Does Time Move Slower for Travelers in Special Relativity Experiments?

[Hak]

In the mental experiment of special relativity (which has been experimentally proven anyway), in which it is shown that for the traveler on the spaceship, time passes more slowly because the clock (the tick-tock of light beams) goes slower... What is the correlation between the traveler's biological passage of time and the clock in question? Using an "ordinary" clock, I would be forgiven for thinking that this experiment no longer holds... I am trying to study special relativity but it is not a subject I master well; however trying to understand this simple experiment I cannot find the answer to this very trivial doubt...

 

[Dale]

What is the correlation between the traveler's biological passage of time and the clock in question?

The correlation is the principle of relativity.

If we had that in some frame a light clock slows down but a biological clock did not, then you could use a light clock and a biological clock to distinguish between that frame and other reference frames. A frame where biological clocks and light clocks agreed would be the absolute rest frame, and a frame where light clocks slowed but not biological clocks would be absolutely moving. This would violate the principle of relativity.

 

[Hak]

The correlation is the principle of relativity.

If we had that in some frame a light clock slows down but a biological clock did not, then you could use a light clock and a biological clock to distinguish between that frame and other reference frames. A frame where biological clocks and light clocks agreed would be the absolute rest frame, and a frame where light clocks slowed but not biological clocks would be absolutely moving. This would violate the principle of relativity.

Thank you. So it is related to the principle of relativity, which states that all laws of physics take the same form in every inertial frame of reference, and that consequently there is no such thing as absolute motion, no one moves and no one stands still intrinsically; so this fact implies that there can be no discrepancy between time measured with a light clock and time measured with an atomic clock, otherwise you could tell whether the system is intrinsically in motion, which goes against the principle of relativity? Now, the consequence of that would be that if one observer sees another in motion relative to him, that observer's time appears slowed down, and the thing is reciprocal, right? This is an anti-intuitive concept, as is the principle of constancy of the speed of light though, or is it?

 

[Dale]

this fact implies that there can be no discrepancy between time measured with a light clock and time measured with an atomic clock, otherwise you could tell whether the system is intrinsically in motion, which goes against the principle of relativity?

Yes

Now, the consequence of that would be that if one observer sees another in motion relative to him, that observer's time appears slowed down, and the thing is reciprocal, right? This is an anti-intuitive concept, as is the principle of constancy of the speed of light though, or is it?

Yes. This is exactly why it is so difficult to learn, it is very much non-intuitive.

 

[Hak]

Thank you very much.

 

[FactChecker]

Now, the consequence of that would be that if one observer sees another in motion relative to him, that observer's time appears slowed down, and the thing is reciprocal, right? This is an anti-intuitive concept, as is the principle of constancy of the speed of light though, or is it?

Remember that the comparison of time and clocks is occurring where different clocks are being compared as time goes by and they move with respect to each other. Each observer is moving toward the rear of the other observer, so they are comparing different clocks in different directions.

 

[phinds]

it is shown that for the traveler on the spaceship, time passes more slowly

Just to be sure you've gotten absolutely clear on this, NO ... time does NOT pass more slowly, either for a person OR for a clock. It APPEARS, to a remote observer, to have done so but locally all clocks tick at the same one second per second.

 

[Mister T]

it is shown that for the traveler on the spaceship, time passes more slowly

You may be misunderstanding this. The traveler in the space ship will see the light clock behaving just the same as if the rocket were at rest.

You can say that the rocket is moving relative to Earth. An observer at rest on Earth will observe the clock on the rocket ticking at a slower rate. An observer at rest in the rocket will observe a clock on Earth ticking more slowly.

This is the symmetry of time dilation, and it cannot be understood without understanding the effect that the relativity of simultaneity has on the situation.

Note that this is not just appearances. The clocks really do run slower, extending, for example, lifetimes.

 

[phinds]

Note that this is not just appearances. The clocks really do run slower, extending, for example, lifetimes.

No, that is completely wrong. The clocks do NOT run slower. They tick away at the same one second per second that every (properly working) clock in the universe does. I already pointed that out in post #7.

You need to Google "differential aging" to understand why time passes at the same rate but by a different amount in, for example, the twin paradox.

 

[Hak]

Just to be sure you've gotten absolutely clear on this, NO ... time does NOT pass more slowly, either for a person OR for a clock. It APPEARS, to a remote observer, to have done so but locally all clocks tick at the same one second per second.

Note that this is not just appearances. The clocks really do run slower, extending, for example, lifetimes.

