I How Does Special Relativity Challenge Our Understanding of Absolute Time?

[Janus]

So what about the situation where the "sausage" spaceship is at rest with the "pastry" spaceship, and they all synchronous their clocks and reset to 0, and then the "sausage" spaceship then accelerates to 0.6v for one second, and then accelerates back to the rest frame of the pastry spaceship.

You can imagine the "sausage" spaceship to be segmented, and for each segment to have its own rockets, and for them to start the moment the clocks reset to 0. Presumably the observers on the "pastry" spaceship will all agree the segments all set off at the same time. Would the observers on the "pastry" spaceship all agree the segments reached 0.6v at the same time? If so would they all agree what the clocks of those segments read when they reached it? Also after the "sausage" spaceship which we can assume is 10 light years long has been going (according to it's frame of reference) for one second what roughly would the observers on the front and end of it think the last "pastry" spaceship clock each had passed was showing on its clock (imagine the "pastry" spaceship to be considerably longer than the "sausage" one)?

This is a lot more complicated than it seems. If you arranged things so that in the sausage frame, the spacing between segments remained constant and all the segments started and stopped accelerating at the same moment, then according to the pastry ship, the segments and thus the distance between them was shrinking due to length contraction during this whole acceleration. But this also means that, at any given moment the Leading segment was traveling at a lower speed relative to the rear segment and thus its clock was exhibiting a greater time dilation rate. In other words, according to the pastry ship, the clocks in the segments wouldn't be ticking at the same rate.
In addition, due to the fact that the rest frame of the sausage ship is a non-inertial one, anyone on the sausage ship would say that clocks at the trailing segment would be running slower than those in the leading segment. Thus, for each segment to stop its acceleration " at the same time" across the ship, each segment would have to stop its acceleration at a different time according to its own clock. So first you would have to work out the end difference between clocks of the sausage ship as measured in the sausage ship, and then apply the relativity of simultaneity to make comparisons between clocks of the relatively moving frames.
Working with extended bodies under acceleration is not a simple problem in Relativity.

 

[SlowThinker]

So what about the situation where the "sausage" spaceship is at rest with the "pastry" spaceship, and they all synchronous their clocks and reset to 0, and then the "sausage" spaceship then accelerates to 0.6v for one second, and then accelerates back to the rest frame of the pastry spaceship.

You can imagine the "sausage" spaceship to be segmented, and for each segment to have its own rockets, and for them to start the moment the clocks reset to 0. Presumably the observers on the "pastry" spaceship will all agree the segments all set off at the same time.

In this scenario yes, but it can be confusing to mix these 2 scenarios. You can refer to it as the train&track.

Would the observers on the "pastry" spaceship all agree the segments reached 0.6v at the same time?

Yes, at time just above 0 as we assume the acceleration to be fast.

If so would they all agree what the clocks of those segments read when they reached it?

Yes, just a bit above 0. But the Sausage's crew would say that for a second the clocks along the Sausage were showing different times - but each crewman would think that their nearest clock is the right one.

Also after the "sausage" spaceship which we can assume is 10 light years long has been going (according to it's frame of reference) for one second what roughly would the observers on the front and end of it think the last "pastry" spaceship clock each had passed was showing on its clock (imagine the "pastry" spaceship to be considerably longer than the "sausage" one)?

This sentence doesn't seem to make sense.
Each Sausage crewman would see the nearest Pastry clocks to slow down, they'd move to clocks that were already a bit in the future (clocks jumped during acceleration), and then the Pastry's clock start going at normal speed. This whole process in total would move Pastry's clock 1.25 seconds into the future (while only 1 second has passed for the Sausage crew).

 

[name123]

Each image is a set of diagrams showing two different times: When the "midpoint" clocks meet and both read zero, and then later when the "sausage" midpoint clock meets the next clock Left of the midpoint clock of the "pastry". So I don't see where you get any asymmetry begin the top and bottom diagrams in each image.

Sorry for the late reply.

What I am slightly confused about is why in one frame of reference the moving clock reads 1.67 when it passes the next clock along, and in the other it reads 1.33. You seem to be applying a 0.8 time dilation from one frame of reference and not the other, and I am not sure why given the seeming symmetry of the situation.

Now obviously, if the clocks weren't set and started from zero until the train started its initial acceleration, then the train observer would never say that they read less than zero. However, if we assume that the track clocks had been running in sync with each other and counting up from negative readings to zero until the train accelerated, then the train observer, could say that some given moment after it reached 0.6 relative to the tracks, that some of the track clocks had not yet read 0 (again taking to account the Rindler horizon)

What if the clocks showed 999 before the event of being set to 0 which was immediately followed by the event of the train accelerating? In such a case no clock showing 999 would be observed post the acceleration event I assume.

 

[name123]

This is a lot more complicated than it seems. If you arranged things so that in the sausage frame, the spacing between segments remained constant and all the segments started and stopped accelerating at the same moment, then according to the pastry ship, the segments and thus the distance between them was shrinking due to length contraction during this whole acceleration. But this also means that, at any given moment the Leading segment was traveling at a lower speed relative to the rear segment and thus its clock was exhibiting a greater time dilation rate. In other words, according to the pastry ship, the clocks in the segments wouldn't be ticking at the same rate.

This seems quite strange. You seem to be stating that from the pastry ships perspective the rate of acceleration of a segment that used its own rockets to propel would depend upon whether it was connected to other segments. If instead of a sausage ship there were two independent segments. One where the rear segment of the sausage ship would have been, and one where the front segment of the sausage ship would have been. Would the front one still appear to be moving slower than the rear one? That the engineers on the pastry ship when calculating the speed of an accelerating segment would have to take into account where it took off from?

 

[name123]

This sentence doesn't seem to make sense.
Each Sausage crewman would see the nearest Pastry clocks to slow down, they'd move to clocks that were already a bit in the future (clocks jumped during acceleration), and then the Pastry's clock start going at normal speed. This whole process in total would move Pastry's clock 1.25 seconds into the future (while only 1 second has passed for the Sausage crew).

So the sausage ship and pastry ship synch their clocks and set them to 0. Then the segmented sausage ship accelerates to 0.6v and maintains that velocity for 1 second. At that point what roughly would the observers on the front and end of the sausage ship think the last "pastry" spaceship clock each had passed was showing on its clock (imagine the "pastry" spaceship to be considerably longer than the "sausage" one)? I had assumed that they would not both report the same time on the last "pastry" spaceship clock they passed, as I had assumed they would not just think the "pastry" spaceship clocks were slower, but also out of synch.

 

[SlowThinker]

At that point what roughly would the observers on the front and end of the sausage ship think the last "pastry" spaceship clock each had passed was showing on its clock?

