Time Travel: How Does a Fast Electron Experience Sunrise?

[jefals]

TL;DR

Twist on twin paradox: Both travelers on earth.

An electron in my gold tooth travels somewhat over half the speed of light.
I don't know the math, but let's say I age 10 years for every 1 year for the electron.
Suppose we had a way where that electron could trigger a counter each time it "experienced" sunrise. (Let's don't get into how the electron could experience sunrise. Let's just say it could.)
After 10 of my years, we check the counter. Would it register 1 year worth of sunrises or 10?
10 years have gone by on Earth - for all us normal folks.
However, only 1 year for the electron, although it is also on earth.
If it registers 10 years of sunrises, doesn't that fly in the face of the statement that it should experience the passage of time normally? For it, 1 year has passed, yet 10 years of sunrises.
If it registers 1 year of sunrises, how is that possible since the sun will have risen 10 times that many times?

 

[trurle]

After 10 of my years, we check the counter. Would it register 1 year worth of sunrises or 10?

10 years of sunrises. Because count of sunrises have nothing to do with the time dilation or speed of internal processes of electrons.

Another answer will be if we count internal processes of moving particle. If for example we replace electron to unstable muon (well, muon orbit is not stable with gold nuclei, but let`s assume it is stable), due to 10:1 time dilation it will survive in average 10 times longer compared to muon just floating nearby.

 

[BvU]

I don't know the math

That's a pity. It would help: the ratio of 10 would dwindle to 1.15 IF your tooth were big enough.

statement that it should experience the passage of time normally?

Did you hear that from the electron itself ?



Yes, you get all kinds of answers

 

[jbriggs444]

Summary:: Twist on twin paradox: Both travelers on earth.

An electron in my gold tooth travels somewhat over half the speed of light.
I don't know the math, but let's say I age 10 years for every 1 year for the electron.
Suppose we had a way where that electron could trigger a counter each time it "experienced" sunrise. (Let's don't get into how the electron could experience sunrise. Let's just say it could.)
After 10 of my years, we check the counter. Would it register 1 year worth of sunrises or 10?

Ten years of sunrises.

The Earth plus sun together form a sort of clock. But it a clock that is more or less stationary relative to your tooth. So it keeps the same time as your tooth. Not necessarily the same time as an electron bouncing hither and yon within your tooth.

At half light speed, the time dilation factor is only about 0.87 to 1.

If, hypothetically, we could mount a clock on an electron and if, hypothetically, that electron were moving in a circular path at a constant speed of 0.5 c then we would expect the moving clock to tick off 8.7 years of clock time during the ten years we watch your tooth.

 

[jefals]

10 years of sunrises. Because count of sunrises have nothing to do with the time dilation or speed of internal processes of electrons.

Another answer will be if we count internal processes of moving particle. If for example we replace electron to unstable muon (well, muon orbit is not stable with gold nuclei, but let`s assume it is stable), due to 10:1 time dilation it will survive in average 10 times longer compared to muon just floating nearby.

I KNEW I should have stayed away from subatomic particles, but had to go with something that made sense. My first choice would have been to have my twin brother traveling at significant pct. lightspeed while staying local -- in my time zone (to avoid the complications of him seeing more sunrises because he's traveling thru multiple time zones). Could we go with that? Let's put him thru the "Honey I Shrunk the Kids" machine, so he can ride on a tiny rocket. My key point is, he's supposed to experience the passage of time normally. What's more normal than the sun coming up each day? His clock in his tiny rocket says 24 hours have gone by -- yet he only sees a sunrise once every 10 days...
So I was wondering if, somehow, in his reality, he would still see a sunrise every one of his days.
Thanks for your response!

Ten years of sunrises.

The Earth plus sun together form a sort of clock. But it a clock that is more or less stationary relative to your tooth. So it keeps the same time as your tooth. Not necessarily the same time as an electron bouncing hither and yon within your tooth.

At half light speed, the time dilation factor is only about 0.87 to 1.

If, hypothetically, we could mount a clock on an electron and if, hypothetically, that electron were moving in a circular path at a constant speed of 0.5 c then we would expect the moving clock to tick off 8.7 years of clock time during the ten years we watch your tooth.

Thanks. Good info. Well, let's go with something with enough "umpfh" to give us a 10/1 ratio, then! Has to be faster than gold electrons...
But I think I have my answer:
The statement that the traveler experiences the passage of time normally, would fail if you include watching the sunrise in your definition of what it means to experience the passage of time normally. ..

