Time dilatation thought experiment

[Simi]

Hello everyone, this is my first post on this forum, I am a new member and the other day was pondering on a question related to the passage of time. So, I have the following thought experiment:

Suppose there is the following setup:

We have two small toy cars, identical, each capable of traveling with a maximum speed of 1 km/h.
We place one car on Earth and the other one on a spaceship. That spaceship is capable of traveling at 99% the speed of Light.
The moment the spaceship starts moving, away from Earth (it has an instant acceleration to 99% the speed of light), both of the toy cars also start moving as well. One of them will move on Earth, and the other inside the spaceship.
After half an hour, the spaceship turns around and travels back to Earth, to the same position it started. When it arrives back to the starting position, after 1 hour, the small toy car on Earth has traveled exactly 1 km.
The question is, how much did the toy car from the spaceship traveled?
I'm not looking for an exact answer, rather to know if it has traveled the same distance as the car on Earth (1 km) or a shorter distance?

PS: Time of travel is measured with a clock found on Earth.

 

[PeroK]

Hello everyone, this is my first post on this forum, I am a new member and the other day was pondering on a question related to the passage of time. So, I have the following thought experiment:

Suppose there is the following setup:

We have two small toy cars, identical, each capable of traveling with a maximum speed of 1 km/h.
We place one car on Earth and the other one on a spaceship. That spaceship is capable of traveling at 99% the speed of Light.
The moment the spaceship starts moving, away from Earth (it has an instant acceleration to 99% the speed of light), both of the toy cars also start moving as well. One of them will move on Earth, and the other inside the spaceship.
After half an hour, the spaceship turns around and travels back to Earth, to the same position it started. When it arrives back to the starting position, after 1 hour, the small toy car on Earth has traveled exactly 1 km.
The question is, how much did the toy car from the spaceship traveled?
I'm not looking for an exact answer, rather to know if it has traveled the same distance as the car on Earth (1 km) or a shorter distance?

PS: Time of travel is measured with a clock found on Earth.

You probably know that the spaceship will have aged less on its return to Earth than the time that has passed on Earth. This means that all physical processes on the ship have evolved less than equivalent processes on Earth. That applies to your toy car.

Note that the car moving along a track at a fixed speed could be regarded as a clock.

 

[Ibix]

Worth noting that both zero and about 0.99 light hours are possible answers to the question as phrased (as well as about 140m, which I suspect was the answer being looked for). Who is doing the measuring?

This isn't pointless nit-picking. About half of people's confusion in learning SR comes from failing to specify which reference frame a measurement is being made in. The other half is forgetting the relativity of simultaneity.

 

[Simi]

Hey guys, thanks for your answers.

@PeroK , I'm not referring to the molecular and atomic structure aging, which we all know that would have been done at a different rate due to different rates of entropy.

I assume you missed some of the text I wrote since I have specified this. Measurements are made on Earth, time is measured by a clock found on Earth and the spaceship travels for half an Earth-hour, away from Earth, and then travels back to Earth for another half Earth-hour.
Also, the distance traveled by the car found in the spaceship, is being measured after the spaceship reached Earth back, and is measured here, on Earth.
So, the question would be: Since the toy that traveled on Earth, made a distance of 1 km after that 1 Earth-hour, what will be the distance traveled by the car found on the spaceship, when measured on Earth after the returning of the spaceship? Will it be 1 km as well, or will it be less than 1 km?

 

[PeroK]

Hey guys, thanks for your answers.

@PeroK , I'm not referring to the molecular and atomic structure aging, which we all know that would have been done at a different rate due to different rates of entropy.

I assume you missed some of the text I wrote since I have specified this. Measurements are made on Earth, time is measured by a clock found on Earth and the spaceship travels for half an Earth-hour, away from Earth, and then travels back to Earth for another half Earth-hour.
Also, the distance traveled by the car found in the spaceship, is being measured after the spaceship reached Earth back, and is measured here, on Earth.
So, the question would be: Since the toy that traveled on Earth, made a distance of 1 km after that 1 Earth-hour, what will be the distance traveled by the car found on the spaceship, when measured on Earth after the returning of the spaceship? Will it be 1 km as well, or will it be less than 1 km?