The Sausage crew would see the newly nearest Pastry clock as all showing 1.00s. Their own wristwatch would show 0.80s. However if the crew in the front and in the back of Sausage compared their wristwatches, they could be hours off. Obviously the Pastry clocks would be off by the same amount AND 0.20s ahead.
The Pastry's clock nearest at the time of start would now be 0.6 light seconds away and showing 0.80s.

If the Sausage crew resynchronized the clocks after the start, that needs to be said explicitly.

 

[Janus]

Sorry for the late reply.

What I am slightly confused about is why in one frame of reference the moving clock reads 1.67 when it passes the next clock along, and in the other it reads 1.33. You seem to be applying a 0.8 time dilation from one frame of reference and not the other, and I am not sure why given the seeming symmetry of the situation.

We are not considering how long it takes for a clock to move from one clock to the next in each frame according to that frame. For instance, if clock C of the pastry is next to clock A of the sausage, it will measure 1.33 yrs until clock B of the sausage reaches it. Just like in our example clock A for the sausage measures 1.33 yrs unitl clock B of the pastry reaches it. But when comparing the two scenarios above, there is no common moment between the two frames that both frame will agree on.

In the example we are working with we are starting from a common moment that both frames agree on (the passing of two clocks when they both read zero.)
And this moment looks like this in the two frames. ( I just noticed something here that might have added to your confusion. In my last version of these images, I forgot the minus sign in front of the 0.6 shown in the bottom diagram.) I further labeled two other clocks as C and D. :

The top diagram is this moment according to the sausage and the bottom is the same moment according to the pastry.
In both frames clock A of the sausage is passing a pastry clock D as it reads zero.
According to sausage frame clock B has already passed clock C on its way to its meeting with clock A, However according to the pastry frame, Clock C has yet to meet up with clock B. If we were rewind the top image back to when B is next to C, then clock C will read -0.2/.6 = -0.333...yrs, and clock B will read 0.6- (0.333...x 0.8) =0.333...yr.
Likewise, if you run the bottom diagram forward until C meets B, then B reads 0.2/0.6 = 0.333... yrs and C reads -.6+(0.333...x 0.8) = -0.333... yrs
Thus both frames agree as to what C and B read as they pass each other. But B passing C is not the same moment as A passing D in either frame.

In the sausage frame, it occurrs before[ A and D pass each other, when A reads -0.333... yrs and D reads -2.666... yrs.
In the pastry frame, B and C meet after A and D pass each other, when D reads 0.333... yrs and A reads 2.666... yrs.
All a result of time dilation, length contraction and the relativity of simultaneity working in concert.
Again, you need to pick one moment that both frames agree upon (such as clocks A and D passing each other) and then work from that moment in both frames.
To supply the symmetry you seem to feel is lacking, you could add two more clocks to the example above: clock F which is a pastry clock to the right of clock D and clock E which is a sausage clock to the right of clock A. Then if you consider what time reads on clock F when it meets clock E you get 1.333... yrs, (the same as clock A reads when it meets clock B), and you get 1.666... yrs for the time on clock E when it meets clock F ( the same reading as clock B reads when it meets clock A)

What if the clocks showed 999 before the event of being set to 0 which was immediately followed by the event of the train accelerating? In such a case no clock showing 999 would be observed post the acceleration event I assume.

Without actual numbers, magnitude and duration of acceleration etc, you can't arrive at an exact answer as what any given observer would see.

 

[Janus]

This seems quite strange. You seem to be stating that from the pastry ships perspective the rate of acceleration of a segment that used its own rockets to propel would depend upon whether it was connected to other segments. If instead of a sausage ship there were two independent segments. One where the rear segment of the sausage ship would have been, and one where the front segment of the sausage ship would have been. Would the front one still appear to be moving slower than the rear one? That the engineers on the pastry ship when calculating the speed of an accelerating segment would have to take into account where it took off from?

Any connection between the segments is not relevant.
Take two ships, one behind the other. Both are accelerating such that, as measured by each ship, the distance between their ship and the other ship remains fixed, and the relative speed between them is zero. They will observe each others clocks as running at different rates, with the lead ship's clock running faster.
It is the frame that they are accelerating with respect to that would measure their relative speeds to that frame as being different and the distance between them contracting.

 

[name123]

The Sausage crew would see the newly nearest Pastry clock as all showing 1.00s. Their own wristwatch would show 0.80s. However if the crew in the front and in the back of Sausage compared their wristwatches, they could be hours off. Obviously the Pastry clocks would be off by the same amount AND 0.20s ahead.
The Pastry's clock nearest at the time of start would now be 0.6 light seconds away and showing 0.80s.

If the Sausage crew resynchronized the clocks after the start, that needs to be said explicitly.

I had thought the crew on the sausage ship would have thought their acceleration to be pretty much instantaneous. Especially given that each segment has its own rockets. But you seem to be suggesting that the crew on the front segment and the crew on the back segment could be in disagreement about this, one of them instead of thinking that it having been an almost instantaneous acceleration and that they had traveled at the velocity of 0.6c for 1 second, would be thinking it had been going on for possibly hours.

Would you mind if I asked you the question again: At that point what roughly would the observers on the front and end of the sausage ship think the last "pastry" spaceship clock each had passed was showing on its clock?

In reply would you mind telling me roughly the actual time on those two clocks.

 

[name123]

To supply the symmetry you seem to feel is lacking, you could add two more clocks to the example above: clock F which is a pastry clock to the right of clock D and clock E which is a sausage clock to the right of clock A. Then if you consider what time reads on clock F when it meets clock E you get 1.333... yrs, (the same as clock A reads when it meets clock B), and you get 1.666... yrs for the time on clock E when it meets clock F ( the same reading as clock B reads when it meets clock A)

Yes, sorry I had misinterpreted the diagrams, thanks for clearing that up.

 

[name123]

Any connection between the segments is not relevant.
Take two ships, one behind the other. Both are accelerating such that, as measured by each ship, the distance between their ship and the other ship remains fixed, and the relative speed between them is zero. They will observe each others clocks as running at different rates, with the lead ship's clock running faster.
It is the frame that they are accelerating with respect to that would measure their relative speeds to that frame as being different and the distance between them contracting.

Which is what I was finding strange. So if we imagine the segmented "sausage" ship, and imagine that the segments are not connected, and all but the first and last segment removed, that from the pastry ship's perspective if they both accelerated (in the direction of last to first) that the first would appear, and a given point of time during the acceleration, to have a higher relative speed than the last.

The reason I find that strange is that supposing there was only one segment, it would seem to imply that where it started from would influence how fast it appeared to be going at a given point in time, from the pastry ship's perspective. Because you seem to be suggesting that if it took off from the position of the last segment, it would be measured as going slower at a given point in time from if it had taken off from the position of the first segment. I have presumably yet again misunderstood. Is it that the slower one appears to accelerate for longer? If so then it would appear to be a similarly weird situation, where where it took of from would influence how long it took to perform the acceleration.