I'm a bit confused...

 

[phinds]

I'm a bit confused...

MisterT h as it wrong. Ignore what he said. I don't know any really advanced physics but I am VERY solid on this aspect of Special Relativity.

People get confused and think, incorrectly, that time passes more slowly because of one person travels away from another at high speed and then comes back, when they meet up again the traveler will have aged less than the stay-at-home.

This is NOT because the traveler's clock ticks at a different rate (it does not), it is because the traveler takes a different path through space-time.

It's like if you and your neighbor got in their cars and both drove from wherever you are to a city 100 miles away and back again, BUT one of you goes WAY out of the way on the trip, when you both got back your odometers would show different amounts even though you both drove at 60MPH the whole trip.

This is called differential aging.

 

[Ibix]

I'm a bit confused...

I agree with @phinds here, that characterising what happens as "time runs slower" is a mistake. It's definitely the case that I measure your clocks ticking slowly in my rest frame if you are moving, but you say the same about my clocks. There are indeed measurable consequences to this, such as the number of muons reaching the ground from the upper atmosphere. So I agree with everything @Mister T says except the first part of his last sentence, which I would say is probably misleading.

 

[Dale]

I'm a bit confused...

In relativity there are two distinct concepts of "time". One is "proper time" and the other is "coordinate time".

@phinds is focusing on proper time, denoted $\tau$. That is reasonable because it is the physical time, what is measured by clocks and what determines the rate of chemical reactions, or other similar things in physics. It is also a frame invariant quantity that all reference frames agree on. The SI second is a unit of proper time. So proper time always passes at a rate of 1 second per second.

Coordinate time is the time of a given reference frame, denoted $t$. It depends on the coordinate system and is therefore frame variant. Time dilation is the rate of change of coordinate time with respect to proper time $\gamma = dt/d\tau$, and in an inertial reference frame where a clock is moving that quantity is always greater than 1. When people speak of clocks slowing down, this is what they mean.

Some people consider frame-variant quantities to be unphysical. Such people make statements similar to @phinds because since $\gamma$ depends on $t$ which is frame variant, that means it is unphysical. Such people are not wrong, but it may be a little confusing if you do not understand what they are saying and why they are saying it.

Other people consider frame-variant quantities to be physical. They will make different statements, like @Mister T did. Such people are also not wrong, but again it may be a little confusing if you do not understand what they are saying and why they are saying it.

Sorry, I sometimes wish human language were unambiguous, but then poetry would be pretty boring.

 

[FactChecker]

"clock running slower" begs the question -- running slower than what? Neither observer, "stationary" or "moving", is able to detect anything unusual with their own clocks in any way. It is only when one observer compares his clocks (synchronized in his frame all along the relative path) with the clocks of another observer who is moving (clocks synchronized similarly in the moving frame) that anything looks strange. Of course, each observer must assume that his clocks are fine since there is no experiment in his frame that will indicate otherwise. So each observer must say that the other observer's frame clocks are running slow. You have to keep in mind that as any time passes, the two sets of clocks are moving, so the direct clock comparisons are made with different clocks at changing locations.

 

[Mister T]

The lifetime of a moving muon is longer than it would be if the muon were at rest relative to the observer. It doesn't just appear to live longer. It actually does live longer. It's a measurable effect and not just a matter of appearances.

 

[Algr]

The lifetime of a moving muon is longer than it would be if the muon were at rest relative to the observer. It doesn't just appear to live longer. It actually does live longer. It's a measurable effect and not just a matter of appearances.

If you were moving with the muon would you still measure it as lasting longer?

 

[Ibix]

The lifetime of a moving muon is longer than it would be if the muon were at rest relative to the observer. It doesn't just appear to live longer. It actually does live longer. It's a measurable effect and not just a matter of appearances.

Agreed. I'd still be dubious of explaining this as "clocks really do run slower" without saying "as measured using the Earth's rest frame".

 

[phinds]

The lifetime of a moving muon is longer than it would be if the muon were at rest relative to the observer. It doesn't just appear to live longer. It actually does live longer. It's a measurable effect and not just a matter of appearances.

Of course. It takes a different path through space-time and thus the effect of differential aging. See post #11.

 

[Mister T]

Agreed. I'd still be dubious of explaining this as "clocks really do run slower" without saying "as measured using the Earth's rest frame".

I agree. Sorry for the confusion that has arisen from my Post #8. I thought it was clear from the context (see the 2nd paragraph) that I was talking about Earth's rest frame. In hindsight, I suppose I should have stated it more clearly, given the confusion it caused.