You must have missed my answer! Time dilation - or, more precisely in this case, differential ageing - applies to time itself. Less time has passed on the spacecraft than on the Earth for the journey.

Your question could be about the motion of a toy car, the boiling of an egg, an atomic clock or any other thing. It's all the same. Less time has passed; therefore, the toy car will have traveled a shorter distance along or round its track in the spaceship.

 

[Ibix]

PeroK is correct. The ship's clocks will read about one seventh of an hour when it returns. Thus the car can only have traveled one seventh of a kilometre relative to the ship.

 

[Simi]

Hey @PeroK, this is actually the thing that I'm trying to debate.
I kind-of tend to see a difference between the mathematical abstraction of the problem which uses space-time as a four-dimensional space, which only translates as a four variables equation as a mean to describe mathematically the phenomena, and the actual dimensions of the real world, which are just three.
Trying to convey the mathematical abstraction into real world, is kind-of silly, just like attempting to find the real world dimensions of the n-dimensional Markov-Chain abstraction of the weather model.
It's unrealistic. So, what I'm saying is that, the math is one thing, real world representation is another.
What if material/molecular/atomic aging is related strictly to mass-energy-gravity and translates into different entropy rates but, process wise (eg. distance traveled by the car found on the spaceship) there are no effects.
In fact, I'm arguing that the car inside the spaceship, is actually traveling 1 km as well.

 

[Simi]

Although, an atomic clock will indeed measure, as @Ibix says, about one seventh of an hour when it returns.

 

[PeroK]

Hey @PeroK, this is actually the thing that I'm trying to debate.
I kind-of tend to see a difference between the mathematical abstraction of the problem which uses space-time as a four-dimensional space, which only translates as a four variables equation as a mean to describe mathematically the phenomena, and the actual dimensions of the real world, which are just three.
Trying to convey the mathematical abstraction into real world, is kind-of silly, just like attempting to find the real world dimensions of the n-dimensional Markov-Chain abstraction of the weather model.
It's unrealistic. So, what I'm saying is that, the math is one thing, real world representation is another.
What if material/molecular/atomic aging is related strictly to mass-energy-gravity and translates into different entropy rates but, process wise (eg. distance traveled by the car found on the spaceship) there are no effects.
In fact, I'm arguing that the car inside the spaceship, is actually traveling 1 km as well.

You mean that physics is one thing, but the real world is something else, that doesn't actually obey the laws of physics. That sort of thing?

PS and, as I've said several times on this forum, you are 113 years too late to be debating whether SR might be correct or not.

It is correct and the only task for the student is to understand why.

 

[A.T.]

In fact, I'm arguing that the car inside the spaceship, is actually traveling 1 km as well.

That would be a personal theory, and off-topic here.

 

[Ibix]

Although, an atomic clock will indeed measure, as @Ibix says, about one seventh of an hour when it returns.

Using the car as a clock is trivial. Proving that all clocks are identically affected by time dilation is also trivial. Thus by making the quoted statement you are agreeing with us about how far the car travels relative to the ship, whether you want to or not.

 

[weirdoguy]

So, what I'm saying is that, the math is one thing, real world representation is another.

At the end of the day it's not, beacuse math is ALWAYS compared with experiments. That's the way physics and other empirical sciences work and develope. If mathematical formalism we are using does not match the experiments we change the formalism. Special relativity matches perfectly with experiments, so there is no reason to argue with it.

 

[PeroK]

Using the car as a clock is trivial. Proving that all clocks are identically affected by time dilation is also trivial. Thus by making this admission you are agreeing with us, whether you want to or not.

@Simi

To add to this. There's an equation linking distance, time and speed: $d = vt$.

In this case, if you have an elapsed time of $1/7$ hours and a distance of $1km$, then you have a speed of $7km/h$.

