All Questions
Tagged with distance special-relativity
30 questions
1
vote
3
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182
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How to deal with square root of negative number when calculating spacetime interval?
I was reading Hartle's Gravity: An Introduction to Einstein's General Relativity and I was doing an exercise from page 57 that asks me to use the metric $\Delta s^2=-(c\Delta t)^2+\Delta x^2$ ...
- 711
3
votes
1
answer
157
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Clarification on Representing Distances and Trajectories in Minkowski Spacetime
In the context of Minkowski spacetime, where the metric has a signature of (-, +, +, +), the $x-t$ plane (spacetime diagram) is commonly used to visualize events and their evolution in both space and ...
- 501
3
votes
2
answers
177
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Schutz description of Galilean invariance of interval
In B. Schutz's textbook "A First Course in General Relativity", there is a sentence on page 172 discussing Galilean relativity and how the distance between events is invariant in coordinate ...
- 147
0
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1
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60
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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
0
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1
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108
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Which experimental setup replicating Michelson-Morley experiment had the longest path of light?
After the Michelson-Morley (MM) experiment many scientists performed similar experiments using the original MM experimental setup, or different derivative experimental setups employing lasers and ...
- 240
1
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0
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45
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How can we accurately tell distances of celestial bodies when considering superluminal expansion [closed]
If parts of the universe are moving away from each other faster than the speed of light relative to my position in space, how can we accurately tell the age or distance of other celestial bodies ...
5
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3
answers
620
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Where does the negative signature case come from in the Pythagorean derivation of distances in spacetime?
I am reading Why does $E=mc^2$ (and why should we care?) by Brian Cox and Jeff Forshaw. I want to understand these three sentences
(from page 76/77):
Once we follow Occam and make these two ...
- 175
0
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1
answer
98
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What symbol is used for 'proper distance'? [closed]
Proper time and proper space are generally defined as what an observer would measure in their own rest frame. If $\tau$ is a commonly used symbol for the proper time, what is the corresponding symbol ...
- 584
3
votes
1
answer
162
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Distance in Hubble law vs special relativity
Came across this very informative website https://astro.ucla.edu/~wright/cosmo_02.htm , and it has the following two diagrams. I'm having trouble figuring out why "But the Hubble law distance $D_{...
- 191
0
votes
1
answer
56
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Is the total interval along a path equal to the sum of the intervals along its segments? [closed]
Context
While working an exercise I was confronted with the terms total invariant interval, and total interval.
Question
Using mathematics, how are the terms total invariant interval and total ...
- 654
4
votes
2
answers
560
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Difference between distance and norm
In special relativity, different observers measure lengths of objects differently, depending on their respective velocities. However, all observers agree on the invariant inner product of two vectors (...
- 920
0
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2
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153
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Is the line element a distance vector or displacement vector?
In my Electrodynamics and Electromagnetism course, the professor is deriving Maxwell equations and the electromagnetic field tensor from differential geometry and wants to show how special relativity ...
- 97
0
votes
1
answer
92
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Spacetime distances and perception
My question is about how things appear in human perception vs how things are in spacetime.
Take as an example my perception of the laptop screen while I am writing this.
As far as I understand it, ...
- 451
0
votes
1
answer
51
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What does $AB$ mean in the paper On the Electrodynamics of Moving Bodies?
When reading through the paper "On the Electrodynamics of Moving Bodies" by Albert Einstein, my friends and I were confused by some of the notation used and how to interpret it.
On page 3, ...
- 286
8
votes
2
answers
1k
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If two reference frames are not moving with respect to each other, do we take into account their distance apart to determine simultaneity of events?
I'm trying to clarify the definition of simultaneity and/or relative simultaneity - for now, only with respect to two different reference frames that are not moving relative to each other.
There ...
- 391
0
votes
1
answer
136
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About comparing distances between different frames of reference, and meter sticks
If a frame of reference $S'$ is moving with respect to a frame of reference $S$ with a velocity $v$ (along the $x$ axis of $S$), then an event $(x,t)$ in $S$ is viewed as an event $(x',t')$ in $S'$ ...
