Reference frame Definition and 230 Threads

In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements within that frame.
For n dimensions, n + 1 reference points are sufficient to fully define a reference frame. Using rectangular (Cartesian) coordinates, a reference frame may be defined with a reference point at the origin and a reference point at one unit distance along each of the n coordinate axes.
In Einsteinian relativity, reference frames are used to specify the relationship between a moving observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes "observational frame of reference" (or "observational reference frame"), which implies that the observer is at rest in the frame, although not necessarily located at its origin. A relativistic reference frame includes (or implies) the coordinate time, which does not equate across different frames moving relatively to each other. The situation thus differs from Galilean relativity, where all possible coordinate times are essentially equivalent.

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  1. S

    I What if one is in 1905 and debating foundational fundamentals?

    Einstein's theories are accepted since 100+ years. Modern science built on it somehow provides a proof of truth of his theories but what if one is living when Einstein proposed his theories and debating its merit? Einstein did two things: 1. He declared velocity of light as invariant c for all...
  2. MatinSAR

    Relative Motion: Understanding the Relationship Between Moving Objects

    My attemp : ##\vec r_1## : Position of the river in reference frame. ##\vec r_2## : Position of the walker in reference frame. ##\vec r_x## : Position of the walker measured by the river. We have: $$\vec r_1 + \vec r_x = \vec r_2$$ $$\vec v = \dfrac {d \vec r}{dt} $$ $$\vec v_1 + \vec v_x =...
  3. C

    B Question about choice of reference frame

    Hello everyone, I might be highlighting my ignorance in this post (it might be ignorance of the particulars of simultaneity) but that's a good thing because then I might be able to figure out what I don't know. If the Lorentz factor is 2 for a spaceship that is launched from Earth then...
  4. cianfa72

    I Wald synchronous reference frame proof

    Hi, on Wald's book on GR there is a claim at pag. 43 about the construction of synchronous reference frame (i.e. Gaussian coordinate chart) in a finite region of any spacetime. In particular he says: $$n^b\nabla_b (n_aX^a)=n_aX^b\nabla_b \, n^a$$Then he claims from Leibnitz rule the above equals...
  5. M

    B How to measure time in reference frame with clock?

    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...
  6. P

    B How to compare the proper times of two spatially distant mass points?

    Do all synchronized clocks in a reference system always show the same time? Is this part of the definition of a frame of reference? Have the clocks always passed the same proper time from zero (see below)? Would the knowledge of the proper time of a clock between two events lead to the...
  7. W

    I Is the position vector a real vector?

    Is the position vector a real vector? I have a hard time with this question because vectors are unchanged if I were to change my reference frame. Example: If I place a pencil such that it points towards the door. It doesn’t matter what I define my origin to be. The pencil’s length and direction...
  8. BadgerBadger92

    B Perception of Velocity in Special Relativity

    If an object is going close to the speed of light, will outside frames of references perceive the moving object as going slow or fast?
  9. AronYstad

    Special Relativity - Which reference frame experiences which time?

    This was a practice question, so it had the answer with it, which is 31 minutes. However, I'm confused as to why Lisa experiences T0. It isn't exactly an event happening in Lisa's rocket, but rather her just moving through space. From her perspective, it should look like Earth is moving at the...
  10. curiousPep

    When to consider body fixed reference frame

    Hello I am studying mechanics and I have been reading about having the reference frame fixed at a certain point, body fixed and also the gyro equations. I an identify the gyro case easily as I am looking for an AAC body which rotates about an axis. I am confused about the other two cases in...
  11. LCSphysicist

    Charge density seen from a moving reference frame S' (SR + EM)

    There are some question involving the statement. One of them is about the charge density in S' frame. It asks to calc it. I thought that i could calculate the electric field in the referencial frame S' and, then, use the formula $$ E = \lambda / 2 \pi \epsilon l $$ In that way, i would obtain...
  12. morrobay