 

[trurle]

My first choice would have been to have my twin brother traveling at significant pct. lightspeed while staying local -- in my time zone (to avoid the complications of him seeing more sunrises because he's traveling thru multiple time zones). Could we go with that? Let's put him thru the "Honey I Shrunk the Kids" machine, so he can ride on a tiny rocket. My key point is, he's supposed to experience the passage of time normally. What's more normal than the sun coming up each day? His clock in his tiny rocket says 24 hours have gone by -- yet he only sees a sunrise once every 10 days...
So I was wondering if, somehow, in his reality, he would still see a sunrise every one of his days.

For time dilation 10:1, observer on rapidly moving (in line) rocket will see 10 sunrises while his internal clock counts for 24 hours.
Actually situation will be more controversial for rocket (or electron) moving in tight circles, because of ongoing discussion about Unruh Effect.

 

[jbriggs444]

My key point is, he's supposed to experience the passage of time normally. What's more normal than the sun coming up each day? His clock in his tiny rocket says 24 hours have gone by -- yet he only sees a sunrise once every 10 days...

This is not making sense.

A clock moving at relativistic speeds in a circular path runs unambiguously slow compared to any inertial clock. The fellow in the tiny rocket will see the sun coming up more rapidly than his clock would indicate should be the case.

You seem to be pulling the "10 days" and the "24 hours" out of thin air.

 

[jefals]

For time dilation 10:1, observer on rapidly moving (in line) rocket will see 10 sunrises while his internal clock counts for 24 hours.
Actually situation will be more controversial for rocket (or electron) moving in tight circles, because of ongoing discussion about Unruh Effect.

10/1 meaning I'm aging 10 times faster than the time traveller. So I'm thinking now his clock in his spaceship would have to register 10 days for each sunrise he sees.
Not sure about the Unruh effect, unless we're talking about centrifugal force. I know that factors into the passage of time for the little guy.

 

[trurle]

10/1 meaning I'm aging 10 times faster than the time traveller. So I'm thinking now his clock in his spaceship would have to register 10 days for each sunrise he sees.
Not sure about the Unruh effect, unless we're talking about centrifugal force. I know that factors into the passage of time for the little guy.

Opposite. Consider aging is to be a clock too. If aging of traveller slowed, all his clocks are slowed proportionally. Slow clock will register more (external) events per tick.

 

[jefals]

Opposite. Consider aging is to be a clock too. If aging of traveller slowed, all his clocks are slowed proportionally. Slow clock will register more (external) events per tick.

Oops! I see now. I had it backwards! (Perhaps the electrons in my brain are running a little slow)!
Still -- the little dude is living in a world that seems out of whack. His spacetime is acting one way, yet his experience of sunrise seems to be part of a different reality. hmm...

 

[Dale]

Well, let's go with something with enough "umpfh" to give us a 10/1 ratio, then! Has to be faster than gold electrons...

Bailey et al did this experiment with ultra relativistic muons in a storage ring. Their acceleration was something like 10^18 g and their time dilated as predicted by relativity.

 

[Dr_Nate]

Jefals, with this and the twin paradox you should be picturing that at some point during the journey one of the twins will be in a non-inertial frame (accelerating). During this time, this observer will see the tick count go wildly up, but in their frame the time between ticks is very short.

Your leap of logic is equating each tick of the sunrise with 24 hours for the twin that has the non-inertial frame. The sunrise is an external clock: it isn't riding along with the observer.

 

[Nugatory]

My key point is, he's supposed to experience the passage of time normally.

He does.
However, he is following a different path through spacetime than you are, and his path is shorter. An analogy, better than many: just as an automobile odometer ticks once for every kilometer a car moves along the road, my wristwatch ticks once for every second that I move along my path through spacetime. Two cars following different routes between two cities will count off a different number of kilometers on their journey, and two clocks following different paths through spacetime will count off a different number of seconds on their journey.

So he does experience the passage of time normally, but on his path through spacetime there are fewer than 24 hours for him to exerience between the events “light from the rising sun hits eyes on day N” and “light from the rising sun hits eyes next day”.

You might want to give this writeup a try.