 

[Mister T]

Of course. It takes a different path through space-time and thus the effect of differential aging. See post #11.

The muon can move in a straight line. As in the original experiment where Rossi and Hall made the measurement. The effect can be explained by time dilation, as asked about by the OP. (Edit: This is a comparison of a proper time to a dilated time.) My understanding of what in this forum has come to be called "differential aging" is a comparison of two proper times that differ because different paths were taken through spacetime.

 

[Mister T]

If you were moving with the muon would you still measure it as lasting longer?

No. But you would observe the muon (and yourself) travelling a shorter distance (compared to the distance observed by an observer stationary on Earth). This is called length contraction.

 

[PeroK]

1) The proper lifetime of the muon is an invariant.

2) The measured lifetime of a muon (in terms of coordinate time) is coordinate dependent.

Whether you claim that coordinate dependent means "an appearence" or "not just an appearance" depends on how you define the superfluous word appearance. IMHO, if you want clarity, you refrain from defining appearance in physics and stick to invariant and coordinate dependent as the key, standard terms.

 

[Nugatory]

I'm a bit confused...

The problem here is that there is more than one way to interpret the phrase "time passes more slowly".

The best way of resolving your confusion is to work at understanding two different cases without ever using that dubious phrase:
a) You and I are moving relative to one another, and we both apply the time dilation formula to conclude that time is passing less quickly for the other. There is of course an apparent paradox here - how can your time be slower than mine and my time be slower than yours? This effect is explained by the relativity of simultaneity, and working through it will clarify the limitations of the time dilation formula and what meaning we're attaching to the phrase "time passes more slowly".
b) The twin paradox case, in which two clocks follow different paths through spacetime between point A (traveller leaves Earth) and point B (traveller returns to Earth). Different paths have different lengths, the length of a path in spacetime is measured in seconds, so there are more seconds along one path between A and B than along the other. This can also be understood as "time passes more slowly", but in a completely different sense.

So don't use that phrase at all, not until you can explain both cases without using the words "time passes more slowly". That will rescue you from the confusion that results when @Mister T and @phinds argue about whether that's right.

 

[Vanadium 50]

there is more than one way to interpret the phrase

Which is why physicists use all that nasty math instead of pretty words.

 

[vanhees71]

The lifetime of a moving muon is longer than it would be if the muon were at rest relative to the observer. It doesn't just appear to live longer. It actually does live longer. It's a measurable effect and not just a matter of appearances.

As has been stressed several times now, you have to be careful to tell people to which "time" you are referring. The "lifetime" of a muon is by definition the average time after which a muon decays as measured by an observer for whom the muon is at rest. That's a definition, and it's a frame-independent definition, because the frame, where it is defined is fixed once and forever, i.e., the rest frame of the muon.

Now in a frame of reference, where the muon is moving with constant velocity $\vec{v}$ this proper time is calculated as $\tau=\sqrt{1-\vec{v}^2/c^2} t$, where $t$ is the time of an observer at rest wrt. this reference frame. That's called the time-dilation effect, and it's indeed measurable with high accuracy in accelerator experiments.

 

[pervect]

Thank you. So it is related to the principle of relativity, which states that all laws of physics take the same form in every inertial frame of reference, and that consequently there is no such thing as absolute motion, no one moves and no one stands still intrinsically; so this fact implies that there can be no discrepancy between time measured with a light clock and time measured with an atomic clock, otherwise you could tell whether the system is intrinsically in motion, which goes against the principle of relativity? Now, the consequence of that would be that if one observer sees another in motion relative to him, that observer's time appears slowed down, and the thing is reciprocal, right? This is an anti-intuitive concept, as is the principle of constancy of the speed of light though, or is it?

It is helpful here to disentangle the notion of time into proper time, and coordinate time. Proper time is what a clock measures. Coordinate time is a convention that assigns time labels to events.

Proper time is always an interval, and is what a clock actually measures. A clock travels some path through space, and it keeps time, and clocks can be compared to other clocks when they are at the same location in space at the same time.

In the language usually used by textbooks, we talk about "world lines" or "time-like worldlines" that represent the motion of an object. Time-like worldlines represent physical objects that always move slower than the speed of light and can have a clock attached or associated with it. This clock essentially measures the "length" of the worldline. You might see a reference to "space-like worldlines". They're not needed for this discussion, except to say that they aren't relevant to clocks, rather they are relevant to rulers. Since we won't need them, I won't discuss them further.

