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  1. Are the explanations involving clocks only valid if the clocks are ticking when light hits?

  2. Is it true that these thought experiments experiment could only be valid due to the invariance of $c$?

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  • $\begingroup$ A simple clock that is not "ticking" is radioactive decay. A useful physical clock is mechanism that shows a well enough characterized change over time and that agrees in its quantitative reading with other clocks. The invariance of c (or any other natural constant) is neither a necessary physical assumption nor a trusted fact. We are commonly performing experiments which try to test the validity of the constancy of natural constants. $\endgroup$ – CuriousOne Dec 18 '14 at 2:06
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If I understand correctly, your question is why would time dilation for any other type of clock.

Light is an electromagnetic wave, all electromagnetic waves travel at the speed of light. If, say, you have a mechanical watch it has a spring, atoms in which exchange electromagnetic signals, which travel at the speed of light. Therefore a mechanical watch can be subjected to the same analysis. Furthermore, there are other fundamental interactions, which also work at the speed of light. For example half-life of certain isotopes is also subject to time dilation.

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  • $\begingroup$ This answer doesn't really explain why a clock based on nuclear decay would agree too though. The most general answer is that all known laws of physics including all quantum field theories are Lorentz-symmetric, meaning the equations are unaltered when you transform from the space and time coordinates of one inertial frame to those of another. The first of the two postulates of SR predicts this will be true of all laws, and so far all evidence supports it. $\endgroup$ – Hypnosifl Dec 17 '14 at 23:19
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The explanations involving clocks ...

Textbook examples or explanations of relativity that involve clocks are often about time-dilation.

... Is valid only if the clocks is ticking ...

These examples/explanations generally assume that any clock they mention is a working clock. It doesn't have to be a clock that ticks. It could be any type of clock of sufficient accuracy and precision. It could be a very large eggtimer - it doesn't matter.

... when light hits, right?

The clock has to be continuously running the whole period covering all events in the example/explanation. Otherwise it can't measure elapsed time.

This experiment could only be valid due to the invariation of c

From what I recall, all the rather striking basic notions of special relativity, like time-dilation, can be straightforwardly derived by working from the observation that light in a vacuum travels at $c$ regardless of the velocity of observer and light source.

I'm not getting the concept

That's because it is unintuitive when you first encounter it (and may remain so).

The essential concept is that light (and any other electromagnetic radiation) in a vacuum always travels at $c$ regardless of the velocity of the observer in relation to the light source.

What necessarily follows from this is that people in motion will often disagree about which events occurred simultaneously, about the physical length of things and how much time has passed between events. yet they will agree that each other's measurements are correct and match the calculated measurements predicted using the equations associated with Relativity.

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Time dilation is just that: time dilation and not simply clock time dilation (although the former implies the latter). Any process or chain of events will take longer when observed from a relatively moving, inertial frame. We can, for example, put unstable particles into high speed rings and their lifetime will increase by the factor $1/\sqrt{1-\frac{v^2}{c^2}}$, where $v$ is the speed at which they move relative to the observer. Since many particle decays are mediated by forces other than the electromagnetic interaction, these experiments show that time dilation is more general light. All clocks will "slow down" in this way. Through experiments like this we have experimentally shown that all clocks behave like this, to a fantastically high accuracy.

Nowadays we understand special relativity independently of light. The speed $c$ comes out of an analysis of what happens to Galileo's Relativity (note I didn't say Einstein) when we relax the assumption of an absolute time. The latter - the bold step of questioning time's constancy and deducing what would follow from nonconstant time - was Einstein's big and bold contribution. I say more about this analysis of Galileo's relativity in my answer to the Physics SE question "What's so special about the speed of light?" here. The particular arguments referred to there show that $c$ is fixed and, moreover, unique: there can be at most one velocity $c$ that transforms in the way it does.

The speed $c$ is understood to be a universal constant that, amongst other things, is the speed that any massless particle moves at. That light is experimentally found to move at this speed (or more correctly, that light's speed is experimentally found to transform between inertial observers in the special way that the nonabsolute time analysis foretells) can now be seen as an experimental proof that light is mediated by a massless particle. Again, these experiments are now fantastically accurate: the Michelson-Moreley experiment can now be done at such an accuracy that shows constancy of the speed of light to within one part in $10^{-17}$ for speeds up to that of Earth relative to the putative "Aether" (which is thus discredited by these experiments). See here

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