 

[Ibix]

My first choice would have been to have my twin brother traveling at significant pct. lightspeed while staying local -- in my time zone (to avoid the complications of him seeing more sunrises because he's traveling thru multiple time zones). Could we go with that? Let's put him thru the "Honey I Shrunk the Kids" machine, so he can ride on a tiny rocket. My key point is, he's supposed to experience the passage of time normally. What's more normal than the sun coming up each day? His clock in his tiny rocket says 24 hours have gone by -- yet he only sees a sunrise once every 10 days...

I'm not sure if you are thinking that sunrises have some significance beyond being just another clock at rest in your frame, or if you are assuming that "both observers see the other's clock ticking slowly" applies to a wildly non-inertial observer like your twin. A sunrise is just another tick of a clock and your twin sees it ticking fast compared to his own clocks (at least, on average - the rate may vary depending on details not in evidence). If he's achieved a time dilation factor of 10 compared to you, he will see one sunrise every 2.4 hours.

 

[Ibix]

one of the twins will be in a non-inertial frame (accelerating).

Point of language - everyone and everything is always in every frame. A frame is just a choice of how to describe a scenario, so everything ought to be in it. I think you mean that one of the twins will be at rest in a non-inertial frame, or just that one of the twins will be moving non-inertially.

 

[Dr_Nate]

Point of language - everyone and everything is always in every frame. A frame is just a choice of how to describe a scenario, so everything ought to be in it. I think you mean that one of the twins will be at rest in a non-inertial frame, or just that one of the twins will be moving non-inertially.

Yes, you are correct! I can now see how a novice would be confused by that ambiguity.

 

[BvU]

I was a bit sarcastic at the start of this thread, but I think @jefals (is that the one on the right in the avatar?) had a very good response.

Read @Nugatory's link at leasure and we'll help with the math if there are more questions -- and there should be !

 

[jefals]

Bailey et al did this experiment with ultra relativistic muons in a storage ring. Their acceleration was something like 10^18 g and their time dilated as predicted by relativity.