    B One way speed of light in one reference frame measurement

    Two clocks with photo detectors are 100 kilometers apart at A and B. On the center of AB axis two light pulses are sent to the clocks , synchronizing them. Then a light signal is sent from A to B. The two stationary observers record the time from event at A to event at B. Is there a one way...
  13. L

    I Reference frame vs coordinate system

    Just want to clarify some concepts. There seems to be difference between reference frame and coordinate system. See https://en.wikipedia.org/wiki/Frame_of_reference#Definition . A reference frame is something has physical meaning and is related to physical laws, whereas coordinate system...
  14. cianfa72

    I Clarification on Rindler coordinates definition

    Hi, starting from this post Basic introduction to gravitation as curved spacetime I would ask for a clarification about Rindler coordinates. From this wiki entry Rindler coordinates I understand that the following transformation (to take it simple drop ##y,z##) $$T = x\sinh{(\alpha t)} ...
  15. V

    B Fluid Continuity Equation in different reference frame

    If I have fluid with area 10 and velocity 10, if the velocity increases to 20 the area will become 5. But if we switch to a reference frame moving at velocity 1 opposite this motion, then it would be 10 and 11 to 5 and 21, violating the continuity equation. What is wrong?
  16. Monsterboy

    Is this a reference frame problem ?

    v1 - velocity of the rain with respect to the ground v2 - velocity of the man with respect to the ground v3 - velocity of the rain with respect to the man So, v1 = v3 + v2 is this right ? So, for the man moving with a velocity v2 with respect to the ground, the rain will have a horizontal...
  17. MattGeo

    I Reference Frame, Difference in Kinetic Energy, Fuel Consumed

    Say 2 cars are traveling side by side at 10 m/s in some flat, wide open space. Relative to each other they are stationary. Relative to someone on the ground they are both moving at 10 m/s. Now say you're in 1 of the cars and you see the other car accelerate, changing his velocity by 10 m/s in...
  18. cianfa72

    I Synchronous Reference Frame: Definition and Usage

    Hi, reading the Landau book 'The Classical theory of Field - vol 2' a doubt arised to me about the definition of synchronous reference system (a.k.a. synchronous coordinate chart). Consider a generic spacetime endowed with a metric ##g_{ab}## and take the (unique) covariant derivative operator...
  19. Rubberduck2005

    Simple conceptual reference frame question

    If a train is moving at some constant V with a bed sitting still on top. When the train decelerates at some rate -A then the bed will move at some acceleration A. I can't seem to get an intuition for how this comes to be. I have looked online and find no help.
  20. S

    I Does the CMB reference frame violate the Cosmological Principle?

    Studies of the Cosmic Microwave Background shows that the Earth is moving roughly 380 km/s with respect to it towards the constellation Leo I think. Yet (I think) the Cosmological Principle and the Michelson-Morely experiments suggest there is no preferred reference frame in the universe --...
  21. RUTA

    Insights No Preferred Reference Frame: Quantum Mechanics Interpretations

    Continue reading...
  22. F

    Body-Fixed Reference Frame -- How is it useful?

    Hello Everyone, I am trying to understand the usefulness of a body-fixed (body-centered) frame of reference ##O'x'y'z'## versus a lab frame of reference ##Oxyz##. The body-fixed frame is attached to the moving body and changes orientation exactly as the body changes orientation. From the...
  23. F

    Reference frame in collision problems

    2 balls (Ball 1 and Ball 2) collide fully elastically and their relative velocity stays the same as but in sign opposite to that before the collision. Is there any sort of reference frame in which Ball 2 is always fixed (at rest) so that one can look at their relative velocity always in that...
  24. cianfa72

    I Reference frame vs coordinate chart

    Hello, here on PF I've seen many threads about the concepts of 'reference frame' and 'coordinate system'. In the context of SR my 'envision' about the concept of 'frame of reference' is basically the 'rods & clocks latticework' as introduced in the book Spacetime physics (Taylor, Wheeler)...
  25. M