 

[stevendaryl]

The reason I find that strange is that supposing there was only one segment, it would seem to imply that where it started from would influence how fast it appeared to be going at a given point in time, from the pastry ship's perspective. Because you seem to be suggesting that if it took off from the position of the last segment, it would be measured as going slower at a given point in time from if it had taken off from the position of the first segment. I have presumably yet again misunderstood. Is it that the slower one appears to accelerate for longer? If so then it would appear to be a similarly weird situation, where where it took of from would influence how long it took to perform the acceleration.

Think of the analogy with circular motion. Suppose you have a car that is traveling in a circle of radius 1 kilometer. A second car keeps at a constant distance of 0.25 kilometers away from the first car. Then the second car is traveling in a circle also, but a circle of a larger radius 1.25 kilometers. If the second car tried to travel in a circle of the same radius as the first car, then you would not keep the same distance between the cars.

A rocket undergoing constant acceleration is not traveling in a circle in space, instead, it's traveling in a hyperbola in spacetime. If you plot $x$ versus $t$ it traces out a hyperbola. A hyperbola is like a circle in two ways: (1) It has a "center" (but the center is a particular value of $x$ and $t$, rather than a point in space), (2) it has a "radius", which characterizes how strongly the rocket is accelerating. In the same way that two cars traveling in a circle can't maintain the same distance unless one is traveling at a greater radius, two rockets traveling along a spacetime hyperbola can't maintain the same distance unless one is traveling at a greater radius, as well.

Mathematically, the path of a circle can be parametrized by:

$x = R cos(\theta)$
$y = R sin(\theta)$

The path of an accelerating rocket can be parameterized similarly by:

$x = R cosh(\theta)$
$ct = R sinh(\theta)$

where $cosh$ and $sinh$ are the hyperbolic cosine and hyperbolic sine. If you work out what the proper acceleration for such a path is (the proper acceleration is the acceleration "felt" by those onboard the rocket), it's given by:

$g = \frac{c^2}{R}$

So a rocket that is farther ahead will have a larger value of $R$ and so a smaller value of the acceleration $g$.

That doesn't mean that the acceleration is position-dependent. A rocket at any position can travel at any acceleration. But if you want two rockets to have the same "center" ($x=0, t=0$) then the rocket with the larger radius will have the smallest acceleration. The rocket that is ahead can have a different center, but in that case, it won't maintain the same distance from the first rocket.

 

[name123]

Think of the analogy with circular motion. Suppose you have a car that is traveling in a circle of radius 1 kilometer. A second car keeps at a constant distance of 0.25 kilometers away from the first car. Then the second car is traveling in a circle also, but a circle of a larger radius 1.25 kilometers. If the second car tried to travel in a circle of the same radius as the first car, then you would not keep the same distance between the cars.

I do not understand why not. If two cars each traveled at the same speed in a circle of the same radius with the same centre, then the distance between them would remain constant I would have thought. I am imagining the chord length, and angle between them would remain the same.

That doesn't mean that the acceleration is position-dependent. A rocket at any position can travel at any acceleration. But if you want two rockets to have the same "center" ($x=0, t=0$) then the rocket with the larger radius will have the smallest acceleration. The rocket that is ahead can have a different center, but in that case, it won't maintain the same distance from the first rocket.

I do not know why the centre is important, I would have thought all observers, regardless of x position in the rest frame will agree on the speeds of the rockets.

 

[stevendaryl]

I do not understand why not. If two cars each traveled at the same speed in a circle of the same radius with the same centre, then the distance between them would remain constant I would have thought.

I meant that they are traveling in concentric circles of different radii.

I do not know why the centre is important, I would have thought all observers, regardless of x position in the rest frame will agree on the speeds of the rockets.

It's not an x-position, it's a center in spaceTIME. So the center is defined by a value of $x$ and a value of $t$.

If you have a rocket moving at constant acceleration (as felt by those on board the rocket), then its path will be described by the pair of equations:

$x = x_0 + R cosh(\theta)$
$t = t_0 + R/c sinh(\theta)$

So there are two different choices to be made (for motion along the x-axis):

1. The "center" of the motion, the point $(x_0, t_0)$.
2. The "radius" of the motion, $R$

If the centers of two different rockets are different, then the distance between the rockets, as measured by those aboard the rocket, will not be constant. So for the rockets to stay the same distance apart, as measured by those on board, you have to have the centers the same, and the only difference is different values of $R$. The acceleration felt by those on board the rocket is $\frac{c^2}{R}$, so the rocket with the greater value of $R$ will feel a smaller acceleration.

You can certainly have two rockets with the same value of $R$ (which means the same acceleration), but with different "centers". But then rockets would not stay the same distance apart, as viewed by those aboard the rocket.

 

[name123]

I meant that they are traveling in concentric circles of different radii.

Oh ok, I was confused when you wrote

If the second car tried to travel in a circle of the same radius as the first car, then you would not keep the same distance between the cars.

But you are actually saying that if the second car tried to travel in a circle of the same radius as the first car, then they would keep the same distance between the cars if they were traveling at the same speed?

It's not an x-position, it's a center in spaceTIME. So the center is defined by a value of $x$ and a value of $t$.

I realize the centre is not an x-position as it has a time coordinate. What I was assuming was that all observers, regardless of x position in the rest frame will agree on the speeds of the rockets, for a given t in that rest frame. So that the "centre in spacetime" would be irrelevant. As the $x$ value in that rest frame did not matter. Only the $t$ value.

 

[stevendaryl]

I realize the centre is not an x-position as it has a time coordinate. What I was assuming was that all observers, regardless of x position in the rest frame will agree on the speeds of the rockets, for a given t in that rest frame. So that the "centre in spacetime" would be irrelevant. As the $x$ value in that rest frame did not matter. Only the $t$ value.

The x-value of the center doesn't matter for the speed as computed by someone at rest, but it does matter for the distance as measured by someone on board the rocket. For the distance between the rockets to be constant, as measured by those on the rockets, then the rockets have to have the same "center".

 

[jartsa]

Is it that the slower one appears to accelerate for longer? If so then it would appear to be a similarly weird situation, where where it took of from would influence how long it took to perform the acceleration.

So now there is even an end to the accelerations of the two ships?

Well, if the reason that the acceleration ends is that all fuel has been burned, then the ship that burns fuel at faster rate, in order to accelerate at faster rate, will stop accelerating first. This is according to the "pastry ship".

The above is a quite good way to have an end of acceleration, as the two ships end up with the same kinetic energy, after burning the same amount of fuel.

 

[name123]

The x-value of the center doesn't matter for the speed as computed by someone at rest, but it does matter for the distance as measured by someone on board the rocket. For the distance between the rockets to be constant, as measured by those on the rockets, then the rockets have to have the same "center".

