gamma = 1/sqrt(1-v^2/c^2)...
  23. P

    Dust in special relativity - conservation of particle number

    Homework Statement My textbook states: Since the number of particles of dust is conserved we also have the conservation equation $$\nabla_\mu (\rho u^\mu)=0$$ Where ##\rho=nm=N/(\mathrm{d}x \cdot \mathrm{d}y \cdot \mathrm{d}z) m## is the mass per infinitesimal volume and ## (u^\mu) ## is...
  24. D

    Simple Special Relativity Problem of Length Contraction

    Hello, I'm self-studying Ta-Pei Cheng's Relativity, Gravitation and Cosmology. Problem 2.8 is the following: Two spaceships traveling in opposite directions pass one another at a relative speed of ##1.25 \times 10^8## m/s. The clock on one spaceship records a time duration of ##9.1 \times...
  25. T

    B Electric+Magnetic Force Between a & b Charges: Inertial Frames

    Let's assume that a and b charges are moving. now in our lab frame there will be a electric+magnetic force whereas in a rest frame of either of the charges, there will be only an electric force. So, two inertial observers will measure different forces?
  26. ohwilleke

    A Corollaries of Lorentz Invariance: Overview & Explanation

    I've commonly heard it said that Lorentz invariance is equivalent to saying that special relativity is obeyed, although I also recall discussions arguing that this is not precisely and technically correct, although the two concepts heavily overlap. I also understand that Lorentz invariance has...
  27. P

    B Minkowski metric, scalar product, why the minus sign?

    In Schutz's A First Course in General Relativity (second edition, page 45, in the context of special relativity) he gives the scalar product of four basis vectors in a frame as follows: $$\vec{e}_{0}\cdot\vec{e}_{0}=-1,$$...
  28. senatorarmstrong

    Calculating the Travel Time of High-Energy Particles Across Our Galaxy

    Homework Statement Our galaxy is about 10^5 light-years across, and the most energectic particles known have an energy of about 10^19 eV. How long would it take a proton with this energy to traverse the galaxy as measured from (a) the galaxy and (b) the particle? Homework Equations I...
  29. Elvis 123456789

    Collision of alpha with Be -> C + gamma

    Homework Statement Before the discovery of the neutron, it was proposed that the penetrating radiation produced when beryllium was bombarded with alpha particles consisted of high-energy &gamma rays (up to 50 MeV) produced in reactions such as α + 9Be --> 13C + γ a.) Calculate the Q value for...
  30. M

    A Can entanglement swapping determine the absolute velocity of an object?

    Hi There, I've been spending some of my free time learning about Quantum Mechanics. This was all going somewhat smoothly, until I encountered something known as "Entanglement Swapping" while learning about loophole free bell tests, such as the one conducted by Hensen et al at TU Delft in 2015...
  31. C

    I Michelson Morley experiment: relativistic explanation

    I don't uderstand how, using special relativity theory (time dilatation and length contraction), one can explain why in the Michelson interferometer there is no delay between the two rays in the reference frame where the interferometer is moving. Consider the picture ##2.## Setting...
  32. A

    B Special relativity and the flow of time?

    Pardon me if this has been asked before, but I'm confused with the implication that SR makes, that there is no objective moment of present. Do the science still believe that the time flows (i don't mean the arrow of time, but the phenomena of flowing/passing, eq. flowing of a river)? I mean, how...
  33. I

    Special Relativity: Traveling to Regulus

    Homework Statement A visit to Regulus is on my bucket list. However, it is 77 light years away. Assuming I will live only another 40 years, can I make it to Regulus? How fast would I have to travel (at constant speed) to get there in 40 years? Homework Equations t1 = t0...
  34. T

    I Relativistic Aberration Formula & Lorentz Transformation

    Let's assume that a light source is moving parralel to x-axis and is in point x,y,z in lab frame. Suppose it emits a light ray. In the rest frame that coincides with the lab frame, the light source is in point x',y and z. However, because of relativistic aberration the two light rays will make...
  35. M

    I Compatibility of Quantum Mechanics and Special Relativity

    Hello, In my free time, I've been learning about an eclectic range of topics (ie. French History, Kinetic Theory etc.). Most recently I've been focused on Quantum Mechanics, which happens to be most complex topic I've ever looked at. Typically I write up summaries after reading from various...
  36. S

    I Traveling at a speed faster than light

    Imagine yourself to be bat. You can't see anything. You don't have eyes. All you can do is echolocate, using ultrasound. Now imagine something is moving away from you faster than the speed of sound. Can you locate it ? Can you perceive its existence ? If the answer is yes, how ? If no , then...
  37. J

    A On the formation of a black hole due to high kinetic energy

    Hello! If energy bends spacetime, then an object moving at high velocity will bend spacetime a lot around it due to its really big kinetic energy. It follows, that an object can become a black hole at extremely high enough velocities. But, since velocity is relative, we can find an observer for...
  38. mpolo

    Does the Photon Defy the Rules of Special Relativity?