    Equations of relative motion with respect to a rotating reference frame

    Hi, I am just writing a post to follow up on a previous thread I made which I don't think was very clear. The question is mainly about how to use the below equations when there is also a rotation of the body around the fixed reference point. Please see the diagram here to see how the vectors...
  26. V

    I Momentary Co-Moving Reference Frame in SR

    In SR, for the momentary co-moving reference frame, U (the velocity four vector) takes the form (1,0,0,0). I'm wondering whether the basis vectors associated with this velocity are zero or if the coefficients in front of the basis vectors are zero. In classical mechanics we would say that the...
  27. M

    Question about Formulae for Motion in a Rotating Reference Frame

    Hi, I am reading the following question: "Particle P moves in a circular groove with radius ## a ## which has been cut into a square plate with sides of length ## l ##. The plate rotates about its corner ## O ## with with angular velocity ## \omega \hat k ## and angular acceleration ## \dot...
  28. K

    B Earth Center of Mass: GR & Inertial Object Acceleration

    Super-basic question that I'm embarrassed to ask. It's just what the summary says: Taking Earth's center of mass as our reference frame, how does GR account for an inertial object near the surface approaching with an acceleration of G? I assume (perhaps incorrectly) that this is an inertial...
  29. H

    I The reference frame for angular momentum components

    In which coordinate system the components of angular momentum are quantized? Better to say, if we can select the coordinate system arbitrarily, how the components of angular momentum, say z-component, are always ##L_z=m\hbar##?
  30. Livio Arshavin Leiva

    Rectilinear movement seen from a rotating reference frame

    Let's suppose there's some platform that is rotating with angular speed omega and has a radius R. At t=0 we release some object from the border, which has an initial speed perpendicular to the radius direction with magnitude \omega R and we want to know its position at t=T with respect to the...
  31. D

    B Time dilation and the reference frame of the vacuum

    The point of the twin paradox in special relativity is that the traveling twin experiences a real, frame-invariant effect in which the time evolution of all moving matter is slowed down. If you read a hundred articles and textbooks on SR, you'll see a hundred variations on the message that the...
  32. D

    A Reference frame of the vacuum -- which forum?

    I have a question about interactions between matter and the vacuum, but I don't see a forum for that. Quantum field theory seems to be the most closely related subject. What would be the best forum for questions related to QFT?
  33. Arman777

    I Comoving Reference Frame in Cosmology

    In cosmology, the preferred reference frame is the comoving rest frame. I am trying to understand why we are using this frame and not another one. The only reason I could come with is this. Since the expansion of the universe is homogeneous and isotropic it seems our best choice is using the...
  34. ruivocanadense

    I Does Conservation of Momentum & Energy Hold in the C.O.M. Reference Frame?

    We know classical equations fail to follow conservation of momentum and energy when we are dealing with speeds closer to the speed of light. But does it fail in the center of mass reference frame of a system?
  35. T

    1st Law of thermodynamics : moving reference frame

    I'd like to apply the 1st law of thermodynamics in a reference frame (RF) moving with constant velocity. We have: ##\Delta{}E = E_{in} - E_{out}## I am limiting myself to rectilinear motion. Suppose we are in a RF moving with a constant velocity ##V##. Let the system consist of a mass ##m##. The...
  36. S

    B Length Contraction in Accelerated Frame

    I was wondering, would there be a length contraction (or expansion) in the z and y axis' if an object was accelerating in x axis? I know that in special relativity there is no deformation in the y and z axis' if the object is moving in the x axis. I was looking a this paper for clarification.
  37. Like Tony Stark

    Acceleration for a non-inertial reference frame

    Well, first a wrote the equation for acceleration in non inertial systems. ##a_I=a_o+\dot \omega \times r+\omega \times (\omega \times r)+2(\omega \times v_{rel}) +a_{rel}##. Then, ##a_o=0## (because the system doesn't move), ##a_i=0## (because it is measured from the non inertial system)...
  38. 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...
  39. M

