Reference Definition and 1000 Threads

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)...

I am trying to figure out what are inertial observer and inertial frames of reference. The law of inertia holds for inertial observers. Inertial observers are objects with zero net force acting on them, and move with constant velocity. Suppose we fix a set of coordinate axis in space, relative...

Hello! I am dealing with a problem of a 2 level system (an ion in my case) placed in a Penning trap. Basically the ion is moving inside the trap under the influence of the magnetic and electric field and I need to study its inner 2 level system (basically the lowest 2 energy states) while it is...

This is not a contextual question, but a stylistic one; hence it doesn't seem to belong in the other threads. I am proof-reading a paper, and I am unsure about the way the author uses square brackets for the indication of (numbered) sources. In order not to be quoting a source without...

Lv = Lo / γ 1/γ =√(1-v^2/c^2) = √(1-0.8^2) = 0.6 Therefore Lv = Lo x 0.6 = 150 x 0.6 = 90m Therefore electron travels 90m in its own frame of reference (answer key solution) However, shouldn't the electron be assigned rest length, Lo, as its frame of reference is at rest with itself instead...

How do I reference a photo taken from the assignment question in Harvard style?

Earth rotate from west to east with 460m/s at equator. Car travel at equator from east to west at speed 460m/s. 1- What is car speed from inertial ref.frame? zero?How is zero if car travel in curved line? 2-What is car speed from rotational frame ? 3-How much is car weight,compare to car...

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...

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...

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...

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...

Suppose we have two spaceships a lightminute apart from each other. Ship A sends a photon to ship B. To my knowledge the photon will arrive at ship B a minute after is was departed from ship A. The photon will travel away from ship A with speed c, and will travel towards ship B with speed c...

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##?

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...

This problem is conventionally solved using the Earth frame of reference. We require that the hyperbolic excess velocity w.r.t. the Earth has the same magnitude as the speed of the Earth around the sun, so that we zero the velocity in the heliocentric frame. Energy conservation per unit mass in...

Hi, consider the following in the context of classic mechanics and SR. We know there exist special "frame of reference" according to free objects stay at rest or keep moving with constant uniform velocities. Suppose you single out a such reference frame according to the Newton law of inertia...

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...

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?

I don't own undergraduate textbooks. I'm looking for a single one that works well as a reference or a refresher for various basic topics. Specifically, I'm thinking of a textbook that I could pick up when I forget some detail in an elementary topic and quickly check it out. So I don't mean one...

I'm interested in looking at birefringence of crystals with a microscope (just for amusement). I'm definitely not a chemist, and don't intend to become one. Does anyone know of a quick online reference for the solubility of common chemicals in different solutes? Every time I search for this I...

I was wondering if anyone knew of sources regarding the history of Dedekind Cuts and its use to construct the Reals. Ie., the mathematical thinking leading to this idea, why it is important, and how it allowed to put Analysis on a rigorous foundation.

I'm reading about the geometry of spacetime in special relativity (ref. Core Principles of Special and General Relativity by Luscombe). Here's the relevant section: ----- Minkowski space is a four-dimensional vector space (with points in one-to-one correspondence with those of ##\mathbb{R}^4##)...

In a previous thread, I referenced an argument from the book the Scientist as Philosopher by Friedel Weinert, in which he talks about the reference frames of two relatively moving observers. He made a statement that I had't thought about before, but when I was reading it this time around a...

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...

I was reading an article about the misconceptions in cosmological horizons and I wanted to clarify an idea. https://arxiv.org/abs/astro-ph/0310808 In cosmological perspective, is there a global inertial reference frame (maybe CMB) ? Or all inertial frames are defined locally and there is no...

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?

Would it be correct to say, that we are moving away from stars at the edge of the universe, at the same rate that these stars are moving away from us? I am relating to stars that are moving in relation to us, at a speed that is faster than the speed of light. Is the symmetry that maintains that...

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...

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...

Since Pi = Pf, 0 = MbVbg + McVcg I just need to express Vbg in terms of Vbc and Vcg (that is, I need to express the velocity of the ball relative to the ground in terms that I know/want to solve for): by reference frames: Vbc = Vbg + Vcg so Vbg = Vbc -Vcg Now I can sub in and solve 0 =...

When we say speed of light = c m/s. Who is measuring meters and second. From SR perspective, that photon is moving towards you at speed of light so there should be time dilation, correct?

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.

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)...

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...

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?

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...

Lately there are many news stories about a tariff being put on a certain "worth of goods". How is "worth of goods" calculated? For example if the tariff was put on , say, pickles, would the "worth" of pickles be computed as the total value of pickles imported in a year before the tariff? Or...

I have a really stupid question. Suppose I am in a car and the car is going around a loop. Yes, the Earth is not inertial -- it rotates -- but let me ignore that and, momentarily, designate the Earth as inertial. Now, we know the frame of the car is not inertial--the car is turning. We...

Suppose we have a stationary metre stick with one end positioned at the origin of a stationary frame of reference, pointing along the positive x axis. The world lines of both ends of the metre stick are consequently vertical. Now consider another primed frame moving at velocity v relative to...

I will refer to the example given in 'On the electrodynamics of moving bodies' concerning a rod moving in a coordinate system, in which a beam of light is sent from one end of the rod to the other and is then reflected back. Usually when calculating relative velocities, we may simply consider...

This is my wrong attempt, the bolt's equation for ##t\geq 2## would be ##y_b(t)=-\frac{1}{2}g(t-2)^2+e(2)+l## where ##e(t)=\frac{1}{2}wt^2## the position of the elevator's floor in the absolute frame of reference. ##d(t)=-\frac{1}{2}(w+g)t^2+2gt+2(w-g)+l## the distance between the bolt and the...

These quantities are evidently not equal unless v1 = v2, but surely the change in kinetic energy should be the same in different frames of reference? I was wondering what mistake or misconception I have made because this has been bugging me for a little while. Thank you in advance!

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...

Hi. This is my first post. Thanks to all who give it a look. I am working on an application that has very stringent power output requirements. There is a rechargeable battery that I am trying to manage through a bi-directional boost/buck converter as is typical of many modern-day electric...

In the attached fig 1 you have a moving frame of reference (MFR) moving in the direction V at velocity V Looking from above in the MFR there are 2 identical train carriages (car 1 and car 2), Car 1 is on a long set of tracks. Car 2 cannot move but is on train tracks. There are also 2 Identical...

Ok, this is the notation I am going to use in this thread: uppercase means vectors, while "[V]c" means coordinates of vector V in frame c. I'm reading from a book: i have a reference frame "a" and a reference frame "b" rotated with respect to "a", the vector connecting the frames origin is R. We...

I am studying the fact that two events that are simultaneous in a frame aren't (in general) simultaneous in another. The lamp is equidistant from the two ends. When the light is switched on an observer on the train sees how both light rays hit the back and the front of the train...

Hello I have learned about conservation of momentum, Newton's law (1st, 2nd, 3rd law + free body diagram), conservation of energy and finding center of mass of several 2 D and 3 D shapes (non - calculus method). I watched youtube video about two objects connected by horizontal spring and in...

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...

Hi, Could you please help me to clarify the following problem? In the gravitational field of a mass, the force on a body in steady state comes from the gradient of the gravitational potential - or the gradient of speed of time. But what about accelerated reference frames? I assume that there is...