    Is it fair to say that the photon does not follow the rules of Special Relativity? I ask this because the photon relative to all other frames of reference has zero mass even though it is traveling at the speed of light. If we increase the speed of any other particle to the speed of light its...
  39. lomidrevo

    I How is SR applied to circular motion?

    Hi all, I have a problem to fully understand how we can apply Special Relativity to a system where one observer is still in the center, and other one is moving in a circle around. For example, like a satellite orbiting Earth. In case of GPS, the clocks carried by satellite are running slower...
  40. learn.steadfast

    I Classical mass vs. relativistic mass for electronic analogy

    I'm working on semiconductor physics and cyclotrons. There's an article that I am trying to understand, but am having difficulties matching with experiment. I asked a question on an electronics site, but apparently the physics is too advanced. The relativity article which sparked my interest...
  41. M

    I Resolving the Three Colliding Observers Paradox in Special Relativity

    I have a random paradox I seem to have found with three colliding observers, though to explain it properly I'm going to use a bit of visual aid and a bit of abstracting it from the math (or setting the math so that it works according to my example). For anyone who wants the TLDR, read this...
  42. S

    I Relativistic mass increase (simple or not)

    Hi, I have yet another question in the field of the special relativity theory. I always thought that the derivation of the relativistic mass is trivial. But I discovered that there is some complexity due to the transverse and longitudinal relativistic mass derivation. I saw a thread where...
  43. T

    I Exploring the Effects of Relativistic Angular Velocity on a Rotating Disk

    Let's assume that a disk is rotating with relativistic speed in a frame. We can find the velocity of a particle using v=rw formula. However, what is the r in this formula? is it the radius of the disk in rest frame or in the lab frame?? And Is the magnitude of velocity same for all points of...
  44. S

    I Time Dilation and the Twin Paradox: A Look at the Relativistic Doppler Effect

    Hello everyone, Reminder: The key of the explanation of the "twin paradox" resides in the acceleration. We know that the time runs slower for the twin in the spaceship (since it was accelerated)...
  45. D

    I Why and how Dirac cones are "tilted"?

    Given a Weyl Hamiltonian, at rest, \begin{align} H = \vec \sigma \cdot \vec{p} \end{align} A Lorentz boost in the x-direction returns \begin{align} H = \vec\sigma\cdot\vec{p} - \gamma\sigma_0 p_x \end{align} The second term gives rise to a tilt in the "light" cone of graphene. My doubts...
  46. mpolo

    B Special Relativity: Time Dilation Explained

    I am trying to get this idea of Time dilation understood. If there exists only two objects in a Universe and one object is stationary and the other object is moving at 99 % the speed of light. Their clocks were both synchronized when both objects were stationary relative to each other. Then the...
  47. V

    Special relativity, gradient of velocity

    Homework Statement I have noticed that in some calculations they use $$ \vec{\nabla}\cdot\vec{u}=\frac{1}{V}\frac{dV}{d\tau}$$. I would like to derive it. Homework Equations ##\vec{u}=(\frac{dt}{d\tau},\frac{dx}{d\tau},\frac{dy}{d\tau},\frac{dz}{d\tau})## ##\vec{A}\cdot\vec{B}=A^{\mu}B_{\mu}##...
  48. T

    Special Relativity - Rocket problem (particle mechanics)

    Problem statement: A rocket propels itself rectilinearly by giving portions of its mass a constant (backward) velocity ## u ## relative to its instantaneous rest frame. It continues to do so until it attains a velocity ## v ## relative to its initial rest frame. Prove that the ratio of the...
  49. Umrao

    SR: Does observation change when changing reference frame

    Homework Statement Special relativity: A rod traveling with the relativistic velocity of 0.866c moving towards a garage. The length of the rod is L, that of the garage is L/2. From the reference frame of the garage, we find the value of Lorentz factor = 2 we say that rod would fit inside garage...
  50. R

    B Special relativity and expansion of the Universe, A paradox

    Consider two bodies A &B are moving apart with a velocity V due to the expansion of space. According to an observer in A the body B is moving away and an observer in B feels the body A is moving apart. Can some one answer in which body the time dilates and why?. ( I am specifying once again that...
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