Probably having a little trouble verbalizing my conundrum with all this. But it seems these "speedy little buggers" - are traveling in two realities. Locally, they are in this measurable time-dilated reality. If they were thinking creatures, they would feel their time going by much slower than normal. Looking outside their storage ring, they would see the sun coming up too fast (have I got that right now?) for their normal day.
So they are inside one reality, which is inside a completely different reality.
(You may have guessed; I'm no physicist. Just fascinated by this stuff).
~~~
So how does this relate to me? Even tho the speeds are much smaller, the same principle applies, right?
I'm sitting still, on my car seat, while it moves at a certain speed. Since I'm still inside the car, my clock ticks as if I'm in my living room -

Jefals, with this and the twin paradox you should be picturing that at some point during the journey one of the twins will be in a non-inertial frame (accelerating). During this time, this observer will see the tick count go wildly up, but in their frame the time between ticks is very short.

Your leap of logic is equating each tick of the sunrise with 24 hours for the twin that has the non-inertial frame. The sunrise is an external clock: it isn't riding along with the observer.

Thanks. I was trying to set up a special relativity scenario, but started out with subatomic particles - gold electrons because of their speed - and inside gold teeth - because that would keep them local eliminating the confusion caused by trying to count sunrises for the 2 while one is passing in and out of multiple time zones while the other stays put.
But this puts us into general relativity with the centrifugal forces. And I know about the accelerating force aspect of the twin paradox.
So -- to simplify: how about, we have shrunk my twin brother to electron size, given him a tiny rocket and a tiny clock.
I'm in Sacramento.
My brother is in San Felipe, Baja Mexico. He aims his rocket north and fires it up. Hits "x"c (where "x" is whatever % of lightspeed is necessary for a 10:1 dilation) - he hits that speed and levels out just prior to reaching the California border. He travels north thru California at this constant speed...
CRAP! This won't work either! I want him to take a day getting thru California, but he's going to make it in half a nanosecond! Well -- back to the drawing board.
Actually, this brings up another question. I know, with the twin paradox, it's actually during the acceleration / deceleration phases where the difference in aging takes place. Let's say when he starts his journey he's slightly older than me. When he turns on his rocket, he starts accelerating - his aging starts slowing down, and continues to do so, till he reaches constant speed "x"c. Let's say at that point, he and I are now exactly the same age, and we both trigger our atomic clocks. He travels 5 units of his time. That should correspond to 50 units of my time. So, after 5 units of his time, he stops his clock and I stop mine after 50 units of my time.

This is not making sense.

A clock moving at relativistic speeds in a circular path runs unambiguously slow compared to any inertial clock. The fellow in the tiny rocket will see the sun coming up more rapidly than his clock would indicate should be the case.

You seem to be pulling the "10 days" and the "24 hours" out of thin air.

...

 

[jefals]

Thanks everybody for adding your insights out here. Glad I finally found a place to discuss this stuff with folks that really know what they're talking about!
I do have more questions. Just thinking of how to word them takes a lot out of me!

 

[Ibix]

I know, with the twin paradox, it's actually during the acceleration / deceleration phases where the difference in aging takes place.

No, although it's fairly common to see this claimed. Actually, your elapsed time behaves a lot like distance travelled. If I travel from A to B on a straight line, and you go from A to B on a triangular route via some other point C, you are going to cover more distance than I. Where on the journey did you cover the extra distance? The question doesn't really make sense, and I think you'd agree that "where you made the turn at C" makes even less sense. Yet that's very closely analogous to claiming what you wrote above.

You keep talking about double realities for the traveller. This isn't the case - all there is here are clocks ticking at different rates. Sure, your rapidly orbiting twin will see Earthly day and night passing quickly. But so what? The landscape will be a huge Doppler shifted blur. Does that mean that there are two realities, one where the landscape is blurred and one where it isn't? Or does it just mean that things (including both the landscape and clocks like the diurnal cycle) look different depending on how you are moving when you measure them?

Your twin will be experiencing horrible g forces, but otherwise his own clocks and experiences are perfectly normal - it's just that other people's clocks behave oddly.

You are correct, by the way, that this happens at any speed. In principle, if you synchronise your watch to your computer clock then walk across the room and back (leaving your computer where it is), your watch will be behind the computer. But not even an atomic clock is enough to detect the difference on that kind of scale.

 

[Nugatory]

But this puts us into general relativity with the centrifugal forces. And I know about the accelerating force aspect of the twin paradox.

One of the more common misunderstandings is that you need general relativity to work with accelerations, centrifugal forces, and the like. In fact special relativity handles these situations just fine. General relativity is only needed when gravitational effects are strong enough to notice (and then only when the gravitational field is noticeably different at different points). The twin paradox is not one of these problems, and if you’ve taken a look at the FAQ I linked in post #13 you’ll see that uses only special relativity.

with the twin paradox, it's actually during the acceleration / deceleration phases where the difference in aging takes place.

And this is another common misconception. There is no meaningful way of saying when the difference in aging does happen (you’ll want to look for some of our many twin paradox threads to see why) but in any case the acceleration is something of a red herring. The twins age differently because they’re following different paths with different lengths through spacetime; the acceleration only appears in the thought experiment because there is no way of setting two people initially colocated and at rest relative to one another on different paths without accelerating at least one of them at some point in their journey.

Two cars drive from point A to point B on different routes with different lengths so we find that their trip odometers read differently when they meet at the destination. At some point on their journeys the drivers will have done something different with their steering wheels - they had to if their paths diverged. But you wouldn’t say that the difference in distance driven appeared when the steering wheels were turned differently; it is similarly fallacious to say that the difference in aging during the twin paradox happens during the acceleration.

 

[jefals]

No, although it's fairly common to see this claimed. Actually, your elapsed time behaves a lot like distance travelled. If I travel from A to B on a straight line, and you go from A to B on a triangular route via some other point C, you are going to cover more distance than I. Where on the journey did you cover the extra distance? The question doesn't really make sense, and I think you'd agree that "where you made the turn at C" makes even less sense. Yet that's very closely analogous to claiming what you wrote above.

