Special relativity Definition and 1000 Threads

  1. mr John wheeler

    I Confused about time dilation -- motion vs energy

    Hey, I’ve been trying to understand time dilation, and I think I might be mixing some concepts. If you’re moving very close to the speed of light (say 0.99999c), your clock slows. If you then enter a strong gravitational field, that also slows clocks. From your point of view, would that mean...
  2. Sciencemaster

    I How do Tensors "work" in relation to linear algebraic objects?

    I've been reviewing some introductory tensor stuff, and I've come to the realization that some of the things tensors do confuse me. For example, the notes I'm reading say that the invariant interval is both ##S=\eta_{\mu\nu} x^\mu x^nu## and ##S=x^T \eta x##. Both of which are totally fine on...
  3. A

    I Please explain how length contraction and time dilation result in a constant c

    if light pulse is to the right, but moving car's velocity is to the left, we would expect c-v, but we get c instead which is greater. but if light pulse is to the right, and moving car's velocity is also to the right, we would expect c+v, but we get c instead which is smaller. how could the same...
  4. omidj

    I Invariance of 4-velocity

    If we don't multiply time by the speed of light C, in Lorentz transformation equatins, the invariant tensor of U.U will not be equal to c^2. So it seems the coefficient of C is an obligation for parameter t. I thought it's just for visual convenience in graphs, besides C is not dimensionless.
  5. C

    I Twin Paradox Resolution

    In what sense is the following explanation of the Twins Paradox faulty in logic: Each twin views the other as length contracted, but the twin on earth only sees the rocket in motion and thus shortened (along with the twin) while the destination planet is at rest in the earth frame and the...
  6. B

    Python relativity game in python

    import pygame # Initialize Pygame pygame.init() # Get the screen resolution info = pygame.display.Info() WIDTH, HEIGHT = info.current_w, info.current_h # Set to the current screen size # Constants WHITE = (255, 255, 255) LIGHT_COLOR = (255, 255, 100) OBJECT_COLOR = (100, 255, 100)...
  7. Kostik

    A Dirac's derivation of the action/Lagrangian for a free particle

    The action for a free particle is $$I=-m\int{ds} = \int \left(-m\frac{ds}{dt}\right) dt \quad\quad\quad(*)$$ hence the Lagrangian is $$L=-m\frac{ds}{dt}=-\frac{m}{\gamma}=-m\sqrt{1-v^2} .$$ Dirac ("General Theory of Relativity", p. 52) infers this by checking that it gives the correct spatial...
  8. LightPhoton

    I Relating orthogonal accelerations in special relativity

    We want to relate acceleration in two frames, an inertial frame S, and the instantaneous inertial reference frame of the particle on which it is being accelerated, S', which is moving in the ##x## direction at the moment. Let the acceleration in S be ##(a_x,a_y)## and in S' be ##(a_x',a_y')##...
  9. stixlee

    Physicist ISO no strings attached fun (see what I did there?)

    Rancher, film producer, writer, AI entrepreneur, US Army veteran/paratrooper and theoretical physicist. Granted, that’s a professional Venn diagram you won’t see often, but I’ve just submitted my first paper for pre-published peer review on viXra and am hoping to contribute to the forum and...
  10. LightPhoton

    I Angles between 4-vectors in special relativity?

    How is the angle between two 4-vectors defined in special relativity? Consider two 4-velocity vectors: $$U^\mu=(1,0), \\ V^\mu=\gamma_{rel}(1,v_{rel})$$ Where the vectors are written in the frame of the particle with ##U^\mu##. The dot product between these is $$U^\mu V_\mu=\gamma_{rel}$$ If...
  11. Trysse

    Relativity Lorentz factor in textbooks on Special Relativity

    I recently had a look at some textbooks to see how they make use of the Lorentz factor. I have seen that many textbooks introduce γ purely as a mathematical shorthand. On the other hand, some books that delve a little deeper into γ use graphs to show how γ and v are related. I have found...
  12. Trysse

    At what age is special relativity taught?

