What happens biologically during time dilation?

[JesseM]

Yes. In an IRF, a cell that takes, for example, 24 hours to divide (measured by a clock that is at rest to them) will divide in 24 hours in EVERY IRF no matter what.

Every frame will agree that 24 hours elapses on the clock at rest relative to the cell, but in terms of the clocks at rest in other frames, the cell may take quite a lot less than 24 hours to divide.

I'm asking the scenario of someone observing someone else's reference frame relatively, in which their clock is no longer local to the cell division taking place.

The language is a little awkward here, a reference frame is just a coordinate system, so you can't really observe "someone else's reference frame", you can only observe physical processes like clock ticks and cell division. And inertial reference frames are defined in terms of a hypothetical network of clocks and rulers at rest relative to each other and spread throughout space, with the time of any event (including an event on the worldline of an object moving at relativistic speed relative to this network) defined in terms of local readings on this network. For example, if I want to know the coordinates in my frame of the event of an alarm going by on a clock moving at 0.8c relative to me, I might see that when the alarm went off the clock was next to the 1.3 light-years mark on my x-axis ruler, and the clock in my network that was located at the 1.3 light-year mark read 0.7 years as the speeding clock went past it and the alarm went off, so I'd assign the event of the alarm going off coordinates x=1.3 light years, t=0.7 years in my frame. Likewise, if I was measuring cell division of a cell moving in my frame, I would still (ideally) use clocks that were "local to the cell division taking place" to measure events that happen to the cell, it's just that these clocks wouldn't be at rest relative to the cell.

Anyway, sorry if I'm being overly nitpicky about your choice of words, just thought this discussion might be helpful...but if I understand your meaning, you want to know what happens to the time for cell division when it's measured in a frame where the cell is in motion. In this case the answer is that the time for the cell to divide will be lengthened in that frame (time dilation).

I'm trying to understand EXACTLY how someone would be younger. I find it logical to believe that for someone to be younger relative to someone then the relativistic observation had to have altered something biologically. At least, relatively, not in anybody's own inertial reference frame.

The problem with seeing it in terms of any process being objectively slowed down is that although all frames agree on the total aging of each twin in the twin paradox, they disagree about which twin was aging faster during particular phases of the journey, and there is no objective basis for judging one frame more correct than another. I gave an example of this in post 63 of this thread:

you can analyze the problem from any inertial frame and all will have the same answer about the age of the inertial twin and the age of the non-inertial twin when they reunite. Let's call the inertial (Earth-bound) twin "Terence" and the traveling twin "Stella", following the Twin Paradox FAQ. First let's look at the numbers in Terence's rest frame. Suppose that in this frame, Stella travels away from Terence inertially at 0.6c for 10 years, at which point she is at a distance of 0.6*10 = 6 light-years from Earth in this frame, then she turns around (i.e. she accelerates, a non-inertial motion which will cause her to experience G-forces that show objectively that she wasn't moving inertially) and heads back towards Terence at 0.6c, finally reuniting with Terence after 20 years have passed since her departure in this frame. Since Terence is at rest in this frame, he has aged 20 years. But since Stella was moving at 0.6c in this frame, the time dilation formula tells us her aging was slowed down by a factor of $$\sqrt{1 - 0.6^2}$$ = 0.8, so she only aged 0.8*10 = 8 years during the outbound leg of her trip, and another 0.8*10 = during the inbound leg, so she has only aged 16 years between leaving Earth and returning.