You keep talking about double realities for the traveller. This isn't the case - all there is here are clocks ticking at different rates. Sure, your rapidly orbiting twin will see Earthly day and night passing quickly. But so what? The landscape will be a huge Doppler shifted blur. Does that mean that there are two realities, one where the landscape is blurred and one where it isn't? Or does it just mean that things (including both the landscape and clocks like the diurnal cycle) look different depending on how you are moving when you measure them?

Your twin will be experiencing horrible g forces, but otherwise his own clocks and experiences are perfectly normal - it's just that other people's clocks behave oddly.

You are correct, by the way, that this happens at any speed. In principle, if you synchronise your watch to your computer clock then walk across the room and back (leaving your computer where it is), your watch will be behind the computer. But not even an atomic clock is enough to detect the difference on that kind of scale.

I guess I'm a little out of the science realm and into the philosophical when talking about double realities. As far back as you want to go, the passage of time as been associated with the earthly cycles. We needed to find a way to tell when to plant. When to reap. And we always had an idea about when the sun was going to rise the next day. If all of a sudden, sunrises started happening 10 times faster than normal, our ancestors would have freaked out big time.
So, given that background, and the hundreds of times I've heard the claim "time passes normally inside the spaceship" - those two taken together spurred me to ponder this scenario. It turns out not EVERYTHING about the passage of time is normal inside the spaceship. 10 sunrises per day is not normal.
Yes -- MOST explanations I've seen on twin paradox claim the answer lies in acceleration / deceleration. Lately I've seen a few that say the answer lies somewhere else. That's good, because this contradicts my understanding of the basics. Which is that if you are moving at a constant speed in a straight line faster than I'm going, then you should be aging less than me.
Of course there's the symmetry thing: If you see me going fast, then I see you going fast. Who's REALLY going fast? Yet one really does age slower than the other.
The answer is out there. I hope I can understand it to some degree. Something tells me that if one takes the time to get the proper tools - the math background - then this stuff likely all clicks together much sharper than it does for us lay-folks! Nevertheless, I find it fascinating thinking about this stuff.

 

[Ibix]

If all of a sudden, sunrises started happening 10 times faster than normal, our ancestors would have freaked out big time.

So what? We are not our ancestors and we have more complex ideas about how time behaves than they could have done. Einstein said it best: time is what clocks measure. The Sun is just one more clock, no more or less important than any other. And its function depends on being more-or-less at rest with respect to it, like any other clock.

So, given that background, and the hundreds of times I've heard the claim "time passes normally inside the spaceship" - those two taken together spurred me to ponder this scenario. It turns out not EVERYTHING about the passage of time is normal inside the spaceship. 10 sunrises per day is not normal.

A blurred landscape outside is not normal either. Why doesn't this bother you?

Which is that if you are moving at a constant speed in a straight line faster than I'm going, then you should be aging less than me.
Of course there's the symmetry thing: If you see me going fast, then I see you going fast. Who's REALLY going fast? Yet one really does age slower than the other.

Neither of us is really going fast. Each of us can regard the other as going fast. Neither of us ages faster than the other because there's no way to compare our ages unambiguously - unless one of us turns round and comes back. And in that case, one of us has done something different from the other - why would you expect symmetry?

Something tells me that if one takes the time to get the proper tools - the math background - then this stuff likely all clicks together much sharper than it does for us lay-folks!

If you can follow Pythagoras' theorem then you can handle the maths for special relativity, at least for instantaneous accelerations or constant speeds. If you can handle calculus you can go a lot further. What you do need is a willingness to let go of ideas like the movement of the Sun somehow being important to anything.

 

[jefals]

One of the more common misunderstandings is that you need general relativity to work with accelerations, centrifugal forces, and the like. In fact special relativity handles these situations just fine. General relativity is only needed when gravitational effects are strong enough to notice (and then only when the gravitational field is noticeably different at different points). The twin paradox is not one of these problems, and if you’ve taken a look at the FAQ I linked in post #13 you’ll see that uses only special relativity.
And this is another common misconception. There is no meaningful way of saying when the difference in aging does happen (you’ll want to look for some of our many twin paradox threads to see why) but in any case the acceleration is something of a red herring. The twins age differently because they’re following different paths with different lengths through spacetime; the acceleration only appears in the thought experiment because there is no way of setting two people initially colocated and at rest relative to one another on different paths without accelerating at least one of them at some point in their journey.

Two cars drive from point A to point B on different routes with different lengths so we find that their trip odometers read differently when they meet at the destination. At some point on their journeys the drivers will have done something different with their steering wheels - they had to if their paths diverged. But you wouldn’t say that the difference in distance driven appeared when the steering wheels were turned differently; it is similarly fallacious to say that the difference in aging during the twin paradox happens during the acceleration.

Thanks much, Nugatory. I've tried to simplify my experiment as follows:
A. Abe will stay put in Sacramento. Velma will be microsized and zoom off, northbound, from the southern tip of Baja, at an acceleration sufficient to reach .995c just before reaching the California border. She then levels out and goes on cruise control. She hits that border at a constant .995c.
B. Calculations have been done beforehand, and at the right moment, Velma sends a signal which starts Abe's clock just as Velma hits the border - at which time her own clock starts as well.
C. Just as we have microsized Velma, we have increases the size of the solar system, so that it takes 1 of her days to reach the Oregon border.
D. Just prior to reaching the Oregon border she sends a signal that will reach Abe's clock and shut it off just as she crosses the Oregon border. At that time, her own clock stops as well.
She slows down. Experiment over. Flys back to Abe in Sacramento with her clock.
Thru out the experiment, there will have been no speeding up or slowing down, etc. As she approached Sacramento, she will have seen Abe moving towards her. He will have seen her moving towards him.
Then they will each have seen the other moving away.
I know, when they compare the two clocks, it will still be Abe who is older. Just not really sure why yet.
~~~
In your comment that they are traveling "different paths and different lengths" - the "length" part is confusing me a little. We're letting Abe stay put in space, so he's only moving thru time. For Velma -- do I need to factor length contraction into my thinking?
I DID take a quick gander at the link you sent me in #13. I'm afraid it's going to open up a lot more questions! :)