    This is a question to school teachers (and all those who know about physics syllabus at school). Is relativity (special and or general) taught in school (pre university) in your country? If yes, at what age are students introduced to relativity? What aspects are taught? As far as I remember...
  13. J

    I Electromagnetic field in different reference frames

    Suppose there are two reference frames. One is rotating with respect to another with rotational velocity ##\omega##. Now if in one of the reference frames the vector potential is $$(1, 0, 0, 0)$$ then in the other reference frame it will be $$(\sqrt{1-(\omega r)^2}, 0, \omega r, 0)$$. Now in...
  14. J

    A Calculating geodesic equation from Hamiltonian in presence of EM

    I have a Hamiltonian $$ H = \frac{1}{2} g^{\alpha \beta}\left(p_\alpha- A_\alpha\right)\left(p_\beta- A_\beta\right) $$ I want to calculate the equation of motion. How can I calculate the equation of motions $$ \frac{dx^\mu}{d\tau} = g^{\mu\nu}(p_\nu - A_\nu) $$ This one is straight...
  15. techsingularity2042

    Interpretation of Negative Time in Minkowski Diagram

    I want to explain my thoughts longer, but since my English is terrible, I will try to keep it as short as possible. This is the Minkowski diagram for the question above. ct-axis is the worldline of the space station, and ct'-axis is the worldline of the spacecraft. What I am confused about is...
  16. Q

    Suggestion Yet another solution to the Einstein field equations

    I've already got "Personal Speculation Warning" and I had a private conversation with @Nugatory, who told me, that I have to publish it in an appropriate peer-reviewed journal before it can be posted for discussion here. I replied with a question, if he is willing to believe, that...
  17. Tony Yuan

    I Robert B. Laughlin (Physics Nobel Laureate, Stanford University)

    In 2005, Robert B. Laughlin (Physics Nobel Laureate, Stanford University), wrote about the nature of space: "It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity]...
  18. J

    A Special Relativity in Rotating Reference frame

    There are two coordinate frames K and K'. A particle is moving. The position of the particle in K frame in (t, x, y, z) and K' frame is (t', x', y', z'). the z axis of K and K' are aligned. and K' is rotating with respect to K with an angular velocity w. Relate the equation of motion in these...
  19. techsingularity2042

    How to read spacetime (Minkowski) diagram for proper length

  20. Trysse

    I The Lorentz factor gamma and proper time

    I’ve been following this recent discussion on the speed of light and its implications in special relativity, and it got me thinking about proper time along light-like curves and the use of the Lorentz factor, ##\gamma##. One point that stood out to me is the claim that proper time along a...
  21. T

    I Need opinions on Youtube video: "From constant moving charge to SR"

    Im utterly confused about this video and I would like some opinions about it: "How Superposition Causes Length Contraction -- And Explains the Principle of Relativity" Approximately content: 1) Length contraction is entirely physical (shorter molecular bonds??). 2) Oliver Heaviside's retarded...
  22. deuteron

    I Physical Difference Between Co- and Contravariant Vectors

    Hi, today I have asked a very similar question on the topic, however now my question is more specific and focused, therefore I wanted to ask this again. From the following thread, Nugatory's answer, I understood that some physical quantities need to be described by contravariant vectors, such...
  23. deuteron

    I Co- and Contravariance

    Hi, I am very confused about the mathematics related to special relativity. I have understood, that a four-vector with an upper index has the form: $$A^\mu = (A^0 , A^1, A^2, A^3)$$ where lowering the index would make the indices other than the ##0##th negative: $$A_\mu = (A_0, -A^1, -A^2...
  24. P

    I No relativistic Bohmian mechanics and superluminal causation

    Even if I do not agree completely with him, I have followed some of the works of Tim Maudlin on explaining Bell's theorem which have been illuminating. He founded the John Bell Institute and he is what I would consider a Bell fundamentalist. However today I found on YouTube two very weird...
  25. M