Or, if you have a time of $1/7$ hours and a speed of $1km/h$ then you have a distance of $1/7 \ km$.

Or, if you have a speed of $1km/h$ and a distance of $1km$ then you need $1$ hour.

 

[Simi]

You mean that physics is one thing, but the real world is something else, that doesn't actually obey the laws of physics. That sort of thing?

No-no-no :) physics describes the real world, and I don't argue that. I was just trying to make you understand that an abstract mathematical model doesn't always have a direct representation into "things". It's abstract for goodness sake.
I was just giving you the Markov-chains weather model as an example, which nobody argues that its about any n-real world dimension, it just iterates the factors which comes into play (using n variables), affecting weather forecast and giving different weather outputs.
In the same manner I'm arguing that SR math should be interpreted.

 

[Ibix]

In the same manner I'm arguing that SR math should be interpreted.

The problem with this is that SR's maths relates very simply to real world measurements: it tells you what a clock would read or where a thing would be. There's no real room for interpretation beyond that, particularly not a wildly inconsistent interpretation that says that a car only capable of doing 1kph somehow traveled 1km while a co-moving clock ticked less than nine minutes.

 

[phinds]

@PeroK , I'm not referring to the molecular and atomic structure aging, which we all know that would have been done at a different rate due to different rates of entropy.

This is completely wrong and one of the most fundamental (and common) misunderstandings of SR. The RATE of aging is exactly the same for all objects --- 1 second per second --- regardless of their motion relative to something else. You are confusing differential aging with rate. That is, the traveler ages at one second per second but fewer seconds pass for him than for the stay-at-home.

 

[Simi]

I'm not arguing Einsteins equations at all.

Here it is the interesting thing Ibix, only the atomic clock would measure 1/7 of an hour, a standard clock will measure a full hour.
Why? Because when you measure the transition of the caesium atom from a certain energy level to another, this frequency is being influenced by gravitation (present or lack of it, that is), speed, energy.
Now, if the standard measurement of caesium atom reads 9,192,631,770 oscillations in Earth's gravitational field, when traveling with 99% of the speed of light, this read will be, let's say 6,434,842,239.
This is what I'm talking about here.

 

[phinds]

only the atomic clock would measure 1/7 of an hour, a standard clock will measure a full hour.

Wow. Just wow.

 

[Ibix]

Here it is the interesting thing Ibix, only the atomic clock would measure 1/7 of an hour, a standard clock will measure a full hour.

Wrong, and trivial to prove wrong, as already noted.

 

[Simi]

At the end of the day it's not, beacuse math is ALWAYS compared with experiments. That's the way physics and other empirical sciences work and develope. If mathematical formalism we are using does not match the experiments we change the formalism. Special relativity matches perfectly with experiments, so there is no reason to argue with it.

Of course the math corroborates with experiments, in this particular instance, I'm not arguing that either.

 

[Simi]

Wrong, and trivial to prove wrong, as already noted.

Could you please enlighten me?

 

[A.T.]

I'm not arguing Einsteins equations at all.

...only the atomic clock would measure 1/7 of an hour, a standard clock will measure a full hour.

This is directly contradicting Einsteins SR.

 

[Ibix]

Could you please enlighten me?

Sure. Set up two clocks of different sorts. Rig up a bomb to explode if they get more than a second out of sync.

Accelerate the clocks (you may have to stop them during the actual acceleration, depending on the kind of clock, but you can restart them once accelerated). By the principle of relativity, someone moving with the clocks regards them as at rest - therefore the bomb does not go off. However you claim that someone not moving along with the clocks will see the clocks ticking at different rates, and hence the bomb must explode. Thus you contradict yourself, unless you throw out the principle of relativity - in opposition to about 350 years of experimental results.

 

[PeroK]

Could you please enlighten me?