In post #61 when I was replying to Janus, I was discussing the perspective of the person at rest (on the pastry spaceship). I think Janus was too, and as I understood it was suggesting that the front segment would appear to be going faster to someone on the pastry spaceship. At least that it what I understood him to be stating when he wrote

If you arranged things so that in the sausage frame, the spacing between segments remained constant and all the segments started and stopped accelerating at the same moment, then according to the pastry ship, the segments and thus the distance between them was shrinking due to length contraction during this whole acceleration. But this also means that, at any given moment the Leading segment was traveling at a lower speed relative to the rear segment and thus its clock was exhibiting a greater time dilation rate. In other words, according to the pastry ship, the clocks in the segments wouldn't be ticking at the same rate.

 

[stevendaryl]

In post #61 when I was replying to Janus, I was discussing the perspective of the person at rest (on the pastry spaceship). I think Janus was too, and as I understood it was suggesting that the front segment would appear to be going faster to someone on the pastry spaceship. At least that it what I understood him to be stating when he wrote

I'm a little confused about the sausage versus pastry thing, but in terms of two accelerating rockets, there are two different frames to consider: (1) the frame of someone on board the rocket (the rocket frame), (2) the frame of someone who is not accelerating (the inertial frame)

If the distance between rockets is constant as measured in the rocket frame, then

1. The acceleration felt by the rear rocket will be greater than that of the front rocket
2. The distance between rockets is shrinking as measured in the inertial frame

If the distance between rockets is constant as measured in the inertial frame, then

1. The acceleration felt by the two rockets is the same
2. The distance between rockets is growing as measured in the rocket frame.

 

[SlowThinker]

I had thought the crew on the sausage ship would have thought their acceleration to be pretty much instantaneous. Especially given that each segment has its own rockets.

Yes.

But you seem to be suggesting that the crew on the front segment and the crew on the back segment could be in disagreement about this, one of them instead of thinking that it having been an almost instantaneous acceleration and that they had traveled at the velocity of 0.6c for 1 second, would be thinking it had been going on for possibly hours.

You are assuming a step, resynchronization of Pastry's clocks, that doesn't happen.

Each Pastry crewman would see, using his wristwatch, that the acceleration started at 0.00s, and ended at say 0.001s. Then they started to decelerate at 0.800s and finished at 0.801s. Again, each crewman would see the same.
But if, during the way (the 0.8s they are moving), they looked around, they would "see" (rather "compute" or "estimate") the wristwatches toward the front showing some time in the past, and the wristwatches behind as some time in the future.
(If you factor in the light delay, everyone should see that the trip occurs from 0.000 to 0.801s Pastry wristwatch time, for everyone. It's better not to think of light delay yet and certainly it's a bad idea to think of it only sometimes).

If everyone resynchronized their wristwatches when they started to move, they would need to agree on a master clock, say the central one. So the crewman in the middle would keep the wristwatch at 0.001s, but those in front would move it from 0.001s to say -750 and those in the back to say +750.
(If the trip never stopped, they could now walk around, comparing wristwatches, and they would agree that indeed all their clocks show the same time.)
Then the trip would stop at 0.8s central clock, -749.2 front clock, 750.8 rear clock. Again, after stopping, they would realize that the clocks are not synchronized any more, and would need to adjust them again.

Would you mind if I asked you the question again: At that point what roughly would the observers on the front and end of the sausage ship think the last "pastry" spaceship clock each had passed was showing on its clock?

In reply would you mind telling me roughly the actual time on those two clocks.

With the resynchronization, it's needlessly confusing. Just add or subtract 750s to Pastry clock as above.
Without the resynchronization,
Front Pastry clock: 0.800s
Sausage clock nearest to Pastry's front: 1.000s
Back Pastry clock: 0.800s
Sausage clock nearest to Pastry's end: 1.000s
Note: Pastry is the accelerating/decelerating one.

 

[name123]

I'm a little confused about the sausage versus pastry thing, but in terms of two accelerating rockets, there are two different frames to consider: (1) the frame of someone on board the rocket (the rocket frame), (2) the frame of someone who is not accelerating (the inertial frame)

If the distance between rockets is constant as measured in the rocket frame, then

1. The acceleration felt by the rear rocket will be greater than that of the front rocket
2. The distance between rockets is shrinking as measured in the inertial frame

If the distance between rockets is constant as measured in the inertial frame, then

1. The acceleration felt by the two rockets is the same
2. The distance between rockets is growing as measured in the rocket frame.

Well from what I quoted from Janus in post #68 I assume Janus was considering it to be the first case. But what case do you think it will be for the following scenario.

There are two spaceships (the "sausage" segments) inside a large tubular spaceship (the "pastry"). They are separated by a distance of 10 light years. All the clocks are synchronised. The two spaceships then at the same point in time (from the "pastry" frame of reference) accelerate to 0.6c.

 

[name123]

You are assuming a step, resynchronization of Pastry's clocks, that doesn't happen.

I wasn't assuming a re-synchronisation, it was that you had written:

However if the crew in the front and in the back of Sausage compared their wristwatches, they could be hours off.

You wrote:

Each Pastry crewman would see, using his wristwatch, that the acceleration started at 0.00s, and ended at say 0.001s. Then they started to decelerate at 0.800s and finished at 0.801s. Again, each crewman would see the same.
But if, during the way (the 0.8s they are moving), they looked around, they would "see" (rather "compute" or "estimate") the wristwatches toward the front showing some time in the past, and the wristwatches behind as some time in the future.

Originally the "pastry" ship was at rest, but I see you have changed them around. So you are saying that the accelerating ship would "compute" the wristwatches at the front showing some time in the past. But they would be wrong, as the clocks at the front would have measured the acceleration to have stopped at the same time, and the journey at 0.6c to have been for the same amount of time. Events would be measured as occurring at the same time.

If everyone resynchronized their wristwatches when they started to move, they would need to agree on a master clock, say the central one. So the crewman in the middle would keep the wristwatch at 0.001s, but those in front would move it from 0.001s to say -750 and those in the back to say +750.
(If the trip never stopped, they could now walk around, comparing wristwatches, and they would agree that indeed all their clocks show the same time.)
Then the trip would stop at 0.8s central clock, -749.2 front clock, 750.8 rear clock. Again, after stopping, they would realize that the clocks are not synchronized any more, and would need to adjust them again.

You seem to be saying that if they synchronised their clocks, then in their inertial frame (when it is cruising at 0.6c) events would be measured as taking place at different times (such as the time each segment started to decelerate). And strangely, those at the front would seem to be stating that the re-synchronisation happened for them say 750 seconds before it did for the clock in the middle. And that the 0.8 second trip ended for them roughly 741.2 seconds before it started for the middle clock, even though they agree that they had all set off at the same time.

Without the resynchronization,
Front Pastry clock: 0.800s
Sausage clock nearest to Pastry's front: 1.000s
Back Pastry clock: 0.800s
Sausage clock nearest to Pastry's end: 1.000s
Note: Pastry is the accelerating/decelerating one.

