Twin Paradox Part 1 - Confusion and Embarassment

Whoever is aware of the Special Relativity developed by Albert #Einstein must have heard about the famous "Twin Paradox" ( #TwinParadox ). This is not what contemporary physicists are concerned about nowadays, but educators, general public and philosophers are still actively discussing it. Mainstream science considers it a "no-paradox" as it is believed to have been adequately explained.

For me it is a big mess that scientists would not like to get involved with. In order to begin with some discussion on the paradox, I should present what the definition of the paradox is. And that is where the mess begins...

1. Definition Inconsistency

Typing on Google "twin paradox definition" on 26/07/2014 that is 109 years after Special Relativity was born, we get thousands of pages and the following prominently displayed definition:

twin paradox - noun - PHYSICS: the apparent paradox arising from relativity theory that if one of a pair of twins makes a long journey at near the speed of light and then returns, he or she will have aged less than the twin who remains behind.

Without going into details now, please take my word for it - it's wrong because it is incomplete.

If so, then why does the main search engine on the Internet choose the wrong definition? Computer/human error perhaps. Embarrassing but errors do happen.
Asking Yahoo search engine we have no preferred definition but the usual list of relevant web pages. In the first one, from dictionary.com we get:

twin paradox - noun: a phenomenon predicted by relativity. One of a pair of identical twins is supposed to live normally in an inertial system whilst the other is accelerated to a high speed in a spaceship, travels for a long time, and finally returns to rest beside his twin. The travelled twin will be found to be younger than his brother

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollinsPublishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

Not much different than the previous one. Oxford online dictionary and many others say more or less the same. Well, people who write dictionaries are not experts in physics. They likely describe what the term means to general public in which case general public is wrong, but this is not of concern to linguists. But why would it be that the public is so wrong? Where does it get the ideas from?

I have consulted an authority on physics and time who is also educating the public in his popular bestsellers: Stephen Hawking in his book A Brief History of Time "sold more than 10 million copies in twenty years [...] on the London Sunday Times best-seller list for more than four years and [..] translated into 35 languages by 2001.[1]. 
And this is what the book says about the paradox in the context of a discussion of the significant difference in age of some twins when... 

[...] one of the twins went for along trip in a spaceship at nearly the speed of light. 

When he returned, he would be much younger than the one who stayed on Earth. This is known as the twin paradox, but it is a paradox only if one has the idea of absolute time at the back of one's mind.[2]

I am not surprised now that popular "definitions" are like those shown above. Stephen Hawking presented the paradox incorrectly. He simply glossed over the most important issue that is not touched at all in the quoted paragraphs. Just differential aging alone of some initially identical objects is not paradoxical at all as it can be demonstrated by using refrigerators. No logical problem whatsoever seeing two twin plants in a different stage of their development when one has been kept in cold and the other in full sun.

I have checked Bing, Encyclopedia Britanica and Wikipedia on line resources and all appear to extract or define the paradox in a different way. In Wikipedia[3] we read:

In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as moving, and so, according to an incorrect naive application of time dilation and the principle of relativity, each should paradoxically find the other to have aged more slowly.

2. Correct Definition

Britanica and Wikipedia definition shown above are the correct definitions. How do I know this?

The paradox has been famously introduced to public domain by Langevin[4] and independently analysed at length by Einstein himself [5], although he did not use twins but focused on clock indications rather than referring to human characters hence this paradox is also known as the "clock paradox".

The nature of the twin paradox is not differential aging but  the claims made in the name of Special Relativity that each of any two systems moving relative to each other may calculate that the partner is aging slower and therefore it is younger. But this is impossible for one system to be younger and older at the same moment.

Many respectable sources then spread misinformation to millions of people. This is a big problem and some might see it as a conspiracy. I see it just as as negligence. 
Dictionaries explain the  meaning of an expression as understood by the English speaking population, not scrutinising the physical accuracy. 
For the origin of Stephen Hawking's error, only he can answer. 
Frighteningly inaccurate is the reference to twin paradox by an online entry originated from New Scientist website[6] which so far I valued for it's high standards. They repeat the same Hawking's truncated - that is incorrect - explanation and refer to The Open University as the source. The very first comment at the very bottom of the comment stack highlights this a follows:

Steve Walker on January 13, 2012 4:50 PM What this doesn't cover is the paradox element. The video says that Bert will come back younger. But look at the problem from Bert's point of view. He has seen Al disappear at near light speed, so then it's *Al's* clock which runs slower. Viewed from Bert's point of view (everything's relative, remember) then Al will be younger when Bert gets back.
That's the paradox: one of them will be younger by the end of the exercise - but which one?

