Twin twin paradox in a pool with running water

Copyright Carl Janssen 2024

Corrections : Go back and use the phrase "platforms with their connected frames" in some places

Corrections : Many of the paragraphs would make more sense if read in a different order than they are currently written.  This probably should be rewritten with the paragraphs in a different order but since the paragraphs reference other paragraphs the style they are written in would have to change and they can not merely be cut and paste to change the order and still make sense.

Book Title : Misconceptions of space and time in popular understandings of special relativity

Short Chapter Title : Twin twin paradox in a pool with running water

Long Chapter Title : Modified twin twin paradox in a pool or running river instead of outer space to account for a uniformly moving medium

This is a modified version of the twin twin paradox

What do I mean by pop or popular special relativity?

By pop special relativity I mean special relativity as it has been presented on a popular level whether or not that is the genuine theory of special relativity if there is such a things as the one and only correct genuine theory of special relativity.

What is it important to know about pop special relativity in regards to the twin twin paradox?

In pop special relativity it is assumed that objects moving relative to a reference frame are shrunk in the direction they are moving relative to the length that would be measured in another reference frame in which they are stationary and the higher the speed the object moves in a reference frame the more it is shrunk in that reference frame.  Whether or not certain objects are shrunk in certain reference frames results in different travel times in different reference frames when comparing the two events which are the start of travel at one destination and the end of travel at another destination.  There is more to pop special relativity than this but that is what I shall discuss in regards to the terms of the twin twin paradox.

What is the twin twin paradox

The twin twin paradox is the idea that if a identical twin flew in a spaceship away from earth to a destination then came back to earth they would turn out to be younger than the twin that stayed on earth when they come back.

The claim is that from the point of view of the twin that stays on earth the twin moving away has the size of their space ship shrunk in the direction that it is moving but the distance to their destination does not change based on the speed the spaceship is moving away from and then coming back to the twin on earth.

From the point of view of the twin in the spaceship, the earth is moving away from the spaceship and then the earth is moving towards the spaceship, but the spaceship is stationary, this results in a decreased distance between the destination and earth.  The ship is not traveling toward the destination but the destination is traveling toward then away from the ship.  This is presuming they are traveling in a straight line going both there and back so that the shrinking is in the direction between earth and the destination.  Since the distance is shrunk and since the speed of the spaceship relative to the twin on earth is the same from both points of view, it seems to take less time for the twin in the spaceship to complete the trip from their point of view.

A implied medium is necessary to tell which twin is younger in order to know what is and is not shrunk

I would suggest that if space is assumed to be a perfect vacuum then you can not actually tell which twin would be younger than the other twin without establishing a preferred reference frame.  This is because if there are no objects other than the earth and the spaceship then the spaceship moving away from the earth and the earth staying still is no different than the earth moving away from the spaceship and the spaceship staying still since you do not have a medium between the earth and the destination the spaceship is going to with a known velocity to determine if it is shrunk or not and by how much as a function of it's velocity.  However, since no perfect vacuum exists and they are actually travelling through a medium no preferred reference frame is required to decide which twin will be younger.  

Misconceptions about the nature of the medium that is unfortunately called the vacuum of outer space in pop science

I will suggest that instead of thinking about the medium that pop scientists and some pop science fiction writers call the vacuum of outer space as either aether and or a perfect vacuum this medium should instead be thought of as a fluid such as a plasma, gas, liquid or other state of matter with a chemical composition just as air is a fluid called gas with a chemical composition.  In some regions this fluid could have a low enough density and or low enough pressure to be called a imperfect vacuum but even in those regions the density and pressure would both be greater than zero and this fluid would still have a velocity and chemical composition.  I am presuming this substance is a fluid and not a crystalline solid because solid objects can move through it although I do not deny that this assumption could be wrong if it were a solid that could be deformed and which some light could pass through.

Please do not ignore known mediums while paying attention to hypothetical mediums

If someone absolutely must insist on thinking of aether then one can assume that aether has exactly the same velocity as a section of this fluid at the location in which one wishes to measure the velocity of aether.  But I really think it is better not to invoke the velocity of some hypothetical aether at a location when the velocity of some actual fluid with a actual chemical composition can be measured at that location.  I will suggest in other chapters that a series of absurd mistakes were made when ignoring the chemical composition, pressure, density and velocity of actual mediums that exist and actually have known methods of measurement in order to pay attention to a hypothetical medium called aether which one hypothesized a velocity of and hypothesized how to measure.  Even though mediums such as air or water, or hydrogen or sodium or cesium or various other chemicals existed at locations and had known velocities at those locations, people in past historical experiments, instead choose another velocity for a hypothetical medium of propagation at the same location called aether which in my opinion resulted in absurd results.  I am not denying the possibility that aether might exist but simply saying not to ignore mediums that are known to exist in the name of aether.

