All Questions
Tagged with spacetime inertial-frames
290
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55
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Length Contraction: is $t'$ or $t = 0$?
To demonstrate my confusion - let's say there is a rod traveling with velocity +v relative to S, and in S, the length of the rod is measured to be $L$.
If I want to go from S to S', the frame where a ...
- 82
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3
answers
130
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Can you tell who is moving through time? [closed]
In relativity, there is no way to tell if you are moving through space. So, if you were inside of a box, there would be no way for you to tell if you were moving or not. However, can you know who is ...
- 33
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3
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175
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Seemingly equivalent linear form of the Sagnac effect
This is a derivative of the question regarding the Sagnac effect. Judging from the metric $ds^2=-dt^2+(rd\phi)^2$ for a constant $r$ for this question, it should be no different from that on a line ...
- 1,030
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3
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193
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Sagnac effect viewed in the rotating frame
Consider the Sagnac effect. It is quite simple viewed from the rest inertial frame what the time difference should be. However, if viewed from the frame fixed to and rotating together with the emitter/...
- 1,030
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3
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161
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Whether nonlinear coordinate transformations are symmetries of flat spacetime
I am editing this question after the answers are posted just to present my question a little clearly (without changing the main theme of the question). Moreover, this question is solely about flat ...
- 11.8k
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104
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Confusion with the Lorentz contraction as explained in "Introduction to Elementary Particles" by D. Griffiths
I am trying to understand how to derive the Lorentz contraction equation using the Lorentz transformations and while I know of a way to do this, I am still confused by a number of things, including ...
1
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2
answers
72
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Train example of special relativity
My friend Eric is at the center of the train. The train is moving forward. The front end and back end of the train flash a light at the same time. From Eric's perspective, both light arrives at him at ...
- 13
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54
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Proof of the invariance of $c$ using the Lorentz group
Apologies if this question was already asked a few times but i could only find proofs of the invariance of $ ds^2 $.
Is there any way of proving the 2nd postulate (that $c$ is invariant in all ...
- 309
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56
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Lorentz transformation of basis vectors in The geometry of Minkowski spacetime by Gregory L. Naber
Gregory L. Naber's book introduces the Lorentz transformation like this:
Now let $L :M→M$ be an orthogonal transformation of $M$ and
${e_1, e_2, e_3, e_4}$ an orthonormal basis for M. By Lemma 1.2.3, ...
- 11
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100
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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 ...
- 121
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28
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Generalizing the Galilean law of addition of velocities using the Lorentz transformation [closed]
I am reading about how to generalize the Galilean law of addition of velocities using the Lorentz transformation, but I am confused about one step.
Here, I have the following equations for Lorentz ...
- 63
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2
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131
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Do the Lorentz transformations contradict reality by implying time had no beginning? [closed]
Consider the following two points, or events as they are more commonly called, in SpaceTime:
Event 1: $(x,t) = (0,0)$
Event 2: $(x,t) = (a,0)$
Take t=0 to correspond to the first moment in time.
As ...
- 179
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4
answers
309
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Do the Lorentz transformations lead to negative amounts of time? [closed]
Consider the following two points, or events as they are more commonly called, in SpaceTime:
Event 1: $(x,t) = (0,0)$
Event 2: $(x,t) = (a,0)$
As you can see they are merely two separate locations, ...
- 179
5
votes
2
answers
892
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Why are there only three independent rotations and three independent boosts?
In what sense, there are only three independent rotations (i.e., rotations $R_x, R_y$, and $R_z$ about $x$, $y$, and $z$ axes, respectively)? Is it because any infinitesimal rotation about an ...
- 11.8k
2
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3
answers
240
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Relativity, Lorentz Transforms and the time it takes to perceive
I've been working a bit at understanding relativity a bit more, and understanding Lorentz transformations. I want to make sure I understand the meaning of a Lorentz transofmration, and when to use it ...
- 160
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5
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2k
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A bar that appears straight in one reference frame appears bent in another?
Is there a relativistic effect at play that explains the following thought experiment, that I am unaware of?
The apparatus depicted in the image has two straight bars in the middle emitting light from ...
- 93
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3
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115
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How does length contraction apply while distances increase in the Lorentz transformation?
I am having trouble settling the difference between the math in the length contraction equation and the Lorentz transformation. Say there is a piece of wood traveling near the speed of light and you ...
- 21
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2
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86
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Time desync with light delay: can we still "look into the future"?
I'm reasonably familiar with special relativity and its effect such as time desynchronization, but I'm having trouble understanding how these effects come into play when we also consider the time for ...
- 728
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2
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112
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Correct interpretation of time dilation using spacetime interval and proper times
I grasped my head around this topic a lot and I want to ask if my interpretation of the problem is now correct in the most clear way.
I'm trying to measure time dilation using the spacetime interval ...
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75
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Doubt about the derivation for the formula of time dilation
If I imagine a photon being released from the plate below as soon as the plates start moving, shouldn't the photon hit the opposite plate a bit behind the point where it would have hit if the plates ...
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398
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Linearity of Lorentz Transformation proof
I was reading this article and got to the part where the homogeneity of space and time leads to the linearity of the transformations between inertial frames.
In particular, the function $x^\prime=X(x,...
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1
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145
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How to calculate positions when switching reference frames in a Minkowski spacetime diagram
The below Minkowski spacetime diagram includes three worldlines, where B is the observer and has a rest frame. A and C both have a velocity of 0.71c.
I then created a second diagram where worldline A ...
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1
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105
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Where is my wrong about deducing Lorentz transformation? [closed]
I want to show the time dilation of Lorentz transformations by Michelson-Morley experiment (the second picture below). But I fail and can't find the wrong. Below is how I derived it:
Assuming the time ...
- 351
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1
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54
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From infinitesimal interval invariance to finite interval invariance in SR
In Landau and Lifshitz's The Classical Theory of Fields, on page 5 about interval invariance between different frames, it reads
Thus, $$ds^2=ds'^2,\tag{2.6}$$ and from the equality of the ...
- 613
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1
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62
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Lorentz transformations using spacetime diagrams (necessity of $\gamma$)
I'm studying the deduction of Lorentz transformations through spacetime diagrams and I have encountered the following:
The mathematical formulas describing the transformations for both of the ...
- 37
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1
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66
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Is the invariance of the 4-dim scalar product the fundamental law behind time dilatation and length contraction?
The Lorentz Group is defined as the group of all transformations that leaves the 4-dim. scalar product invariant. An implication of this definition is that the absolute value of the first matrix ...
- 189
4
votes
2
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818
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Difficulty understanding Lorentz Transformation
I don't understand the lorentz transformation. Consider:
$ \Delta x=\gamma (\Delta x^{'}+v\Delta t^{'})\\
\Delta x^{'}=\gamma (\Delta x-v\Delta t) $
For simultaneous events:
$ \Delta x=\gamma (\Delta ...
- 75
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2
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67
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Question about length contractions [duplicate]
So I'm kind of confused about length contractions, whenever I think about length contractions I think about the faster an object goes it will be able to impair more photons which would create an ...
0
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1
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175
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How is special relativity explained by general relativity?
To be more specific about this, I am under the below assumptions and then will explain my question further. Please let me know if any of the assumptions are incorrect.
(1) Special relativity describes ...
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1
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65
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Lorentz transform causes Faster than light motion for Spacelike-separated object?
Consider a 5-meter rod which exists on the x-axis of a frame of reference:
Now consider an observer moving at a velocity $0.1c$ relative to this reference frame, from right to left. Their frame of ...