Two years later no one has reacted to the comment and misinformation spreads.

So before we have even started discussing the problem we find a possibly nontrivial obstacle:

Many people discussing the twin paradox or time may not have an idea what are they talking about.

To be continued...

[1]http://en.wikipedia.org/wiki/Brief_history_of_time
[2] Hawking S., A Brief History of Time, Bantam Books London 1998
[3]http://en.wikipedia.org/wiki/Twin_paradox
[4] P.Langevin, Scientia 10 31 (1911).
[5] Einstein A., Dialogue about Objections to the Theory of Relativity Die Naturwissenschaften 6(1918): p 697-702. English Translation in The collected Papers of Albert Einstein vol 7 p 66 Princeton University Press 
[6] http://www.newscientist.com/blogs/nstv/2012/01/physics-in-a-minute-the-twin-paradox.html#.U9LzzHazjZg.blogger

The Perception of Time

To understand time I have to understand my own perception of it first. 

The perception of time does not start with the clock. Firstly I am aware of myself, secondly I am aware of the immediate environment, then I perceive a change through senses. The change comes to my attention by becoming aware of a difference between the current sensation and the memory of this sensation being absent or by remembering other characteristics of it (No pain then pain, or less pain, more pain). In the normal state of mind I distinguish between current and not current, so the primary perception of time is Now and the Past. There is no immediate need to realise the Future. The sense of the future comes late in brain development and according to evidence available to G.J Whitrow[1], animals do not perceive the future. Contemporary adult human has a well developed concept of Now, the Past and the Future, and can cognitively time travel back and forth. Significant part of awareness can be a-temporal, such as a mental process elaborating some logical problems related to coexisting concepts, for example while performing an arithmetical operation in memory.

Apart from the ability of remembering facts and things, human memory is also capable of recording the order of events. Events are sensed changes of state in memory believed to be the representation of some real world changes of a state. The necessary ingredients in the perception of time are:

1. A perceiving process in human brain or in a computer.
2. State memory being continuously updated from sensor sources by the perceiving process.
3. Algorithms ordering and retrieving information from sensors and long term memory.
4. Ability to see different states in memory and ordering them  successively as they appear.

Ingredients 1-3 are natural properties of human mind or a computer system, ingredient 4 is the ability which equates to an elementary perception of time in terms of "before" and "after". The ordering and memory allow counting reoccurring events which can be a measure of duration, which is one of the faces of time.  Apart from immediate real time sensation of events appearing in order, the stored information allows off-line reasoning about the order of events and hence about the passage of time.
What it has been said above is nothing new. Aristotle in his Physics[2]  (350 BC) says:

• But neither does time exist without change; for when the state of our own minds does not change at all, or we have not noticed its changing, we do not realize that time has elapsed [...] On the other hand, when we do perceive a ‘before’ and an ‘after’, then we say that there is time. For time is just this — number of motion in respect of ‘before’ and ‘after’.

Physically significant are events pertaining to physical objects coming to existence or becoming present in my field of observation. A glass mirror broken brings to existence a number of irregular pieces and such sequence perceived by me is a physically significant and unique change that can be said to occur in time in a particular order. The memory of the real change is retained even if some subsequent process disintegrates glass pieces into dust. We should examine later if such apparently unique order can be linked to the concept of time used in theory of relativity, and would it be relative to any observer to a degree that it can even be reversed.

At this point I conclude that my innate perception of time gives me the capability of ordering events in terms of "before" and "after" as well as enables primitive measure of duration by counting reoccurring events recorded in memory. In that context it appears that those two capabilities can be related to time defined either by Newton or the theory of relativity and there is nothing subjective or mystical in those capabilities. There is limited precision problem but it can be eliminated with adequate choice of time scales used in experiments with reality. Therefore I believe that this common sense perception of time can be validly used in reasoning in the context of relativity and time reversal discussions.