- 1,292
30
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6
answers
7k
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Is a light year a different distance if measured from a moving object?
The speed of light is absolute, but time is relative. So would a light-year for us on earth be a different distance from a light-year on a different uniformly moving object? Why or why not?
- 435
1
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2
answers
165
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Paradox are all 4D distances zero?
The 4 dimension distance from the origin of a point is $\sqrt{x^2+y^2+z^2-t^2}$. Which means the 4 dimensional distance on the light-cone is zero.
Take a point A and a point B in the future at ...
user84158
3
votes
4
answers
5k
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Understanding the difference between timelike and spacelike separations
From Woodhouse's General Relativity:
If $A$ is the origin and $B$ is a nearby event with coordinates $dt, dx, dy, dz$, then,
$$ds^2 = dt^2 - dx^2 - dy^2 - dz^2$$ is the same in all local inertial ...
- 895
35
votes
2
answers
5k
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Why isn't the GPS location calculated from the Schwarzschild metric?
The GPS uses the flat space light propagation formula to calculate the distance from the source (the satellite) to the receiver (observer on Earth):
$$ d=c \cdot \Delta t$$
where $c$ is the speed of ...
- 535
2
votes
3
answers
277
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Can length contraction help the moving observer reach a star system 'faster'? [duplicate]
Would an observer moving with close to the speed of light ($\sim 99\%$) towards a star system that's $20$ light years away perceive the distance as being less than $20$ light-years? If yes, how much ...
- 133
9
votes
4
answers
3k
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Are any of Euclid's 5 postulates false in Minkowski spacetime?
I often hear that Minkowski spacetime is non-euclidean. Euclidean geometry is characterized by Euclid's five postulates being true. Which of those postulates are untrue in Minkowski spacetime (if any),...
- 259
0
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1
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265
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Shortening of distances in Relativity Theory
I am studying relativity theory and I have understood why distances become shorter from the perspective of someone who is travelling close to the speed of light. However, later on I read that the ...
- 559
6
votes
1
answer
165
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How much energy needed to cross the galaxy in time $t$?
Sorry if this is a dumb question.
A friend of mine just asserted that it's possible to get anywhere in the universe in less than 30 seconds of your time due to time dilation. I do imagine that'll ...
- 931
3
votes
3
answers
519
views
Use of angular diameter to determine distance in special relativity
Summary: at relativistic speeds, if you compute a planet's relative distance using angular diameter (roughly proportional to 1/angular diameter), will that computed distance increase or decrease ...
user854
3
votes
1
answer
1k
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Distance from redshift
I am looking for a exact derivation of a relation between redshift $z$ and distance $d$.
What I know is the definition
$$z=\frac{\lambda_{\text{observed}}}{\lambda_{\text{unshifted}}}-1=\sqrt{\frac{1+...
- 393
3
votes
1
answer
217
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A problem with a basic thought experiment in Special Relativity
This is for a class on special relativity I am to give to some school children.
Moe is moving at 0.9c. At the instant he passed Joe he emits a flash of light. One microsecond later, Joe(at rest) sees ...
- 31
6
votes
1
answer
578
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Does length contraction affect travel time?
If an astronaut leaves planet $A$ for planet $B$ at speed $v$, will the time (measured by the astronaut's clock) that it takes for the astronaut to reach planet $B$ be less than the distance between ...
- 2,525
0
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2
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251
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Distance travelled in spaceship Newton vs Einstein
If you get in the canonical 1G windowless spaceship and accelerate for 5 years as determined by your trusty wristwatch, then decelerate for 5 years, then decide its time to see where you are would the ...
- 1,418
6
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4
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2k
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In relativity, what is the difference between a rod that is perpendicular to direction of motion and a rod parallel to the direction of motion?
In Feynman's Lectures on Physics , chapter 15, page 6 he writes about 2 identical, synchronized light signal clocks. These are clocks that consist of a rod (meter stick) with a mirror at each end, and ...
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