Now let's analyze the same situation in a different inertial frame--namely, the frame where Stella was at rest during the outbound leg of her trip (she can't also be at rest during the inbound leg in this frame, since this is an inertial frame while Stella accelerated between the two legs of the trip). In this frame, Terence on Earth is initially moving away from Stella at 0.6c while she remains at rest. In Terence's frame, remember that Stella accelerated when she was 6 light-years away from Earth, so we can imagine she turns around when she reaches the far end of a measuring-rod at rest in Terence's frame and 6 light-years long in that frame, with Terence sitting on the near end; in the frame we're dealing with now, the measuring-rod will therefore be moving along with Terence at 0.6c, so it'll be shrunk via length contraction to a length of only 0.8*6 = 4.8 light-years. So, Stella accelerates when the distance between her and Terence is 4.8 light-years in this frame, and since Terence as moving away from her at 0.6c in this frame, they will be 4.8 light-years apart after 4.8/0.6 = 8 years have passed. During these 8 years, it is Terence's aging that is slowed down by a factor of 0.8, so while Stella ages 8 years during this leg, Terence only ages 0.8*8 = 6.4 years. Then Stella accelerates to catch up with Terence, while Terence continues to move inertially at 0.6c. Using the relativistic velocity addition formula, if Stella was moving at 0.6c in Terence's frame and Terence is moving at 0.6c in the same direction in this frame, then in this frame Stella must be moving at (0.6c + 0.6c)/(1 + 0.6*0.6) = 0.88235c during the inbound leg. And since Terence is still moving at 0.6c in the same direction, the distance between Stella and Terence will be closing at a "closing speed" of 0.88235c - 0.6c = 0.28235c. Since the distance was initially 4.8 light years at the moment Stella accelerated, in this frame it will take 4.8/0.28235 = 17 years for Stella to catch up with Terence on Earth. During this time Terence has aged another 0.8*17 = 13.6 years, so if you add that to the 6.4 years he had aged during the outbound leg, this frame predicts he has aged 20 years between Stella leaving and Stella returning, same as in Terence's frame. And since Stella is traveling at 0.88235c her aging is slowed by a factor of $$\sqrt{1 - 0.88235^2}$$ = 0.4706, so during those 17 years in this frame she only ages 0.4706*17 = 8 years during the inbound leg. If you add that to the 8 years she aged during the outbound leg, you find that this frame predicts she has aged 16 years between departing and returning, which again is the same as what was predicted in Terence's frame.

So, to sum up:

Aging between event of Stella departing Earth and event of Stella turning around to return to Earth (i.e. total aging during the outbound leg of the journey):

--in Terence's rest frame, Terence (who was at rest) aged 10 years and Stella (who was moving at 0.6c) aged 8 years between these events (so Stella was aging slower during the outbound leg in this frame).
--in second frame where Stella was at rest during outbound leg, Terence (who was moving at 0.6c) aged 6.4 years and Stella (who was at rest) aged 8 years between these events (so Terence was aging slower during the outbound leg in this frame).
--the coordinate time between these events was 10 years in Terence's frame, 8 years in the second frame.

Aging between event of Stella turning around and event of Stella arriving back at Earth (i.e. total aging during the inbound leg of the journey):

--in Terence's rest frame, Terence (who was at rest) aged 10 years and Stella (who was moving at 0.6c) aged 8 years between these events (so Stella was aging slower during the inbound leg in this frame).
--in second frame where Stella was at rest during the outbound leg, Terence (who was moving at 0.6c) aged 13.6 years and Stella (who was moving at 0.88235c) aged 8 years between these events (so Stella was aging slower during the inbound leg in this frame, by an even greater ratio than in Terence's frame).
--the coordinate time between these events was 10 years in Terence's frame, 17 years in the second frame.

Both frames agree that when Stella returns to Earth and meets Terence, Terence has aged 20 years while Stella has only aged 16 years. But clearly they don't agree on the details of the rates each of them were aging during each phase of the journey, and there is no basis for preferring one perspective over the other.

 

[DaveC426913]

Yes, completely understood. As long as the cell is at rest relative to the observer watching it divide and as long as their reference frame is inertial, it will take 3 minutes. I honestly don't know if I'm COMPLETELY missing something you're trying to tell me.

OK, good. Just wanted to make sure we weren't on completely different pages. Sorry to beat it to death.

 

[danielatha4]

Every frame will agree that 24 hours elapses on the clock at rest relative to the cell, but in terms of the clocks at rest in other frames, the cell may take quite a lot less than 24 hours to divide.