Having said that I immediately recall inspirational thoughts on time written by Ernst Mach in 1883 in his book "The Science of Mechanics"[3]

• When we say a thing A changes with the time, we mean simply that the conditions that determine a thing A depend on the conditions that determine another thing B, The vibrations of a pendulum take place in time when its excursion depends on the position of the earth. Since, however, in the observation of the pendulum, we are not under the necessity of taking into account its dependence on the position of the earth, but may compare it with any other thing (the conditions of which of course also depend on the position of the earth), the illusory notion easily arises that all the things with which we compare it are unessential. Nay, we may, in attending to the motion of a pendulum, neglect entirely other external things, and find that for every position of it our thoughts and sensations are different. 
• Time, accordingly, appears to be some particular and independent thing, on the progress of which the position of the pendulum depends, while the things that we resort to for comparison and choose at random appear to play a wholly collateral part. But we must not forget that all things in the world are connected with one another and depend on one another, and that we ourselves and all our thoughts are also a part of the nature. It is utterly beyond our power to measure the changes of things by time. Quite the contrary, time is an abstraction, at which we arrive by means of the changes of things ; made because we are not restricted to any one definite measure, all being interconnected.[...]
• We arrive at the idea of time, — to express it briefly and popularly, — by the connection of that which contained in the province of our memory with that which is contained in the province of our sense-perception. When we say that time flows on in a definite direction or sense, we mean that physical events generally (and therefore also physiological events) take place only in a definite sense.

[1]Whitrow G.G, Time In HistoryOxford University Press 1989
[2]Aristotle, Physics, Grece 350 BC
[3]Mach E. The Science of Mechanics Chicago The Open Court Publishing Company London 1901
     http://ia600406.us.archive.org/35/items/sciencemechanic00machgoog/sciencemechanic00machgoog.pdf

Why Am I Writing This...

While looking into the sky I have two kinds of reflections. One is the awareness of the enormous size and complexity of the universe, the other is quite the opposite. The feeling of knowing it all at once, the sense of togetherness that permeates all boundaries. Even the most sophisticated theory of the universe has to create a simple picture of it  that holds together in my mind. It all has to be expressible by common language in a logical manner no matter how abstract mathematical ideas hide behind the full explanation of the physical phenomena. Surely the elements of simple explanation have to be accepted by faith in underlying mathematical content. 

The reason for starting this blog was to explore the role of the common sense and logic in understanding the world around us. Modern science generally provides excellent description of reality and we see the effect of it every day. There are a few areas where science becomes controversial and one of those areas is Time.

As previously mentioned, there are claims resulting from Einstein theories which allow time travel. Relativity of time leads to paradoxes which are hard to explain. General picture emerges according to Einstein and his followers that: "Common sense is the collection of prejudices acquired by age eighteen"[1]. This is only because the properties of time after Einstein defy the common sense, while experimental evidence confirms predictions of Relativity Theory.

The common sense appears to be so bad when it comes to time that science educators invest serious resources do develop new methods to retrain the brains in order to fix innate human temporal logic to accept relativity of simultaneity. Scherr, Shaffer, and Vokos[2] report serious cognitive problems among students learning relativity - problems of a kind unheard of in other areas of science: 

"Excerpts from taped interviews and classroom interactions help illustrate the intense cognitive conflict that students encounter as they are led to confront the incompatibility of their deeply held beliefs about simultaneity with the results of special relativity".

Common sense is a basic ability to perceive, understand, and judge things, which is shared by ("common to") nearly all people, and can be reasonably expected of nearly all people without any need for debate [4]

Common sense reasoning is not much different than strict scientific reasoning. The difference lies in the level of knowledge, precision of available data. The rules of logic are the same. No statement about reality from the common sense perspective should contradict scientific view of the same unless the knowledge of fact is incomplete or incorrect or reasoning is simply flawed by human error. Common sense so criticised after Einstein is in fact the very foundation of relativity. One of the important rationale behind  was an assumption that the laws of physics should at least be the same on two systems moving relatively with constant speed. That is the main postulate of Relativity Theory as presented by Einstein[5]: 

"If,relative to K, K1 is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to K1 according to exactly the same general laws as with respect to K. This statement is called the principle of relativity (in the restricted sense)"

Common sense reasoning about time comes from direct experience. If somebody claims common sense reasoning about time is wrong, then there should be scientific proof to show where the error is.