And presumably here, when the ship decelerates a difference in clock times would be measured. The clocks on the ship that did the accelerating having ticked less. The longer it had traveled for the greater the difference between the clocks.

I find this slightly confusing also, and I'll explain why. Supposing there were 7 ships, A, B, C, D, E, F, G. They are all at rest with each other. And they are all tubular. B fitting in A, C fitting in B, D fitting in C and so on. And all several hundred light years long.

A remains at rest and B accelerates to 0.1c, Presumably B's clock would have ticked less than A's if after its journey it returned to A's rest frame.
C accelerates to 0.2c. Presumably C's clock would have ticked less than B's if they both stopped (with respect to A).
and so on until F and G which both accelerate to 0.6c. Presumably both would have ticked less than the A, B, C, D and E ships if they all came to rest with A.

But now imagine F and G were in fact the "pastry" and "sausage" ship we were referring to. So when G accelerates to be at rest with A, wouldn't it actually be F's clock that is ticking slower than G's. Such that if G stayed at rest with A for a few years, and the accelerated to be at rest with F, F's clock would show the lower amount of time passing, not the other way around?

Thanks for your patience by the way. As you can see I am still finding what are presumably basic things still quite confusing.

 

[SlowThinker]

Well from what I quoted from Janus in post #68 I assume Janus was considering it to be the first case.

If they accelerate simultaneously by the same amount, it must be scenario 2.

But what case do you think it will be for the following scenario.

You are introducing 3rd or so scenario in the same thread. It won't help you at all. Understand one and move to the next.

In particular, it seems you still haven't quite understood what happens when a short train starts moving along a track that has a clock mounted every meter. While you answered the questions correctly, you aren't applying that in other places.

Also I think the Pastry used to be the accelerating ship.

 

[name123]

If they accelerate simultaneously by the same amount, it must be scenario 2.

So when Janus wrote:

This is a lot more complicated than it seems. If you arranged things so that in the sausage frame, the spacing between segments remained constant and all the segments started and stopped accelerating at the same moment, then according to the pastry ship, the segments and thus the distance between them was shrinking due to length contraction during this whole acceleration. But this also means that, at any given moment the Leading segment was traveling at a lower speed relative to the rear segment and thus its clock was exhibiting a greater time dilation rate. In other words, according to the pastry ship, the clocks in the segments wouldn't be ticking at the same rate.

I presume he had changed the scenario which caused me some confusion.

You are introducing 3rd or so scenario in the same thread. It won't help you at all. Understand one and move to the next.

In particular, it seems you still haven't quite understood what happens when a short train starts moving along a track that has a clock mounted every meter. While you answered the questions correctly, you aren't applying that in other places.

Also I think the Pastry used to be the accelerating ship.

The scenario is pretty similar to the one in post #34 accept that the clocks start in synch and one ship undergoes acceleration. In post #34 the pastry ship was the one that was being considered to be analogous to the track, though then given the symmetry in the space it allowed it to be relative which one was considered moving. But in post #47 for example where there is acceleration, it seems as though the sausage ship was being considered to be the one accelerating. But it may have changed throughout the conversation.
.

 

[ZapperZ]

I don’t recognize “relative truth” as a standard term in SR. Do you mean “reference frame”?

Your scenario is simply a bunch of twin paradoxes in parallel. The resolution is exactly the same:

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

This is definitely late, but I agree with this. In light of Giuliani's idiotic "Truth isn't truth" comment, maybe this thread should be re-titled with something more appropriate, especially considering that "relative truth" is never popularly used in Relativity.

Zz.

 

[SlowThinker]

Originally the "pastry" ship was at rest, but I see you have changed them around.

Sorry, the thread is running for too long and on iPad it's sometimes not possible to review older posts while typing.

So you are saying that the accelerating ship would "compute" the wristwatches at the front showing some time in the past. But they would be wrong

The resynchronized timing would not be wrong. If they didn't do it, and the crewmen from the head of the ship went to meet those at the tail, they would notice that their wristwatches are off.
It's simply a different reference frame. If the clocks are showing the same time in one, they won't be in the other.

You seem to be saying that if they synchronised their clocks, then in their inertial frame (when it is cruising at 0.6c) events would be measured as taking place at different times (such as the time each segment started to decelerate). And strangely, those at the front would seem to be stating that the re-synchronisation happened for them say 750 seconds before it did for the clock in the middle. And that the 0.8 second trip ended for them roughly 741.2 seconds before it started for the middle clock, even though they agree that they had all set off at the same time.

No. They started at the same time in the, uh, Pastry time. But let's have crewman Head who does this:
clock shows 0; I set the clock to 750; wait for 0.8s; what's the time now?
Crewman Tail does this:
clock shows 0; I set the clock to -750; wait for 0.8s; what's the time now?
In their life, they might say that it all took 0.8s, but really, they stopped at different times because their clocks were showing different numbers.

I find this slightly confusing also, and I'll explain why.
...
wouldn't it actually be F's clock that is ticking slower than G's. Such that if G stayed at rest with A for a few years, and the accelerated to be at rest with F, F's clock would show the lower amount of time passing, not the other way around?

There is really no "slower" clock, in particular each of them is slower than the other. Distance is important. Sausage moves to meet new Pastry's clock, that, despite running slower, are already showing higher time.
What I said about Sausage and Pastry clocks doesn't change if there is ship A flying around. But A's crew might say that neither Sausage nor Pastry clocks are properly synchronized.

If you want to define a new scenario with ships A, Sausage and Pastry, you need to specify how they synchronize the clocks along each ship, in which frame the acceleration appears to be simultaneous, and other things.
If Sausage starts to move, Pastry waits a second, then accelerates to match Sausage, it's the same scenario as with Sausage slowing down instead.

 

[Sorcerer]

This is definitely late, but I agree with this. In light of Giuliani's idiotic "Truth isn't truth" comment, maybe this thread should be re-titled with something more appropriate, especially considering that "relative truth" is never popularly used in Relativity.

Zz.

According to the link below, Einstein wanted it to be called the theory of invariance.

http://www.f.waseda.jp/sidoli/MI404_23_Einstein.pdf

 

[name123]

No. They started at the same time in the, uh, Pastry time. But let's have crewman Head who does this:
clock shows 0; I set the clock to 750; wait for 0.8s; what's the time now?
Crewman Tail does this:
clock shows 0; I set the clock to -750; wait for 0.8s; what's the time now?
In their life, they might say that it all took 0.8s, but really, they stopped at different times because their clocks were showing different numbers.

I accept that it is "pastry time" that they all started off together. But when crewman Head's clock is set to -750, is not crewman Head of the opinion that the middle clock will not show 0.8 seconds until 750.8 seconds have passed, because when it does it will do so simultaneously to crewman Head's clock showing 0.8 seconds? What I am also not clear on is what crewman Head would be thinking the middle clock was showing simultaneous to it's clock showing -750.