Making the case that a medium is necessary in order to resolve the special relativity twin twin paradox thought experiment through another thought experiment

I will try to make the case that what is important is not the reference frame or the reference frame alone but the medium, using a modified version where someone is swimming between two platforms with a body of water that can be stationary or moving relative to the platforms starting with the assumptions of pop special relativity as best as I understand it.

By left and right I do not mean rotation to the left or right but the direction of moving in a straight line to the right or left which is sometimes called translation instead of rotation

This is a thought experiment and I do not believe it can be done in real life exactly as described in the experiment because the uniform flow of water and air as described could not be achieved since the objects involved would distort the flow

Default scenario to which other scenarios will be compared

Imagine there are two platforms with water and air and ground between them.  Each platforms is connected to the ground below it with a frame with gaps allowing water to go through the frame looking much like some guard towers in movies, cartoons and video games or like the frame of a transmission tower.

https://pixabay.com/photos/transmission-tower-electric-tower-3387882/

https://web.archive.org/web/20210816031520/https://pixabay.com/photos/transmission-tower-electric-tower-3387882/

Image produced using combination of these three online programs

Data on the geogerbra table was used to make picture above but is not relevant or used in the physics equations or scenarios.  Screenshot was taken of section of geogebra graph.  Colors were filled in using Pixlr and text was added using imgflip 

One of the meme templates or images called "horizontal line" was used on imgflip which was added to draw a straight line that was resized and which was modified with imgflip draw to form a double arrow with a thickness of 10 and black color

https://imgflip.com/i/9b80wo

https://imgflip.com/i/9b3i2j

https://imgflip.com/i/9b3p1f

https://pixlr.com/editor/

https://www.geogebra.org/geometry

The platforms are a distance L0 between them when the water and air and ground is stationary relative to the platforms from a reference frame in which the platforms are stationary.  You could measure the length of the section of ground between the two frames attached to the ground or the section of water between the platforms or platform frames or the section of air between the two platforms and any and all of those measurements would result in a length of L0 when the water, air, ground, frames and platforms are stationary relative to one another and stationary in this reference frame.

I will now compare different scenarios.  In all scenarios the air between the platforms will be stationary relative to the platform frames and the ground between the platform frames will be stationary relative to the platform frames and the platforms will be stationary relative to the platform frames.  But in some of these scenarios the water will move through the platform frames with uniform flow and move relative to the platform frames where as in other scenarios the water will be stationary relative to the platform frame with uniform flow if you can call it flow when it is stationary.  In all the scenarios the air will be assumed to be stationary relative the the platform frames with uniform flow.  

Realistically as I already mentioned earlier the flow of the water and air could not be uniform when the water is moving relative to the platform frames because the flow of the water would be distorted by the objects around it and the flow of the air would be distorted by the flow of the water but this is a thought experiment not a real experiment.

The two twins have separate stop watches that both display the same time of 0 seconds at the event of the start of each scenario but may display different times at different later events in the scenario

alpha = ( 1 - ( v ^ 2) / ( c ^ 2 ) ) ^ 0.5

https://wikimedia.org/api/rest_v1/media/math/render/svg/bce2537b3a8f5029c517044add6f297e01da1b97

https://wikimedia.org/api/rest_v1/media/math/render/svg/5fa55fc5785e8c6fcc7251f8c169aea9a0d2dbfe

https://en.wikipedia.org/wiki/Lorentz_factor

Scenario 1

Twin twin paradox in which the water is stationary relative to the platform

One twin called the waiting twin stays on the left platform the other twin called the swimming twin swims from the left platform to the right platform and then back to the left platform again 

Scenario 1A 

From the point of view of the swimming twin in which the swimming twin is stationary and the left platform is moving away from and then toward the swimming twin at a speed of v

Because the water, ground and air are moving relative to the twin the section of those mediums between the two platforms all shrink to change length from L0 to L0 times alpha

Length of mediums between platforms for swimming twin = L0 * alpha

Time for platform to go away and then back to swimming twin = 2 * L0 * alpha / v

Scenario 1B

From the point of view of the waiting twin in which the swimming twin is moving away from and then back to the platform a a speed of v

Because the water, ground and air are stationary relative to the waiting twin they do not shrink from the viewpoint of the waiting twin

Length of mediums between platforms for the waiting twin = L0

Time for swimming twin to go away and then back to platform for the waiting twin = 2 * L0 / v

Scenario 2

There is a waiting twin on the left platform stationary relative to the left and right platforms and platform frames and the ground and air.