    Studying Seeking advice about a quantum mechanics self-study plan

    How did you find PF?: Google search Hello, I am a semi-retired management consultant specializing in procurement and supply chain. Most of my work involves collection and analysis of a company's procurement data and identification of value creation opportunities from initiatives such as...
  26. L Drago

    B Special relativity thought: Traveling to the future relative to a particle

    I think that we travel to future all the time. As all intertial frame of motion is relative. We are currently travelling at very high speeds with relative to a particle accelerator's particle and time is slowing down for us with relative to the particle. I think so we are also travelling to...
  27. TheStick

    B Calculating Time taken to reach speed with Time Dilation

    So I've learned about time dilation and how getting close to the speed of light can have affects of time dilation. Looking into a bit more I see that when you are really close to the speed of light, say getting to the point of 99.9999999999% the speed of light, then it starts to become that...
  28. L Drago

    B What is the relationship between speed and time dilation in special relativity?

    Please clear any misunderstanding I have and if I am correct, kindly give me some more details and depth of SR time dilation which I am missing.
  29. murshiddreamengineer

    I Proof of Lorentz transformation

    What are the supporting arguments for the assumption that space and time are homogeneous?
  30. Abivarman

    Help needed on mass-energy equivalence

    TL;DR Summary: problem help pls :( so i have a presentation competition on physics. and I chose the energy mass equivalency topic. while researching, I came across a video stating that if we compress a spring, it's energy increases, so it's mass also increases. same thing with a cup of coffee...
  31. SummeryWinter

    Courses Special Relativity by Prof. Shiva Prasad on NPTEL (a lecture course)

    Hi everyone, I am a grade 12 high schooler(high school almost completed) who has gone through mechanics, some linear algebra, calculus and currently working through electrodynamics and EM, I would like to get an introductory view of Special Relativity, so I found this lecture course on NPTEL by...
  32. redtree

    I Lorentz invariance of the 4-momentum

    I apologize for the simple question, but here it is. The energy momentum relation models changes in energy ##E## and 3-momentum ##\textbf{p}_3 = \{ p_1,p_2,p_3 \}## with changes in velocity given ##(\textbf{p}_4)^2 = M^2##, where ##M## denotes mass and ##\textbf{p}_4## denotes 4-momentum, where...
  33. Sciencemaster

    I Series Expansion of the Infinitesimal Spacetime Interval

    I was watching an explanation of why the spacetime interval is invariant in all inertial frames (even when it's not lightlike) and the author made the assertion that if we have the relationship ds'=f(ds), we can expand the function as A+B*ds+C*ds^2+... (where C is not the speed of light). That's...
  34. D

    Probability distribution of outgoing energy of particle

    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...
  35. curiousburke

    I Muon travel distance vs Atmosphere Thickness?

    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...
  36. Sidsid

    Special Relativity: spaceships heading toward each other

    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...
  37. cianfa72

    I EM Faraday tensor transformation for conductor carrying current

    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...
  38. cianfa72

    I Is time dilation a real effect?

    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...
  39. djanni_unchained

    A How do we interpret measurements of Mercury's position?

    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...
  40. J

    Relativistic elastic proton collision

    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.
  41. cianfa72

    I On the physical meaning of Minkowski's spacetime model

    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...
  42. Q

    "Retired" but still active

    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...
  43. PLAGUE

    I Why "time part" represents energy in Four-momentum?

    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.
  44. PLAGUE

    I Proof of Invariance of Spacetime Interval

    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...
  45. m082844

    I Why doesn't relativity of simultaneity lead to a contradiction?

    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...
  46. F

    Confused by Lorentz transformation equation

    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...
  47. lambdadandbda

    How Does Special Relativity Affect Photon Emission Angles?

    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...
  48. M

    I Physical meaning of zero time metric

    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
  49. Sciencemaster

    I Observational Astronomy Project Ideas to Show Special Relativity

    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...
  50. J

    I How Can You Approach Steve Without Being Doppler-Shifted?

    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...
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