Inertial motion is relative. For example, the Earth is orbiting the Sun, the Sun is orbiting the galactic centre and our galaxy and the Andromeda galaxy are moving towards each other. So, you cannot say that a clock on Earth is absolutely at rest. And, in fact, you cannot say that any clock is absolutely at rest.

The clocks in the spaceship and the clocks on Earth have a relative velocity, but both sets of clocks are inertial. If the clocks on Earth remain synchronised, then so must the clocks on the spaceship.

Otherwise, you would have different laws of physics in different inertial reference frames.

In other words, you are ascribing some asbolute state of motion to the spaceship that makes its clocks behave differently. Some, bizarrely, keep time with Earth clocks (why Earth clocks in particular?) and other run slow compared to Earth clocks.

 

[Mister T]

I kind-of tend to see a difference between the mathematical abstraction of the problem which uses space-time as a four-dimensional space, which only translates as a four variables equation as a mean to describe mathematically the phenomena, and the actual dimensions of the real world, which are just three.

The three dimensions of space are not any more or less "actual" than the four dimensions of spacetime.

The fact of the matter is that, upon reunion, the two clocks show a different amount of elapsed time since the departure.

So, what I'm saying is that, the math is one thing, real world representation is another.

I'm having trouble drawing a distinction betweed a real world representation and an unreal world representation. Is it that the "real" representation is a description of how Nature behaves and an unreal one isn't? If that's the case, then the "real" representation is physics and the unreal one isn't.

What if material/molecular/atomic aging is related strictly to mass-energy-gravity and translates into different entropy rates but, process wise (eg. distance traveled by the car found on the spaceship) there are no effects.

You seem to be drawing a distinction without a difference. Time is what we measure with a clock. So if you note the clock-reading at one event, and the clock-reading at another event, and subtract the two clock-readings, you have the time that elapsed between the two events.

Either clocks measure time or they don't. You can't have it both ways.

In fact, I'm arguing that the car inside the spaceship, is actually traveling 1 km as well.

But there's no way to distinguish between what you are calling the "actual" distance between two events and other determinations of the distance between those same two events.

As I sit here I note that my clock reads 11:58 am . One minute later I note that it reads 11:59 am. How far did I travel between those two events. Did I "actually" move or not? I didn't move relative to my chair, I didn't move relative to the floor underneath the chair. But I did move some distance relative to the sun. So which is the "actual" distance? One person can claim one of them to the "actual" one and someone else claim it's the other measurement that gives the "actual" distance. And there is no way to say that either person is any more or less correct than the other person. In other words, the very notion that one of them is the "actual" distance cannot be supported by any experiment or observation. Thus there is nothing physical to be associated with the use of "actual" here.

 

[Janus]

Hey guys, thanks for your answers.

@PeroK , I'm not referring to the molecular and atomic structure aging, which we all know that would have been done at a different rate due to different rates of entropy.

I assume you missed some of the text I wrote since I have specified this. Measurements are made on Earth, time is measured by a clock found on Earth and the spaceship travels for half an Earth-hour, away from Earth, and then travels back to Earth for another half Earth-hour.
Also, the distance traveled by the car found in the spaceship, is being measured after the spaceship reached Earth back, and is measured here, on Earth.
So, the question would be: Since the toy that traveled on Earth, made a distance of 1 km after that 1 Earth-hour, what will be the distance traveled by the car found on the spaceship, when measured on Earth after the returning of the spaceship? Will it be 1 km as well, or will it be less than 1 km?

Less than 1 km.

Here's another way to look at it:
The car on the spaceship is, as measured by the Earth, subject to the rules of relativistic velocity addition or
$$ w = \frac{u+v}{1+\frac{uv}{c^2}}$$
with w being the velocity of the car relative to the Earth, u the velocity of the ship relative to the Earth and v the velocity of the car relative to the ship ( as measured from the ship).
Plugging in you numbers, we get value of w which is ~0.02 km/hr greater than that of the ship on both legs. Put another way, we on Earth would measure the car as moving at ~0.02 km/hr with respect to the ship, and after the one hour trip, it would have traveled ~0.2 km with respect to its starting point on the ship.. This is ~1/50 as far as the Earth car has traveled relative to the Earth. However, according to the Earth, the ship also undergoes length contraction and is 1/7 the length that the ship would measure itself as being. If the ship was 1km long as measured by the ship, then it would be 1/7 km long as measured by the Earth, and .02 km is ~1/7 of 1/7 km*. You get the same fraction of the ship's length traveled as you do if you just used the time dilation factor answer already given.