The language is a little awkward here, a reference frame is just a coordinate system, so you can't really observe "someone else's reference frame", you can only observe physical processes like clock ticks and cell division. And inertial reference frames are defined in terms of a hypothetical network of clocks and rulers at rest relative to each other and spread throughout space, with the time of any event (including an event on the worldline of an object moving at relativistic speed relative to this network) defined in terms of local readings on this network. For example, if I want to know the coordinates in my frame of the event of an alarm going by on a clock moving at 0.8c relative to me, I might see that when the alarm went off the clock was next to the 1.3 light-years mark on my x-axis ruler, and the clock in my network that was located at the 1.3 light-year mark read 0.7 years as the speeding clock went past it and the alarm went off, so I'd assign the event of the alarm going off coordinates x=1.3 light years, t=0.7 years in my frame. Likewise, if I was measuring cell division of a cell moving in my frame, I would still (ideally) use clocks that were "local to the cell division taking place" to measure events that happen to the cell, it's just that these clocks wouldn't be at rest relative to the cell.

Anyway, sorry if I'm being overly nitpicky about your choice of words, just thought this discussion might be helpful...but if I understand your meaning, you want to know what happens to the time for cell division when it's measured in a frame where the cell is in motion. In this case the answer is that the time for the cell to divide will be lengthened in that frame (time dilation).

The problem with seeing it in terms of any process being objectively slowed down is that although all frames agree on the total aging of each twin in the twin paradox, they disagree about which twin was aging faster during particular phases of the journey, and there is no objective basis for judging one frame more correct than another. I gave an example of this in post 63 of this thread:

So, to sum up:

Aging between event of Stella departing Earth and event of Stella turning around to return to Earth (i.e. total aging during the outbound leg of the journey):

--in Terence's rest frame, Terence (who was at rest) aged 10 years and Stella (who was moving at 0.6c) aged 8 years between these events (so Stella was aging slower during the outbound leg in this frame).
--in second frame where Stella was at rest during outbound leg, Terence (who was moving at 0.6c) aged 6.4 years and Stella (who was at rest) aged 8 years between these events (so Terence was aging slower during the outbound leg in this frame).
--the coordinate time between these events was 10 years in Terence's frame, 8 years in the second frame.

Aging between event of Stella turning around and event of Stella arriving back at Earth (i.e. total aging during the inbound leg of the journey):

--in Terence's rest frame, Terence (who was at rest) aged 10 years and Stella (who was moving at 0.6c) aged 8 years between these events (so Stella was aging slower during the inbound leg in this frame).
--in second frame where Stella was at rest during the outbound leg, Terence (who was moving at 0.6c) aged 13.6 years and Stella (who was moving at 0.88235c) aged 8 years between these events (so Stella was aging slower during the inbound leg in this frame, by an even greater ratio than in Terence's frame).
--the coordinate time between these events was 10 years in Terence's frame, 17 years in the second frame.

Both frames agree that when Stella returns to Earth and meets Terence, Terence has aged 20 years while Stella has only aged 16 years. But clearly they don't agree on the details of the rates each of them were aging during each phase of the journey, and there is no basis for preferring one perspective over the other.

Right, so Stella ages 16 years and Terence has aged 20 years. Now let's suppose that each were carrying a petri dish with, two cells initially. Let's say that both start with the same types of cells and cell divides once every day. Let's give the number of cells an ideal exponential equation to explain it's growth.

n=2^365t where t is in years

So, Stella's cells have now created 2^16*365 cells which is 1.03*10¹⁷⁵⁸ cells

However, Terence's cells have created 2^20*365 cells which is 3.30*10²¹⁹⁷

Terence's 2 cells have created, in only 25% more time, 3.2*10⁴⁴¹% more cells

 

[JesseM]

Terence's 2 cells have created, in only 25% more time, 3.2*10⁴⁴¹% more cells

Yes, that's just how exponential growth works, nothing to do with relativity. If you had two petri dishes on Earth at rest relative to each other, and you allowed one to grow for 16 years before freezing it and the other to grow for 20 years before freezing it, then despite the fact that the second had only 25% more time to grow before being frozen, it grew 3.2*10⁴⁴¹% more cells too.

Anyway, did you get my point about how different frames disagree about whether Terence or Stella aged faster during the outbound leg of the trip, even though they all agree on how much they aged over the entire trip? And do you understand that in SR there can be no basis for preferring one frame's perspective over another's?