After conducting my own study, the preliminary results presented there [3] let me to believe that the common sense in its temporal aspect is not bad at all. It appears there is a serious failure in scientific approach to understand the properties of time defined and used in Relativity Theory in the context of time perception in humans. As much as there is no need to question the Theory of Relativity, there is a reason to question interpretation of time as defined by Einstein in relation to time perceived by us and the temporal logic we use. Hopefully in the subsequent posts it will become clear that we do not need to re-train our brains to absorb new temporal logic as the one we posses is still adequate.

[1] http://www.brainyquote.com/quotes/quotes/a/alberteins125365.html#vr9WBSUQjpT0ohmr.99

[2] http://www.aapt.org/doorway/TGRU/articles/Vokos-Simultaneity.pdf

[3] A Study on Invariance of Temporal_Coincidence

[4] http://en.wikipedia.org/wiki/Common_sense
[5]A.Einstein, Relativity: The Special and General Theory (1916)

Many Faces of Time

Time has many different faces. One word, multiple meanings. Merriam-Webster on line dictionary[1] describes above 20 different flavours of the word "time". The most popular understanding is: "the thing that is measured as seconds, minutes, hours, days, years, etc" which is more like Newton's measure of duration.

A different use of word time is to express multiplicity of occurrences.You can do things once, twice, but not trice. It has to be three times. Not all languages have this association of time and multiplicity. In Slavic languages the word "raz" means more or less a unity and it is used in combination with a number from 2 onwards. It looks like it was once more obvious for some ancestors to associate multiplicity with repetition of events occurring in time rather then with a number of objects of the same kind.

My particular interest in time is: "The continued progress of existence as affecting people and things"[2]. This goes beyond a simple measure. This is the space for events to happen and the mode of our existence in which we also perceive existence of things other than ourselves, unless this is all one big illusion.

For a physicist time is a variable t and numbers that can be assigned to it. Experimentally, that would correspond to some clock indication as per Einstein's definition. It is interesting, how does then t relate to the progress of existence?

Finally time despite its operational definition given by Einstein is postulated to exist beyond clocks in the form of space-time continuum. So in my view then clocks as devices must be affected by the flow of local time. I do not like the concept of flow of time, in particular time that is a driving force of the clock, in the same way I would not like to say that inertial motion can sustain only due to a force.

The progress of existence like life of everyone of us appears to be in one direction only while other things progress in repetitive cycles such as grandfather's mechanical watch or a toy train on closed loop tracks. This is of course a simplistic view as none of the cycles can be exactly the same. There is always at least a tiny disturbance that makes each cycle different from the previous one. 

The irreversibility of physical processes made British astronomer Arthur Eddington creating the concept of "the arrow of time"[3]. The term is now widely used. Why time has to have an arrow or a direction? 

This is a convention by which we allow clocks to increase the number of second minutes etc. in an increasing order. We could equally build the clocks that count down rather than up and the world would not be any different. There is nothing unique about that. The direction is arbitrary yet some believe it may change.

If one recalls Newton's definition of time, it flows (where?,when?)  and the flow has to have a direction. 

The question is, where is time? Is that direction the same everywhere? Is it changing with distance,speed,gravity?  Arrows shot from the bow generally don't change direction but they could turn around with gusts of wind. Can time do the same?

I am highly skeptical about the time arrow concept because time that is poorly defined in science appears to be made responsible for the direction of physical processes while each process generally is directed due to initial conditions and continues in a direction due to some form of force or inertia.

The questions whether time travel is possible and whether spontaneous processes can revert their direction is not yet answered by science although such claims are frequently made.  At least that gives us some space for discussions.

[1]"Time." Merriam-Webster.com. Merriam-Webster, 6 July 2014. http://www.merriam-webster.com/dictionary/time

[2]"Time." www.oxforddictionaries.com. 6 July 2014.http://www.oxforddictionaries.com/definition/english/time

[3]http://en.wikipedia.org/wiki/Arrow_of_time

Does Time Exist?

 

This is a multi-billion dollar question. How can it not exist if there is a name for it?

Salvador Dali

OK, so ghosts, tooth fairies, Santa Claus exist too.

The tooth fairy, as drawn by a five-year-old girl from Illinois.