Water moves at a speed of v relative to the platform frames and then moves at a speed of v in the opposite direction relative to the platform frame resulting in the floating twin traveling from the left platform to the right platform and then back to the left platform again

There floating twin will not exert effort to swim but merely float from the left platform to the right platform and then back to the left platform again.  From the reference frame in which the water is moving the floating twin floats at the same velocity that the water is moving at.  From the reference frame in which the water is stationary, the floating twin is stationary and  the left platform moves away from and then back towards the floating twin.

Scenario 2A

Scenario 2B

Does the geometry of scenario 2 show absurdity in the pop special relativity idea of length contraction?

One might argue that is does show absurdity because the length of the material of water between the two platforms is shorter than the length of the material of ground or air between the two platforms with their connected frames in a way that is geometrically impossible.  One might counter argue that actually when the water is shrunk it is not only the water between the platform frames that is shrunk but also the water to the left of the left platform frame and to the right of the right platform frame resulting in the water to the left and the water to the right filling in the gaps.  The problem with this argument is it would change the travel distance from L0 * Alpha back to L0 in order to fix the geometric problem which would result in changing the travel time from L0 * Alpha / v to L0 / v which would negate the idea of the different clocks having different times displayed because of different travel times in different reference frames which is so core to pop special relativity that one might argue that it would negate or at least partially negate pop special relativity.

Length of objects, distance between objects and distance traveled are not the same thing.  Comparing and contrasting them in Newtonian Physics versus Special Relativity

I would suggest a different solution that there is no length contraction in reality but that the clocks display different times not because of different travel differences but because they are running at different reaction rates.  I would also like to point out that the distance traveled is not the same as the length of objects or the distance between objects.  

It is important to note that objects traveling different distances in different reference frames is not unique to special and general relativity but also occurs in Newtonian Physics.  However in Newtonian Physics the length of objects and the distance between objects is the same for all reference frames for the same event where as in pop special relativity it is not.  

For example in Newtonian Physics, if the distance between a runner and a race track start line, increases at a speed of v then from one reference frame the runner would not travel any distance at all but the start line would travel a distance of v*t  where as from a second reference frame the start line would not travel any distance at all but the runner would travel a distance of v*t and from a third reference frame they would both travel an equal distance of 0.5*v*t in opposite directions, but in all reference frames including the ones I have not listed, the distance between the object of the runner and the object of the start line would be equal to the same quantity of v*t which would not necessarily be the case in pop special relativity

Reaction rates and different displayed values on clocks

Actual Time

Actual time is a quantity related to the order of events and is not the same as the time displayed on clocks.  The time displayed on clocks is a way for people to estimate the actual time.  I am not claiming that the earth revolves around the sun in a perfect circle at a constant speed but I will pretend it does so from some frame of reference in which the sun is stationary to make things simpler to explain this concept.

Let's suppose there was an event called the start of a calendar in which people were to track how far the earth travels in that specific reference frame described above.  How far it traveled could be measured in terms of the length of the arc it traveled.  How far it traveled could alternatively be measured in terms of an angle that is equal to a constant times the length of the arc it traveled in divided by the radius of the circular path it travels in.  At the date of the event of the start of the calendar it will be said that it travels progressed a distance of 0 meters or 0 degrees.

The amount of actual time between the date of any event and the date of the start of the Calendar would be equal to a constant times the how far the earth travel has progressed as measured in that reference frame since the event of the start of the calendar.  

The actual time between any two events could be got by taking the actual time between each event and the date of the start of the Calendar and then subtracting each of those actual times from the other actual time.

Now in this case the change in actual time between any two events is equal to a constant times the distance a certain object traveled in a certain reference frame between those two events but this is only because the object is traveling at a constant speed in that reference frame, this is only theoretical and does not apply to real life clocks as real life clocks are designed to estimate that actual time but can not get the actual time correct.  