Edit: Sorry for being so slow here, I assume the answer is that the paradox of crewman Head claiming that it is true that crewman Head and crewman Middle accelerated at the same time, and claiming that it is true that both it and crewman Middle decelerated 0.8s after each of them accelerated, while also claiming that it is true that crewman Middle won't decelerate until 750 seconds after crewman Head did comes about because the statements involve different frames of reference, and that the truth is relative to the frame of reference (in the special relativity interpretation of the Lorentz transformations).

If you want to define a new scenario with ships A, Sausage and Pastry, you need to specify how they synchronize the clocks along each ship, in which frame the acceleration appears to be simultaneous, and other things.
If Sausage starts to move, Pastry waits a second, then accelerates to match Sausage, it's the same scenario as with Sausage slowing down instead.

If they synchronise the clocks in the frame of rest frame A. Then presumably G and F's clocks will appear to tick 0.8s for each tick of 1s in rest frame A at the point they are both cruising at 0.6c. And when G comes to rest with A then presumably it is back to a 1:1 tick with A. And so F's clock will tick 0.8s for each 1s tick of G's.

But is it that G and F are cruising at 0.6c and they then both synchronise their clocks, and then G comes to rest with A, that G's clock will tick 0.8s for each 1s tick of F's?

If so then I do find it strange that adjusting the time of F for example in the synchronisation event would alter the relative tick rate.

Edit 2: As a side note, presumably if what I experience corresponds to my neural state, then what my neural state was at a given point in time would vary depending on the frame of reference of the observer. What neural events were simultaneous would vary. Would the variations in simultaneity not imply variations of experience?

 

[SlowThinker]

because the statements involve different frames of reference

Yes, start and end is in Pastry frame while the cruise is in Sausage frame. Either the clocks are left running, in which case they are, in a sense, showing meaningless value during the cruise. Or you can resync them, but in this new clock scheme the trip starts at different times for different crewmen.

But is it that G and F are cruising at 0.6c and they then both synchronise their clocks, and then G comes to rest with A, that G's clock will tick 0.8s for each 1s tick of F's?

As seen from F, yes. As seen from A or G, it would be the F clock running slower.

If so then I do find it strange that adjusting the time of F for example in the synchronisation event would alter the relative tick rate.

Right, it doesn't. It's the motion of the observer that changes the numbers. Your own time is always the fastest.

 

[name123]

Right, it doesn't. It's the motion of the observer that changes the numbers. Your own time is always the fastest.

Ok but earlier you wrote:

The Sausage crew would see the newly nearest Pastry clock as all showing 1.00s. Their own wristwatch would show 0.80s.

Which seems to be suggesting that the sausage crew would have seen their own time as slower.

Also I previously added an edit which would have been after you started responding:

As a side note, presumably if what I experience corresponds to my neural state, then what my neural state was at a given point in time would vary depending on the frame of reference of the observer. What neural events were simultaneous would vary. Would the variations in simultaneity not imply variations of experience?

The point being would there be disputes about what you were experiencing given the interpretation, but an absolute truth with regards to the evidence as to what you were experiencing?

 

[SlowThinker]

Ok but earlier you wrote:

The Sausage crew would see the newly nearest Pastry clock as all showing 1.00s. Their own wristwatch would show 0.80s

Which seems to be suggesting that the sausage crew would have seen their own time as slower.

Just before deceleration, the Pastry clock nearest at the time of start, now 0.6*0.8=0.48 light seconds away, would indeed be showing only 0.8*0.8=0.64s. But the new clock, that jumped ahead to 0.36 when the Sausage suddenly accelerated, despite running slower, still show 1.00s when they arrive nearby.
(I'm not sure if I made a mistake in the numbers but it seems reasonable).

The point being would there be disputes about what you were experiencing given the interpretation, but an absolute truth with regards to the evidence as to what you were experiencing?

I'm not sure what you're talking about. The theory of relativity describes the one objective truth (as far as we can tell). It is very logical and consistent.

One of the consequences of relativity is that you can't really use the concept of "now" for things that are far away.
You can talk about how much time elapsed on someone's clock, which is the same as what they experienced (if they didn't adjust the clock).
You might use "now" if you don't change your speed and you're in an empty universe, but someone else may disagree with what you say (e.g. clock X showing time Y). Both of you are right. The Theory of relativity says how your claims are related.

 

[stevendaryl]

Well from what I quoted from Janus in post #68 I assume Janus was considering it to be the first case. But what case do you think it will be for the following scenario.

There are two spaceships (the "sausage" segments) inside a large tubular spaceship (the "pastry"). They are separated by a distance of 10 light years. All the clocks are synchronised. The two spaceships then at the same point in time (from the "pastry" frame of reference) accelerate to 0.6c.

I'm assuming that the large spaceship is not accelerating?

In that circumstance, then we're in the second situation:

1. Both smaller spaceships feel the same acceleration.
2. The distance between the spaceships remains constant as viewed in the frame of the large spaceship.
3. The distance between the spaceships grows as viewed in the frame of either smaller spaceship. To those on board the smaller spaceships, the ships seem to be getting farther and farther apart.

 

[stevendaryl]

If so then I do find it strange that adjusting the time of F for example in the synchronisation event would alter the relative tick rate.

In Special Relativity, you have to be very careful what you mean by something like "the relative tick rate".

Lets look at our two different scenarios from the point of view of discrete jumps, instead of continuous. That might help explain what's going on.

Instead of firing the rocket continuously, assume that the way the acceleration works is that there is a schedule: At time t=0, rockets are fired to accelerate to speed 10% the speed of light. At time t=1 (according to the clocks on board the spaceships), rockets are fired again to accelerate to 10% of the speed of light relative to the first speed. Etc.

So let's assume that the initial distance between the spaceships is $L$.

The rear spaceship fires its rockets at event $e_1$ with coordinates $(x_1, t_1)$ (using the coordinates of the inertial frame of the larger ship).
The second spaceship fires its rockets at event $e_2$ with coordinates $(x_2 = x_1+L, t_2 = t_1)$. (Same time, different location.)