Now my favourite traffic analogy: Traffic does exist but we cannot put our hand on it. If we do we are hit by a car not by a traffic.
The idea that time may not be an existing entity is not new. Before 55 BC Lucretius in his work De Rerum Natura [1] wrote:

• "...time exists not of itself; but sense reads out of things what happened long ago,what presses now, and what shall follow after:No man, we must admit, feels time itself, disjoined from motion and repose of things".

I tend to think that the most important thing in making the concept of existence less ambiguous is to assign the existence an attribute that is a degree of independence. People exist independently because you can select an individual and isolate him/her from all the others. Love also exists but not without people in love. So when we want to answer the question whether time exists, we have to agree on a definition and then assess the level of independence from other entities based on this definition. The problem is, there are many definitions. The most relevant to science which I am mostly concerned with will be definitions given by Newton and Einstein.

Newton [2]:

• Hitherto I have laid down the definitions of such words as are less known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place, and motion, as being well known to all. Only I must observe, that the common people conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.
• Absolute, true, and mathematical time, of itself, and from its own nature, flows equably without relation to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

Newton clearly emphasises independence of mathematical time as an essential attribute of it's existence.
How did he manage to see time flowing? Answer: It is a definition so it cannot be questioned unless it leads to contradictions.
Einstein's Definition of time [3]:

• Strictly speaking, it would be more correct to define simultaneity first,somewhat as follows: two events taking place at the points A and B of the system K are simultaneous if they appear at the same instant when observed from the middle point, M, of the interval AB. 
• Time is then defined as the ensemble of the indications of similar clocks, at rest relatively to K, which register the same simultaneously.

The difference between two definitions is striking. Einstein's time is the concept entirely dependent on clocks capable of indicating it. Exactly like love is dependent on people, but far less romantic...

To determine whether time exists we have a difficult choice. We either accept Newton's definition which has been discredited by the official science, or the one given by Einstein, which is currently approved by consensus. Such defined time has no independent existence though - just like traffic and love.
The choice is yours :)

[1] Lucretetius T., De Rerum Natura, Book 1 http://www.gutenberg.org/cache/epub/785/pg785.txt
[2] Scholium to the Definitions in Philosophiae Naturalis Principia Mathematica, Bk. 1 (1689); trans. Andrew Motte (1729), rev. Florian Cajori, Berkeley: University of California Press, 1934. pp. 6-12. as published in http://plato.stanford.edu/entries/newton-stm/scholium.html
[3] A. Einstein,  "The Meaning of Relativity" Four lectures delivered at Princeton University, May, 1921, PRINCETON
PRINCETON UNIVERSITY PRESS 1923 as published in http://www.gutenberg.org/files/36276/36276-pdf.pdf

Simultaneous or Not ...

The most puzzling issues that have emerged after Einstein's Special Relativity Theory (SRT) are 

• Speed affects time of the object in motion
• Simultaneous events for one observer are not simultaneous for the observer that is in motion relatively to the first one.

Speed affecting time i.e. the age of an object is not logically incomprehensible as we can see on example of two identical plants one in the sunlight, and another one in a refrigerator. Under different physical conditions their biological age will be different after a while.

The second issue defies common sense (whatever that is) as two things happening at once at distant locations from the point of view of observer 1 can happen in succession for the observer 2. Such possibility is called the relativity of simultaneity.

I have analysed this problem and published results in a draft article "A Study on Invariance of Temporal Coincidence". The conclusion is that relative simultaneity is only an apparent effect of a particular clock synchronisation required by the framework of the STR. 

Follow me on Academia.edu, Follow me on ResearchGate

In rough terms this is a similar situation when simultaneous distant events: one in Time Square in NY and one in Times Square Sunnybank, Brisbane Australia are identified by their local clocks. Because there is different time recorded from the clocks in each place it does not mean events are not simultaneous as the clocks have been synchronised according to respective time zones.

The Longest Journey Starts With Just One Step

After life time in the hiding I have decided to confront the public with my views on time and time travel. Everyone brags about almost anything on the net so why not me.

There is a continuous influx of opinions that time travel is a reality. I love the science fiction in this context, and "Back to the Future" is my favourite movie so is "The Time Machine", however I believe that entertainment should meet science only in the media such as it does in "Big Bang Theory". 

Scientific publication should be fiction free.

In the subsequent posts I will try to explore the subject from many different angles and hopefully in an interesting way so help me Einstein and Rollex :)