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The answer by Vincent Thacker is correct, but I hope I can clarify further.
The term "length contraction" or "Lorentz contraction" does not refer to a distance between any given pair of events. Rather it refers to a separation between two worldlines. The worldlines are typically the ones at the two ends of a given solid object. But how do ...
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This may seem like a weird thing to require but to measure the length of a line, every point along that line has to exist at the same time. Let's say I want to measure the length of (a 1-dimensional) stick. I can give each of the points along that stick a pair of coordinates $(t,x)$. When I want to measure the length I will require by definition that each of ...
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In special relativity, there is no smallest length or shortest time beyond which the theory stops working. It is a theory that applies to all length and time scales. There may be theories other than special relativity that predict that time dilation breaks down at some length/time scale, but such theories have no bearing on the predictions of special ...
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Acceleration, in and of itself, does not cause time dilation. This is the clock postulate and is well confirmed by experiment e.g. in particle accelerators. So only the speed (relative to the observer) causes time dilation. If that speed is constant (even though the velocity is changing) then you can just use the ordinary SR time dilation formula. In the ...
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To add to the answer by @AndrewSteane ,
the key idea is that
"the [proper] length of an object is the distance between the parallel lines [of its endpoints]"
and this distance is taken along a line perpendicular to those lines.
In relativity, "perpendicular to timelike lines" corresponds to "simultaneity", as suggested below.
...
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First, imagine a stopwatch at rest that measures a time interval $\Delta t$. This concretely means there are two events: event 1 is that we start the stop watch at time $t_1$ and position $x_1$, and event 2 is that we stop the watch at time $t_2=t_1+\Delta t$ while the watch is still at position $x_2$. The spacetime interval in the stopwatch frame is then
\...
3
Consider the laser beam to consist of a stream of photons emitted at a certain rate. The gap between each photon emission has one value according to ship A and another according to ship B because of the relative time dilation.
So yes, ship B receives the photons for a longer period of time, but it receives them at a lower rate. The overall number of photons ...
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What physics says is that what you have proposed is strictly impossible. The energy required to accelerate the train could not be delivered to it. Gravity would not be sufficiently strong to constrain the train to the track. The train would burn-up with friction long before it reached a tiny fraction of light speed. The passengers would die as a result of ...
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The biggest problem with understanding special relativity is to understand that events that are simultaneous in one frame are not simultaneous in any other frame. Length in $S$ is measured by taking two measurements at the same time in $S$. The phrase "same time" should immediately alert you that it will not be the same time in another frame $S'$.
...
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You have a mixed up idea of what time dilation means. The glass breaks when it breaks- it is not broken in one frame and unbroken in another. The two observers simply disagree on how long it took to fall and what time it was when it hit the ground.
From the point of view of the clumsy person on the moving spaceship who dropped the glass, the fall started at ...
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You proved something by thinking about a clock. You are worried that you couldn't have proved it by thinking about some other clock. Okay, you also couldn't have proved it by thinking about the 1959 World Series. All you need is one proof, and you have that proof. The fact that some other attempted proof might not work won't change that fact.
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which interestingly has the same value.
I feel like I ought to be able to multipy these together
It is not a coincidence that they have the same value. They are both the same time dilation from different perspectives. The velocity formula is the time dilation from the perspective of the inertial frame. The potential formula is the time dilation from the ...
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Not only can space ships not travel at the speed of light, there are no inertial frames traveling at the speed of light. The question is ill-posed.
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SITTING PASSENGERS:
What they see outside:
looking back, the light they observe is so much redshifted (lowered in frequency) that their eyes see nothing. Not even expensive radio equipment could detect those such long waves.
looking forward, the light they observe is so much blue shifted, that it's in the gamma ray range, destroying their DNA and probably ...
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A hint that the evolution of the physical state of $A$ and $B$ are not indiscernable (not interchangeable, not symmetrical):
Let’s make the experiment a bit more specific and let $A$ and $B$ be two identical rockets $A$ and $B$, each fitted with an accelerometer and some recording device.
$A$ stays on planet $Pa$ and $B$ goes to planet $Pb$ and back. Both ...
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Following is the extract from Wikipedia page on Time Dilation
Given a certain frame of reference, and the "stationary" observer described earlier, if a second observer accompanied the "moving" clock, each of the observers would perceive the other's clock as ticking at a slower rate than their own local clock, due to them both perceiving ...
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Yes, objects in orbit are affected by gravitational time dilation. Time dilation is not directly connected with acceleration (this is the clock postulate); it is only indirectly connected insofar as acceleration (may) change a clock's speed. In the case of a clock in orbit, the clock experiences the same gravitational time dilation as an observer in a fixed ...
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The rule is that a length that is stationary in one reference frame will always be shorter in a frame moving relative to it.
The discrepancy arises from the relativity of simultaneity.
In the frame in which the length is moving, the observers believe that they are pinning down each end of the object simultaneously- however, from the perspective of the ...
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The second equation is a special case of the first.
The first calculates the time measurement from a relatively moving frame (at x-velocity $\beta$) of an event which has (ct,x) coordinates in another frame, with a synchonization of the ($t=0,x=0$) and ($t'=0,x'=0$) coordinates.
The second would be true for an event which occurs at $x=0$. That's probably not ...
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One of the principles of special relativity states that the speed of light in vacuum is the same for all inertial frames of reference and that it does not depend on the relative motion of the source. Equivalently: in every inertial reference system there is a limiting speed for the propagation of physical entities (signals, particles).
One of the most ...
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I think your question is a variation of " why isnt time dilation invalid at quantum scales "
I think the answer is that, it IS invalid. Relativity is not applicable in the quantum scale. Relativity and quantum mechanics are famously not compatible. A unified theory that is applicable at both scales would be some sort of holy grail in physics.
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Your question is whether the simple argument to show the necessity for time dilation by observing a moving light clock might break down if the length of the clock is less than the Planck length.
The question is very much one of principle, since it is impossible to exaggerate how utterly impractical it would be to create and operate such a clock.
There are ...
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