Now, after accelerating, the spaceships are (momentarily, until the rockets fire again) at rest in a new frame. This new frame has a different coordinate system, $x', t'$ related to the first coordinate system through:

$x' = \gamma (x - vt)$
$t' = \gamma (t - \frac{vx}{c^2})$

where $v$ is 10% of the speed of light. So in this new coordinate system, $e_1$ has the coordinates:

$x_1' = \gamma (x_1 - v t_1)$
$t_1' = \gamma (t_1 - \frac{v x_1}{c^2})$

$e_2$ has the coordinates:

$x_2' = \gamma (x_2 - v t_2) = \gamma (x_1 + L - v t_1)$
$t_2' = \gamma (t_2 - \frac{v x_2}{c^2}) = \gamma (t_1 - \frac{v x_1}{c^2} - \frac{v L}{c^2})$

Now, if we subtract the coordinates, we get:

$\Delta x' = x_2' - x_1' = \gamma L$
$\Delta t' = t_2' - t_1' = - \gamma \frac{vL}{c^2}$

Note: In this new reference frame, we find two weird things:

1. The distance between the rockets has grown from $L$ to $\gamma L$.
2. The two rocket firings were not simultaneous. Since $\Delta t' < 0$, that means that, according to this new reference frame, the front rocket fired earlier than the rear rocket. What that means is that the way things look in this new frame, first the front rocket fires, when its clock shows time $t_1$. Then a time $\Delta t'$ later, the rear rocket fires when its clock shows time $t_1$. So in this frame, the clock in the front rocket is ahead of the clock in the rear rocket by an amount $\Delta t'$, since that's how long it has been at rest in this frame waiting for the rear rocket to fire.

So at this point, you can see that pattern: If every second according to the clock aboard the two rockets, the rockets fire, then the rockets will drift farther and farther apart (as measured by those aboard the rockets) and the clock in the front rocket will get farther and farther ahead, also.

If the two rockets want to keep the same distance, then it's necessary for the front rocket to fire either less frequently, or with less intensity.

 

[name123]

Just before deceleration, the Pastry clock nearest at the time of start, now 0.6*0.8=0.48 light seconds away, would indeed be showing only 0.8*0.8=0.64s. But the new clock, that jumped ahead to 0.36 when the Sausage suddenly accelerated, despite running slower, still show 1.00s when they arrive nearby.
(I'm not sure if I made a mistake in the numbers but it seems reasonable).

So when a member of the sausage crew passes a member of the pastry crew, the sausage crew member will see the pastry crew members clock as showing 1s and their own to be showing 0.8s?

I'm not sure what you're talking about. The theory of relativity describes the one objective truth (as far as we can tell). It is very logical and consistent.

One of the consequences of relativity is that you can't really use the concept of "now" for things that are far away.
You can talk about how much time elapsed on someone's clock, which is the same as what they experienced (if they didn't adjust the clock).
You might use "now" if you don't change your speed and you're in an empty universe, but someone else may disagree with what you say (e.g. clock X showing time Y). Both of you are right. The Theory of relativity says how your claims are related.

I thought that with the theory of relativity there is an eternal universe idea, and that there is no changing "now" in an eternal universe model. There is only what event is simultaneous with what event and the answer to that would be relative. I also did not know that the theory of relativity was an objective truth because is it not a metaphysical theory that shares mathematics with theories such as LET or neo-LET theories.

What I was talking about was the idea that your experience is based on your neural state. With the theory or relativity an observer passing at a high velocity would disagree with an observer in the same rest frame as you with regards to which of your neural events were simultaneous could they not? So what your neural state was would be a relative observation.. So would it not entail a claim that the truth regarding what you were experiencing was relative?

 

[name123]

In Special Relativity, you have to be very careful what you mean by something like "the relative tick rate".

Lets look at our two different scenarios from the point of view of discrete jumps, instead of continuous. That might help explain what's going on.

Instead of firing the rocket continuously, assume that the way the acceleration works is that there is a schedule: At time t=0, rockets are fired to accelerate to speed 10% the speed of light. At time t=1 (according to the clocks on board the spaceships), rockets are fired again to accelerate to 10% of the speed of light relative to the first speed. Etc.

So let's assume that the initial distance between the spaceships is $L$.

The rear spaceship fires its rockets at event $e_1$ with coordinates $(x_1, t_1)$ (using the coordinates of the inertial frame of the larger ship).
The second spaceship fires its rockets at event $e_2$ with coordinates $(x_2 = x_1+L, t_2 = t_1)$. (Same time, different location.)

Now, after accelerating, the spaceships are (momentarily, until the rockets fire again) at rest in a new frame. This new frame has a different coordinate system, $x', t'$ related to the first coordinate system through:

$x' = \gamma (x - vt)$
$t' = \gamma (t - \frac{vx}{c^2})$

where $v$ is 10% of the speed of light. So in this new coordinate system, $e_1$ has the coordinates:

$x_1' = \gamma (x_1 - v t_1)$
$t_1' = \gamma (t_1 - \frac{v x_1}{c^2})$

$e_2$ has the coordinates:

$x_2' = \gamma (x_2 - v t_2) = \gamma (x_1 + L - v t_1)$
$t_2' = \gamma (t_2 - \frac{v x_2}{c^2}) = \gamma (t_1 - \frac{v x_1}{c^2} - \frac{v L}{c^2})$

Now, if we subtract the coordinates, we get:

$\Delta x' = x_2' - x_1' = \gamma L$
$\Delta t' = t_2' - t_1' = - \gamma \frac{vL}{c^2}$

Note: In this new reference frame, we find two weird things:

1. The distance between the rockets has grown from $L$ to $\gamma L$.
2. The two rocket firings were not simultaneous. Since $\Delta t' < 0$, that means that, according to this new reference frame, the front rocket fired earlier than the rear rocket. What that means is that the way things look in this new frame, first the front rocket fires, when its clock shows time $t_1$. Then a time $\Delta t'$ later, the rear rocket fires when its clock shows time $t_1$. So in this frame, the clock in the front rocket is ahead of the clock in the rear rocket by an amount $\Delta t'$, since that's how long it has been at rest in this frame waiting for the rear rocket to fire.

So at this point, you can see that pattern: If every second according to the clock aboard the two rockets, the rockets fire, then the rockets will drift farther and farther apart (as measured by those aboard the rockets) and the clock in the front rocket will get farther and farther ahead, also.

If the two rockets want to keep the same distance, then it's necessary for the front rocket to fire either less frequently, or with less intensity.

Thanks for that, I can see how there would be disagreements in which events were simultaneous.

I was thinking that special relativity allow for clocks to have objectively ticked less than other clocks, for example in the Hafele-Keating experiments. But in the example I gave I think I should have considered the situation using Minkowski space diagrams. I think I was making the same mistake I was making earlier in this thread, which I recognised and then subsequently forgot. Thanks for you patience and detailed response.

 

[Dale]

With the theory or relativity an observer passing at a high velocity would disagree with an observer in the same rest frame as you with regards to which of your neural events were simultaneous could they not? So what your neural state was would be a relative observation..

Neural states form and change far too slowly for relativistic effects to be relevant. For the time scales at which neural states change the brain can easily be considered a point.

 

[SlowThinker]

So when a member of the sausage crew passes a member of the pastry crew, the sausage crew member will see the pastry crew members clock as showing 1s and their own to be showing 0.8s?

Yes. (Assuming they didn't mess with the clocks after start).