    I Inertial Mass as Speedometer: Physics & Universe

    I get that the concept of relativistic mass has sort of been deprecated in physics these days and that relativistic momentum is supposed to be seen as more well useful. So let momentum equal ##\mathtt ~~ \frac {mv} {\sqrt {1 - \frac {v^2} {c^2}}} ~~## or ##~~{mv\gamma}~~##. So mass is supposed...
  40. Like Tony Stark

    Measuring position and velocity from a non inertial reference frame

    I) For ##A##, the positition is ##\vec r=(0;V_0 . t;0)##. For ##B##, we have ##\vec r_A=\vec r_B + \vec r_{A/B}##, but ##\vec r_{A/B}## is equal to zero because they have the same origin, so the position measured from ##A## is equal to the position measured from ##B## II) For ##A##, velocity...
  41. H

    Entropy in a non inertial reference frame

    I know that the entropy of a system is the same in different inertial frames. Is this still the case for non inertial frames? For example, is the entropy of a body as seen from a rotating reference frame the same as the entropy seen from a fixed frame?
  42. x-vision

    B Reference frame symmetry in Special Relativity

    Hello, I have a couple of questions related to reference frames in Special Relativity. Let's consider a rocket that is inertially moving towards a star with a relative velocity 0.9c. I'd like to look at this example from both the rocket's and the star's perspectives. In the reference frame of...
  43. S

    B Attribution of Reference Frame: A Dilettante's Question

    I can't find an answer on my dilettante question about how we attribute reference frame to complex objects, where different parts move with different velocity or where different parts experience different influence of gravitation. For example, we can take a human's body. If we take the full...
  44. G

    A Can an object be at rest in its own reference frame?

    In classical physics, every object is obviously at rest with itself, and it makes perfect sense for this to be true. But would this violate the uncertainty principle for a particle? If you are the particle and you know that you're at rest with respect to yourself, you know both your location...
  45. P

    Solving for c: Speed of Q2 in Q1 Reference Frame

    I've tried using this equation: Where: u' = 0.86c v = 0.3c u = Is the speed of Q2 as measured by an observer in the reference frame of Q1 = 0.922c Where have I gone wrong? Have I missed a negative symbol?
  46. M

    B Polarized Electron in a Rotating Reference Frame

    I tried asking a similar question in cosmology but got no answer there so here goes... Suppose I am on a windowless spacecraft in the middle of an intergalactic void. I know that the spacecraft is spinning from measuring the centrifugal forces but have no way of observing the outside...
  47. D

    Angular momentum of a system relative to a moving reference frame.

    I don't have too much of a clue of how to begin the problem. I first wrote the angular moementum of the system of particles: →M=∑mi(→ri×→vi)M→=∑mi(r→i×v→i). Then I know that the angular momentum from of the moving reference frame would have the velocity as the sum of the velocity of the frame...
  48. Pencilvester

    I Locally inertial reference frame problem

    Hey PF, I am working on a problem set, and one of the problems is proving that the Christoffel symbols vanish at the origin of the coordinates ##y^{\alpha}## given by the coordinate transformation: $$y^\alpha (x) = x^\alpha - x^\alpha_{(0)} + \frac {1} {2} (x^\mu - x^\mu_{(0)} )(x^\nu -...
  49. physicschick21

    Deriving Ball Movement on Northern Hemisphere with Rotating Reference Frame

    I have a ball of mass m that is situated on horizontal plane on the northern Hampshire. I am asked to show that the ball is moving, clockwise, in a manner of r = v / ( 2Ω*sin(λ) ) where v is the ball's velocity, Ω is Earth's angular velocity, and λ is the terrestrial latitude So here's what...
  50. H

    A Reference frame conversion for a moving sphere

    Hi here is the situation; There's a spherical particle contained with a MEMS sensor (3D accelerometer and gyroscope) moving down a bed. What we want is to estimate the total kinetic energy of the particle. The total kinetic energy has two parts, translational part and rotational part. for the...
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