With this view, the twin paradox is no more inconsistent than to say that if you drive in space a straight line from one city to another, with an odometer attached to y our car, your trip as measured by the odometer which measures the distance your car moves is shorter when you drive in a straight line than when you take a detour. Notably, though, there is an important sign difference in this simple analogy. In space, the path of straight-line motion minimizes the distance. In space-time, the path of "straight-line" motion, which is the natural inertial motion of a body with no forces acting on it, give the longest proper time, not the shortest. But aside from this key difference, the ideas are the same. There's no prior reason to expect that clocks that follow different paths and meet up again will read the same time when they re-unite wihtout additional assumptions, just as there is no reason to think that the odometer readings for two cars taking different paths through space will remain the same.

Coordinate time is typically invoked by creating an unlimited number of clocks, all arranged in some particular fashion in space. And, importantly, in order to define a coordinate system, these clocks must be synchronized. And this is where the fun starts.

In special relativity, different observers have different notions of synchronization, depending on their state of motion. Fully exploring the consequences of this turns out to be trickier than one imagines, and typically one does not imagine it's easy. In fact, I think much of resistance to this concept comes from the nagging feeling that one hasn't figured out all the logical consequences it entails. The only remark I can say is that while this is true, someone just introduced to relativity is unlikely to imagine all the logical consequence, and furthermore that one is unlikely to find all of the consequences written down in one place to be studied, the relativity of simultaneity is nonethelss a keystone result of special relativity.

Some of the more obvious issues arise with our notion of cause-and-effect. I won't go into them at this point, I'll just point out that it's one of many consequences, and it takes a considerable amount of work to understand how causality works in special relativity. I'll mention that this is typically done via "light cones", but I won't go into any more details than that. This is in contrast to the classical idea that "the past" (a singular agreed upon notion by everyone) can cause "the future". In special relativity the idea of "the past" as a singular agreed upon entity gets replaced with the "past light cone", which is unique to each observer.

So - to recap. The twin paradox isn't that hard to explain, (in my honest opinon) once one understand that simultaneity is relative. The hard part is understanding (again in my honest opinion) is understanding the relativity of simulttaneity and it's consequences.

 

[Hak]

Thank you so much.

 

[vanhees71]

It is helpful here to disentangle the notion of time into proper time, and coordinate time. Proper time is what a clock measures. Coordinate time is a convention that assigns time labels to events.

Of course also coordinate time can be realized, at least in principle, by real-world objects, defining physically a frame of reference. As Einstein already in his famous paper of 1905 realized, an "event" in spacetime is defined by something happening at a place at a time measured by a clock at this place. To compare times of events in different places thus needs a "synchronization convention" between clocks at different places.

Now in Einstein's special theory of relativity is based on the problem with the asymmetry of the Maxwellian electrodynamics against Galilei boosts. While most (if not all) physicists thought that electromagnetism has either to be modified such as to make it Galilei invariant or that finally, via electromagnetic phenomena, an absolute inertial frame of reference was definable. Usually the latter was related to the idea that electromagnetic fields are nothing else than excitations of a medium, called the "(a)ether". On the other hand it was pretty clear that Maxwell's equations described all electromagnetic phenomena correctly, and that brought Einstein to the insight that it was the Galilei-Newtonian spacetime model which had to be modified such that Maxwell electrodynamics becomes invariant under the change from one inertial reference frame to another. In modern terms: Einstein kept all the symmetries of Galilei-Newtonian spacetime, particularly the homogeneity of time and the Euclidicity of space as observed by any inertial observer but modified the boost transformation precisely by establishing the synchronization convention as described in the 1905 paper. The upshot is that in principle the coordinate time of an inertial frame in SRT can indeed be physically realized by a continuous family of Einstein-synchronized clocks.

The next step is to define an idealized clock in arbitrary motion against any inertial reference frame as a clock that measures its proper time along its (time-like) worldline. As established by experiment such clocks are (in principle) realized by unstable particles or nuclei (lifetime) or (to a certain extent) atomic clocks or (more robustly) by future nuclear clocks (like the envisaged Th-clock).

 

[robphy]

The problem here is that there is more than one way to interpret the phrase "time passes more slowly".

Which is why physicists use all that nasty math instead of pretty words.

...and draw spacetime diagrams (which, for some, is also regarded as nasty math).

 

[Ibix]

...and draw spacetime diagrams (which, for some, is also regarded as nasty math).

Nah, it's maths with pretty presentation. That means it's Data Science.