I also did not know that the theory of relativity was an objective truth

I meant it in the sense that both Pastry and Sausage crew's observations are correct and precise, yet they disagree on the clock rates etc. Theory of relativity explains that both are simply different views of the same reality. To my knowledge, it doesn't explain why.

What I was talking about was the idea that your experience is based on your neural state. With the theory or relativity an observer passing at a high velocity would disagree with an observer in the same rest frame as you with regards to which of your neural events were simultaneous could they not?

They may disagree on relative ordering of events that are far away from each other, so their ordering doesn't really matter.
Obviously if both observers know Theory of relativity, they will agree on pretty much everything.

 

[name123]

Neural states form and change far too slowly for relativistic effects to be relevant. For the time scales at which neural states change the brain can easily be considered a point.

I was considering that if one neuron was in a different state it would be a different neural state, and I wasn't aware of a minimal time delay between different neurons firing. I didn't think all fired synchronous to a brainwave.

 

[name123]

They may disagree on relative ordering of events that are far away from each other, so their ordering doesn't really matter.
Obviously if both observers know Theory of relativity, they will agree on pretty much everything.

How far away do they have to be? Could there not be a difference in simultaneity if things were 15cm apart if one observer was moving fast and the other was at rest?

 

[SlowThinker]

How far away do they have to be? Could there not be a difference in simultaneity if things were 15cm apart if one observer was moving fast and the other was at rest?

Of course anything farther than 0 has its timing shifted. It depends on the precision which you can achieve. If you can measure nanosecond delays, 15cm is far enough. If you measure in miliseconds, 100km is close. If the observers move slowly relative to each other, the whole Solar system can be considered small. Lorentz transformation quantifies actual time (and space) shifts.

 

[Dale]

I was considering that if one neuron was in a different state it would be a different neural state,

A single neuron’s single action potential is 1 ms so that would mean relativistic effects are irrelevant for brains less than about 300 km in size. However, the state of the brain doesn’t change as fast as the state of a single action potential (neurons encode strength in the frequency of action potentials). A better upper limit for that frequency would be the rate of the gamma waves in an EEG, which tops out at about 150 Hz. That would correspond to a brain size of about 2 million m before relativistic effects would be relevant. The human brain is about 20 cm, so essentially a point compared to the relevant length scales.

 

[name123]

A single neuron’s single action potential is 1 ms so that would mean relativistic effects are irrelevant for brains less than about 300 km in size. However, the state of the brain doesn’t change as fast as the state of a single action potential (neurons encode strength in the frequency of action potentials). A better upper limit for that frequency would be the rate of the gamma waves in an EEG, which tops out at about 150 Hz. That would correspond to a brain size of about 2 million m before relativistic effects would be relevant. The human brain is about 20 cm, so essentially a point compared to the relevant length scales.

I can see your point, but I am not sure that the issue is how often a single neuron could fire, or how long it took. I thought it might be the brain state.

If there were say 100 billion neurons in the brain, and say 10% were firing in any given second and that each of those that fired, fired on average 5 times per second. Then there would be 50 billion neural firings per second, and the number of neurons starting to fire any given nanosecond would be about 50 and the number of neurons ceasing to fire for any given nanosecond would be about 50. Also the firings are not "on" "off" affairs, and the action potential will vary over the firing. How significant it would be to the experience I do not know. But presumably it would be slightly significant else if you counted each ns step as equivalent to the next then when considering the sum of lots of such differences you would consider it to make no difference. In the sense that if e₁ = e₂ and e₂ = e₃ and e₃ = e₄ and so on such that e_n = e_n+1 then e₁ = e_n+1. I have ignored brain waves and the extent to which some of the firings might be "synchronised".

Could the experience not be thought to reflect the simultaneity of neural events?

 

[name123]

Of course anything farther than 0 has its timing shifted. It depends on the precision which you can achieve. If you can measure nanosecond delays, 15cm is far enough. If you measure in miliseconds, 100km is close. If the observers move slowly relative to each other, the whole Solar system can be considered small. Lorentz transformation quantifies actual time (and space) shifts.

I was not thinking about measurement, but theoretical implications. Is what you are experiencing a relative truth?

 

[SlowThinker]

I was not thinking about measurement, but theoretical implications. Is what you are experiencing a relative truth?

I really have no idea where this neurobiology talk comes from.
The brain of an astronaut orbiting Earth works just as well as down here, and neither is affected at all by an alien flying around at 0.9c. Also the alien's brain works just fine. Everyone's viewpoint is equally correct.

 

[Dale]

I can see your point, but I am not sure that the issue is how often a single neuron could fire, or how long it took. I thought it might be the brain state.

I can dig up my neurobiology textbook and find references, but this is standard well known stuff in the field. From a neural signaling perspective an action potential is an all-or-nothing event and the information is encoded in the frequency of action potentials.

the number of neurons starting to fire any given nanosecond would be about 50 and the number of neurons ceasing to fire for any given nanosecond would be about 50.

And there would be a million bazillion molecules jiggling in thermal motion and quantum fluctuations and other things that are irrelevant to “the truth regarding what you were experiencing”. Your own subjective experience should confirm that “what you were experiencing” simply doesn’t change on the scale of nanoseconds and even one nanosecond is about 30 cm at c which is already larger than the brain.

Could the experience not be thought to reflect the simultaneity of neural events?

Not in the sense of the relativity of simultaneity.

 

[name123]

I really have no idea where this neurobiology talk comes from.
The brain of an astronaut orbiting Earth works just as well as down here, and neither is affected at all by an alien flying around at 0.9c. Also the alien's brain works just fine. Everyone's viewpoint is equally correct.

The issue is whether what you are experiencing corresponds to the simultaneous brain activity or not. Perhaps you could make your position clear on this matter.

 

[name123]

Could the experience not be thought to reflect the simultaneity of neural events?

Not in the sense of the relativity of simultaneity.

So if what you are experiencing does not reflect the simultaneity of neural events, what were you thinking it does reflect?

 

[SlowThinker]

The issue is whether what you are experiencing corresponds to the simultaneous brain activity or not. Perhaps you could make your position clear on this matter.

I don't understand your question. My brain is always at rest with respect to itself, and so its parts are always simultaneous in the same way, whether I'm in my bed, or flying an airplane.

 

[name123]

I don't understand your question. My brain is always at rest with respect to itself, and so its parts are always simultaneous in the same way, whether I'm in my bed, or flying an airplane.

Well it depends upon what you mean by simultaneous. Let me put it another way. Are you thinking that the truth of what you are experiencing is relative or is there an absolute truth about the matter?

 

[Dale]

So if what you are experiencing does not reflect the simultaneity of neural events, what were you thinking it does reflect?

Neural events simply don’t happen fast enough for the relativity of simultaneity to matter. Simultaneity in the relativistic sense can never cause anything so it also cannot cause “what you were experiencing”.