All Questions
Tagged with spacetime inertial-frames
290
questions
0
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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 ...
0
votes
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 ...
1
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3
answers
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 ...
2
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3
answers
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
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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 ...
0
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1
answer
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 ...
0
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1
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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 ...
1
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1
answer
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, ...
0
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1
answer
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 ...
1
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0
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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 ...
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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 ...
-4
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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, ...
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 ...
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 ...
9
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5
answers
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 ...
2
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3
answers
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 ...
0
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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 ...
0
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2
answers
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 ...
0
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1
answer
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 ...
5
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1
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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,...
1
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1
answer
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 ...
-1
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1
answer
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 ...
0
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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 ...
0
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1
answer
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 ...
0
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1
answer
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 ...
4
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2
answers
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 ...
0
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2
answers
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
answer
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 ...
-2
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1
answer
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 ...
0
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6
answers
173
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If time runs slow for moving train, how can it cover same distance in less time than someone on the ground unless the track decreases in its view?
According to special relativity,
Δt=γ*Δt' ... (1)
Where,
Δt is the time the train takes to completely pass by me according to my watch,
Δt' is the time I should see has passed for someone on the train....
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4
answers
163
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Relativity of simultaneity in flat spacetime
In Einstein’s (1917) thought experiment on the relativity of simultaneity…
The lightening flashes at A and B are both equal distance from the center of the train and the center of the platform.
The ...
1
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1
answer
174
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Homogeneity of space doubts [duplicate]
This question might have been asked so many times, but here we go again. I'm wondering what homogeneity of space means. All the descriptions say:
there's no special point in space, every point looks ...
-1
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3
answers
104
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Why doesn't Galilean relativity lead to a contradiction in SR?
Two identical spaceships commanded by Alice and Bob are at rest next to each other in outer space. The clocks of the spaceships are synchronised; and when they are close by Alice can see Bob's clock ...
0
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1
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54
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Can we see the rest-energy of a mass as its kinetic energy in the $ct$-direction?
A mass $m$ at rest has an energy $E=mc^2$. Can we say this is its kinetic energy in the $ct$-direction?
-1
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2
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116
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Does special relativity imply that there's such a thing as absolute time, or base time?
If time measured by one observer moving at a greater velocity than another observer is observed to be passing more slowly, does this imply that there's such a thing as "absolute time" or &...
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2
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86
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Problem with deriving the Lorentz Contraction [duplicate]
I am trying to prove the contraction. I know there are several ways one can do it. The way I am trying to solve is said to be complicated and that there is an easier way to do so. Because I don't have ...
0
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1
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143
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Lorentz Transformations derivation
I was reading derivation of Lorentz transformation but I don't understand why the constant a here is equal to -c^2.
Full pdf: http://www2.physics.umd.edu/~yakovenk/teaching/Lorentz.pdf
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1
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57
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What is the reason of different clock's measurements in different frames? [closed]
I tried to understand what is the reason of different clock's measurements in different frames.
For this I looked at easy example with distance S traveled by man with moving clock (velocity V1=2m/s) ...
1
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1
answer
45
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Alternative to Susskind's way to derive the equation of the $x'$ axis in relativistic spacetime diagram?
Note : sorry for the poor drawing above.
Note : in what follows, the speed of light is taken as unit : $c =1$ and the trajectory of a light signal sent from $(0,0)$ is $x = ct = t$.
In his ...
0
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2
answers
95
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The Lorentz factor $γ$, and Fermilabs derivation of it
Before diving into my question, we first must acknowledge Einsteins two assumptions:
The laws of physics are the same for every observer and reference frame.
The speed of light is constant for ...
3
votes
3
answers
221
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Please explain $E = γmc^2$ more intuitively [closed]
My name is Shaun and I am 14 years old.
Lately I have been trying to learn about $E = mc^2$, and I came across Fermilabs video about $E = γmc^2$, where $γ$ is the Lorentz factor.
My question is how ...
0
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2
answers
69
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Ambiguous special relativity between two sources?
I am currently confused about things I read about special relativity (I'm a CS major and not as well-versed in physics as I would like to be).
I just watched a video on evaluating a Lorentz ...
23
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7
answers
5k
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Is there a *geometric* explanation for why photons have no rest frame?
I've read the various threads on this site that talk about it being impossible for photons (or massless particles in general, really) to have a rest frame, and the answers all seem to boil down to &...
0
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0
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51
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Geometric definition absolute velocity in affine spaces
currently I am reading the following paper by Halvorson and Clifton (https://arxiv.org/abs/quant-ph/0103041) where they try to argue that localizable particles are inconsistent with relativistic ...
0
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0
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54
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Lorentz transformation in extra-dimension
The Lorentz transformation is usually defined In 4D spacetime, how can we derive the generalized transformation in extra-dimensional space-times like 5D or more dimensions?
0
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2
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54
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Time-Like Separated Events: Can there be more than one reference frames for which 2 events can happen at same place?
For time-like separated events, reading of 2nd event of any observer from central event (i.e. at origin)
should lie within top light cone (we will consider only future events and ignore the bottom ...
6
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2
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431
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Confusion regarding bundle structure of Galilean spacetime in Penrose's The Road to Reality
I am reading Roger Penrose's The Road to Reality. In section 17.3, I encounter the following passage. To give a context, Penrose was explaining that even though an Aristotelian spacetime can be ...
0
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1
answer
141
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Mathematically rigorous derivation of Einstein-Lorentz transformation
Many elementary explanations of the Einstein-Lorentz transformation derive it using Einstein's special relativity postulates, combined with some thought experiments considering light sources and ...
1
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2
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113
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Trying understand the argument on Special Theory of relativity on Goldstein book
I am reading Goldstein and trying to understand the special theory of relativity. I am not sure how did he make this following argument.
The books explain that $ds^2$ is invariant in spacetime. He ...