It would be a foolish mistake to assume the change in display time in flawed clocks between any two events is always the same as the change in the actual time between those two events.  If two people started different stopwatches at the start of the same event and stopped the stopwatch at the end of the same event, it would be absurd to assume a different amount of actual time passed for each person between the two events.  Now maybe they did not really start and or stop the stopwatches at the same time as each other, or maybe the stopwatches were flawed and although both estimated the actual time, the time they displayed was not a perfect representation of the actual time and they both had a different quantity of error.

| Theoretical Error | = | Display Time - Theoretical Actual Time |

I call this theoretical actual time since although I propose actual time exists we can not know it perfectly but only estimate it.  We might say one clock has a better estimate than another clock and sort of get an idea of the error of one clock compared to a better clock but we can not know the error between a clock and a perfect clock

Length, distance between objects and distance traveled are all different than time

Even though in the thought experiment example I gave I said that the change in actual time is equal to a constant times the change in a distance a specific object traveled in a specific reference frame, I am not claiming that time is a fourth spatial event, nor am I claiming that space is the same thing as time nor that time can be measured in terms of length nor that length can be measured in time nor that length and time have the same units.  They distance traveled needs to be multiplied by a constant because length is not the same as time and because length and time have different units.  Although length, distance between objects and distance traveled all have the same units they are different things as I already mentioned.

Actual Time and Order of Events.  The order of events in is the same in all reference frames but some reference frames describe some events differently.

If the actual time of each event was listed as measured relative to some other event such as a start of a calendar then the order of events always occurs such that events which occurred with a actual time that has a lower quantity always happen before events which occur with a actual time that has a higher quantity.  This should be so obvious and I should not even have to say or write it but in pop special relativity I will suggest some people have confused the display time with the actual time and allowed the order of events to be scrambled using phrases like non-simultaneous and even claimed that some events do not occur in one reference frame but occur in another reference frame.  I am not denying that some people might observe some events at different times but I am talking about when the events actually happen in each reference frame.

Academic study or back to the fiction

Movies like "back to the future" in my opinion seem to use the equations of pop special relativity that I would argue predict the change in the time displayed on clocks to claim you can travel back in time to the past or forward in time to the future by confusing the time displayed on clocks with the actual time.

I would suspect that most people even most medical students and medical doctors would actually prefer to watch a entertaining actor who plays a doctor on television who is not an actual doctor than listen to a actual medical doctor who is not an actor give a boring lecture about anatomy and biochemistry.  In the same way I would also suspect that most people even people with PhDs would rather watch a entertaining fiction show about time travel than do a boring study about how much the displayed time on one clocks changes compared to the display time on another clock between two events.  

Some of these people who claim to have PhDs in Physics also show up on actor profiles for fiction shows and I would suggest that even when they are supposed to be doing their non-fiction shows they maybe tempted to say what is more entertaining like they are in their fiction shows than to tell the boring truth.  I would also suspect that the line between fiction and non fiction has been blurred as many people go into science fields after being entertained by science fiction which may in some cases but not all cases cloud their judgment.

Many people just find it more fun to believe the predictions involve actual time and time travel occurs than to believe the equations involve predicting how wrong the value displayed on clocks is compared to the actual time and that there is no time travel involved.  Someone for example who was working on a physics bachelor degree and eventually graduated with a bachelor's degree in something told me that it is just more fun to believe in time travel so he wants to believe it.

I am not saying that it is wrong to be entertained by science fiction nor am I denying that science fiction may inspire people to do experiments that are scientifically sound but I am simply suggesting that some people in academic positions may have been inspired by science fiction to do work in their academic field in a way that is not scientifically sound.  Writing research proposals involving far fetched claims that are more entertaining but have less scientifically sound methodology might entertain third party individuals who grant the funding for research more than more scientifically sound experiments that are more boring.  

I am not saying that there is anything morally wrong with entertainment nor that entertainment reduces the quality of experiments but simply that a problem may occur when people sacrifice sound research and good ethics for entertainment and that I suspect that pop special relativity has more to do with what makes entertaining fiction than to do with what makes good physics.

But that is fiction not academics

If you watch a show that is labeled as educational and or non fiction about special or general relativity they often have people who are claimed to have actual PhDs in Physics or ( in a field with a different name that might be in the physics department in one university but a separate department or degree in another University )

When these people who are claimed to have PhDs are interviewed instead of saying the equations are not about traveling in time but about predicting the value displayed on clocks they spend a lot of time talking about time traveling paradoxes or how people might theoretically find a way to travel through time which I suspect the audience simply finds more entertaining.

