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