* 7*7= 49 and not 50, but we are using rough estimates fin this example, and this is close enough.

 

[Simi]

@Ibix , someone not traveling with the clocks, will see different speed rates between the one at rest and the one accelerating, due the Doppler effect of the light waves. I'm not suggesting anything else.

@PeroK , when I say clock, I don't imply anything atomic or quantum phenomena based. I'm just thinking that probably distance traveled by the car in the spaceship, is still 1 km after arriving on Earth and the time experienced inside the rocket is still one hour. The only difference being the fact that due to speed increase, matter at it's fundamental level is being affected, ageing as a buy-product of different entropy rates generated by gravity/mass/energy and speed.
Also, I'm a bit confused about your last paragraph.

@Mister T, people do tend a lot and try to visualize objects and nature in 4D or multidimensional spaces, which, is of the realm of Sci-Fi and misinterpretation/misleading. When speaking of a multidimensional mathematical model, I think it is best to present it as a mean of computation and variables dependencies, as a function describing the problem domain, not as spatial dimensions which are not. I think it's more healthy to draw a hard line here between actual physical dimensions and mathematical variables. This is what I'm referring to.
Also, the distance is measured from the starting point, to the final stopping point, after the rocket has reached back Earth. In both of the cases, the frame of reference is Earth and the distance is relative to the car' starting position.

 

[PeroK]

[

@PeroK , when I say clock, I don't imply anything atomic or quantum phenomena based. I'm just thinking that probably distance traveled by the car in the spaceship, is still 1 km after arriving on Earth and the time experienced inside the rocket is still one hour. The only difference being the fact that due to speed increase, matter at it's fundamental level is being affected, ageing as a buy-product of different entropy rates generated by gravity/mass/energy and speed.
Also, I'm a bit confused about your last paragraph.

That's your personal theory and it is out of step with mainstream physics. You won't be able to study physics at any reputable university and be taught that SR is wrong and time is absolute.

You have a choice to learn SR and engage with the mainstream physics community. Or, you can remain outside that community with your own theories, including non-acceptance of SR.

We cannot discuss your own personal theories here. It is against our rules and, in any case, a waste of time.

 

[Ibix]

@Ibix , someone not traveling with the clocks, will see different speed rates between the one at rest and the one accelerating, due the Doppler effect of the light waves. I'm not suggesting anything else.

Indeed. You are suggesting that two clocks on board a single rocket ship, one atomic clock and one of another type, will show different tick rates as viewed by someone who sees the ship moving. That's what leads to self-contradiction.

 

[A.T.]

people do tend a lot and try to visualize objects and nature in 4D or multidimensional spaces, which, is of the realm of Sci-Fi and misinterpretation/misleading. When speaking of a multidimensional mathematical model,...

The geometrical interpretation of SR is completely irrelevant here. Your ideas are not consistent with the 2 postulates of SR.

 

[Simi]

@Ibix , that's accurate, an atomic clock, which measures energy-level transitions, will be out of sync when compared to a mechanical one, this is indeed what I am thinking. I didn't understand your statement initially, my mistake.

I do tend to see time as an abstract construct, which is more of the realm of a convention, as an aid, not an actual physical property woven in the fabric of the Universe like, let's say mass. I would rather see entropy rates being relative to different frame of references and contextual, taking place of what you are thinking time should be.

 

[Nugatory]

This thread has reached the point of diminishing returns, as Physics Forums is here to help people understand how modern physics works, and th original poster neither understands nor is interested in understanding this.

The thread is closed.