I suspect that fiction on the media has influenced the general worldview of pop special relativity shared by many people more strongly than the history of physics experiments.

Describing something from a different perspective can not change the physical nature of an object. 

Changing what reference frames you describe an event in does not change the nature of the event, it can not change the length of objects during that event, it can not change the distance between objects during that event and it can not change the shape and size of objects during that event, it can not change any other physical property of objects during that event I have not listed,  it can only change how that event is described mathematically or how the physical properties of objects involved in the event are mathematically described as being during that event.  Describing two different events from a different perspective can not change the amount of actual time between those two events.  In fact describing an event from a different reference frame not only fails to change the actual time but does not even change the time displayed on a clock, because a clock is a physical object and the physical configuration of the clock that displays the time can not be changed simply because it is described from a different reference frame.

Progress

Each type of clock has a mechanism that is different.  Depending on the mechanism progress could for example mean how much sand is on the bottom of a hourglass, the position of a shadow on a sundial or the percent composition of an element involved in radiometric dating.  Progress could be the number of times light is emitted from a object and reflected off a mirror to return back to the same object in the thought experiment clocks of special relativity.  If a person counted the number of times the sun rose then progress could be the number of sunrises the person counted.

Physical or Chemical Reaction Rate and Display time reaction rate

Physical or Chemical Reaction rate is the rate that progress changes over actual time this could be for example how much volume of sand moves down a hour glass per actual time and in such a case the progress would be the volume of sand in a section of an hour glass.  Display time reaction rate is the rate at which the display time on the clock changes per actual time.  If the clock is undergoing a physical change then it is called physical reaction rate but if it is a chemical change then it is called a chemical reaction rate.

Notation on reaction rate equations that are listed next

 

A different function is used to to get display time from actual time than to get display time from progress so I wrote out the word function in entirety instead of f or two different letters because people might not associate another letter with meaning function

I might switch the phrases display time and time displayed on clock they mean the same thing but one sounds better than the other to me in different context or phrases

Display time reaction rate

Final Time displayed on clock - Initial Time displayed on clock = Change in Time displayed on clock

Change in Time displayed on clock = Display time reaction rate * Actual change in time

Display time reaction rate = d Time displayed on clock / d Actual time

Time displayed on clock = function ( Actual time )

Change in Time displayed on clock = function ( Initial Actual time ) - function ( Final Actual time )

Physical or Chemical reaction rate

Time displayed on clock = function ( progress )

Change in Time displayed on clock = function ( final progress ) - function ( initial progress )  

Final progress = Initial progress + Change in progress

Change in progress = Physical or Chemical reaction rate * Actual change in time

d Progress / d Actual time = Physical or Chemical reaction rate

What does reaction rate have to do with two clocks displaying different times in pop special relativity

I would suggest that the so called time dilation in pop special relativity is a result of the reaction rate on cesium atomic clocks changing when moving at different velocities relative to the source of the cosmic microwave background which is simply black body radiation from a fluid in the so called vacuum of outer space.  I would suggest that the radiation is maximized when the cesium atomic clock is stationary relative to this fluid which requires moving at a certain speed in a westward direction and going at a different speed results in more radiation.  

I would suggest that the multiplier of this radiation is exactly equal to the constant Alpha due to the equations for Doppler shifting for a source traveling perpendicular to a source of radiation being exactly equal to the constant Alpha in pop special relativity.  This answer is problematic because it ignores radiation from the fluid of the so called vacuum of outer space from other directions and other sources.  

This might be because the distance of air or the atmosphere that is at least a certain density or higher is longer vertically than horizontally.  If you take two circles each with a different radius but the same center and pick any point on the smaller circle and draw line segments that reach the other circle, different line segments will have different lengths giving reason to believe my claim about radiation having to travel through a longer distance through air of a certain density or greater horizontally than vertically.  The radiation from other directions might be so greatly reduced that it can be ignored.

I also find this answer problematic because it ignores radiation from the sun, from the ground and water on the earth and from man made sources of radiation.  I would suggest that the radiation from the cosmic microwave background happens to be measured close to the frequency involved with cesium in atomic clocks and so if it gives off more radiation in this specific range than other sources than it might influence it more.  

In addition to these other sources of radiation that I am ignoring there is the issue of B fields which might influence some clocks when they move relative to charges or sources of electricity which could also potentially change the reaction rate of clocks as a function of their velocity relative to certain objects.

Although I have not mathematically explained this I will explain this more in other chapters

Where did the idea of the length of objects changing in reference frames come from