 

[danielatha4]

Yes, I understood your point. Let me see if I got this right.

In Terence’s frame:

During outbound trip: Terence aged 10 years, and Stella aged 8 years. Therefore, Stella
aged slower by 20%

During inbound trip: Terence aged 10 years, and Stella aged 8 years. Therefore, Stella aged slower by 20%

In Stella’s frame:

During outbound trip: Terence aged 6.4 years, and Stella aged 8 years. Therefore, Terence aged slower by 20%

During inbound trip: Terence aged 13.6 years, and Stella aged 8 years. Therefore, Stella aged slower by 41%

I think the point I was trying to make about the exponential growth is that according to the billions of people on Earth Stella has created significantly less cells than everyone else in 20 years.

However, if time is slowing for Stella at any point in the trip then wouldn’t that increase a rate, which inversely proportional to time passed? For example, in the exponential growth equation n=2^t the change in time does not decrease for Stella, but more cells are able to divide during that time due to a decrease in the flow of time. Therefore, effectively increasing the rate at which the cells divide.

 

[sylas]

Yes, I understood your point. Let me see if I got this right.

In Terence’s frame:

During outbound trip: Terence aged 10 years, and Stella aged 8 years. Therefore, Stella
aged slower by 20%

During inbound trip: Terence aged 10 years, and Stella aged 8 years. Therefore, Stella aged slower by 20%

Yes.

In Stella’s frame:

Oops. There is no one inertial frame associated with Stella.

During outbound trip: Terence aged 6.4 years, and Stella aged 8 years. Therefore, Terence aged slower by 20%

During inbound trip: Terence aged 13.6 years, and Stella aged 8 years. Therefore, Stella aged slower by 41%

No. "During" the two trips, both inbound and outbound, Stella is motionless in an inertial frame, and in that frame Terence ages 6.4 years, each time. The only reason this appears paradoxical is because people simply assume that the end of the first period is the same as the start of the second period.

What makes a difference is that when Stella turns around, you get a change in what is simultaneous. Hence, as Stella approaches the turn around point (or, in Stella's rest frame, as the turn around point approaches Stella) Terence is "now" 6.4 years older than at departure.

Then Stella turns around, and is in a new rest frame. In this new rest frame, Terence is "now" 13.6 years older than at the departure point. This is the key thing that lies behind pretty much every confusion on the twin thought experiment. Simultaneity is relative. When you try to identify things happening "at the same time" as Stella suddenly reversing direction, it makes a difference whether you use simultaneous in the inward rest frame or the outward rest frame.

Cheers -- sylas

 

[JesseM]

Yes, I understood your point. Let me see if I got this right.

In Terence’s frame:

During outbound trip: Terence aged 10 years, and Stella aged 8 years. Therefore, Stella
aged slower by 20%

During inbound trip: Terence aged 10 years, and Stella aged 8 years. Therefore, Stella aged slower by 20%

In Stella’s frame:

During outbound trip: Terence aged 6.4 years, and Stella aged 8 years. Therefore, Terence aged slower by 20%

During inbound trip: Terence aged 13.6 years, and Stella aged 8 years. Therefore, Stella aged slower by 41%

As sylas said, the second frame cannot be said to be "Stella's frame" throughout the trip, it is the inertial frame where Stella was at rest during the outbound trip but moving at 0.88235c during the inbound trip. One could equally well do the analysis from the perspective of an inertial frame where Stella was at rest during the inbound trip, and in this frame it'd be the reverse of the above, with Stella aging 41% slower during the outbound trip and Terence aging 20% slower during the inbound trip. This frame, too, would agree that Stella had aged 16 years and Terence had aged 20 when they reunited.

However, if time is slowing for Stella at any point in the trip then wouldn’t that increase a rate, which inversely proportional to time passed?

But do you see from the above that there can be no frame-independent sense in which "time is slowing for Stella" during any phase of the trip? No matter what phase you're talking about, there are some inertial frames that say Stella was aging slower during that phase and other inertial frames that say Terence was aging slower, but they all make the same predictions about local physical events like what age each twin is when they reunite, so there's no physical basis for preferring any of these frames.