 

[Ibix]

In your comment that they are traveling "different paths and different lengths" - the "length" part is confusing me a little.

The "length" here is more properly called the "interval". It's the spacetime generalisation of length in space, and the interval along the path you follow through spacetime turns out to be the time elapsed on your watch. Interval and length aren't quite the same (because the time dimension is different from the space ones) but there is a lot of read-across. In particular, the interval along two paths through spacetime can be different even if they start and end together. And, just like with paths through space, asking "where the extra length/interval is" is a bit difficult to make sense of.

 

[jefals]

So what? We are not our ancestors and we have more complex ideas about how time behaves than they could have done. Einstein said it best: time is what clocks measure. The Sun is just one more clock, no more or less important than any other. And its function depends on being more-or-less at rest with respect to it, like any other clock.

A blurred landscape outside is not normal either. Why doesn't this bother you?Neither of us is really going fast. Each of us can regard the other as going fast. Neither of us ages faster than the other because there's no way to compare our ages unambiguously - unless one of us turns round and comes back. And in that case, one of us has done something different from the other - why would you expect symmetry?

If you can follow Pythagoras' theorem then you can handle the maths for special relativity, at least for instantaneous accelerations or constant speeds. If you can handle calculus you can go a lot further. What you do need is a willingness to let go of ideas like the movement of the Sun somehow being important to anything.

1. I'd never claim the sun is no more important than any other clock.
2. A blurred landscape. I was going to get to that -- if we ever finish up with this! :)
But since you mentioned it -- in all the youtubes, PBS specials, episodes of Cosmos or whatever, when they depict a person speeding along at some goodly pct of c, it always appears as tho he's looking thru a fishey

The "length" here is more properly called the "interval". It's the spacetime generalisation of length in space, and the interval along the path you follow through spacetime turns out to be the time elapsed on your watch. Interval and length aren't quite the same (because the time dimension is different from the space ones) but there is a lot of read-across. In particular, the interval along two paths through spacetime can be different even if they start and end together. And, just like with paths through space, asking "where the extra length/interval is" is a bit difficult to make sense of.

Uh...yeah...hmm... Gonna have to chew on this one a while :)
But THANX!

 

[jefals]

Uh...yeah...hmm... Gonna have to chew on this one a while :)
But THANX!

 

[BvU]

MIT gamelab have a nice relativity game. It won't help you with your time dilation conundrum, but perhaps it will with demystifying the blurring

 

[jefals]

MIT gamelab have a nice relativity game. It won't help you with your time dilation conundrum, but perhaps it will with demystifying the blurring

Thanks! Maybe I'll check it out

 

[Dale]

But it seems these "speedy little buggers" - are traveling in two realities. Locally, they are in this measurable time-dilated reality. If they were thinking creatures, they would feel their time going by much slower than normal. Looking outside their storage ring, they would see the sun coming up too fast (have I got that right now?) for their normal day.
So they are inside one reality, which is inside a completely different reality.

In science the link to reality is through experiment. Both the non-inertial reference frame of the muons and the lab can be used to predict the outcome of any experiment. Both frames will agree on all of their predictions. Therefore there is only one reality. In that one reality both the muon frame and the lab frame predict that muons will detect a sunrise every 49 minutes according to their clocks ($\gamma = 29.3$) and the scientists will detect the same sunrise every 24 hours according to their clocks.

Since both frames agree on all experimental outcomes there is one reality, it is just a far more interesting reality than our low-speed experience leads us to believe.