"Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration ..." (Absolute Time and Space)Einstein's replaced classical time with relativistic time, in which, if there be two distant points A and B, there is no a-priori time relation between them.

We have so far defined only an "A time" and a "B time". We have not defined a common "time" for A and B, (On the Electrodynamics of Moving Bodies)This absolutely remarkable statement, which has since become universally accepted in scientific circles, has received very little philosophical analysis, except in one book that I could find in an old library, Harald Nordenson's Relativity, Time and Reality, a critique of the philosophical underpinnings of Einsteinian Relativity.

The book is unfortunately out of print, but I have scanned, compressed and uploaded the first two chapters which are the most pertinent.

I invite anyone deeply interested in physics, philosophy and the conception of time to point out the flaws, if any, in Nordenson's critique. I couldn't, and neither could I find any article, book, paper which did.

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Some more articles and links of interest:

http://www.wbabin.net/physics/marcus.htm

http://www.springerlink.com/index/T8295557N23TN44N.pdf

http://redshift.vif.com/JournalFiles/V15NO2PDF/V15N2MCC.PDF

www.eng.uwi.tt/depts/elec/staff/sgift/special_relativity.pdf

http://books.google.co.in/books?id=vuTXBPvswOwC

http://books.google.co.in/books?id=EY8KVI-05P0C

Another contributed link:

http://www.antidogma.ru/english/relbookeng.html

(Thanks to the anonymous contributor)

The entire website is topical:

http://www.antidogma.ru/

http://www.heretical.com/science/dingle1.html

http://cas.sunderland.ac.uk/webedit/allweb/news/Philosophy_of_Science/PIRT2004/PIRT%209%20(2).doc

http://www.iop.org/EJ/abstract/1751-8121/40/29/B01

(Thibault Damour, the well known Belgian astrophysicist gives a brief but incisive overview of the philosophical underpinnings of relativistic time--still not firm after a century).

From: http://en.wikipedia.org/wiki/Talk:Twin_paradox

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Some people get lost in the twin paradox presented here (with accelerations and all), so maybe a simpler, symmetrical paradox is in order. So, here is that "gedanken" experiment:

Let's have two identical rockets, carrying two identical high precision (in today's technology that would be atomic) clocks, with digital displays. The displays show the number of ticks (cycles) that each clock recorded (this could be for instance number of nanoseconds - a simple integer) since last reset. The rockets and clocks include a mechanism that fires the thrusters on detection of blue light and resets the clocks on detection of red light.

These two rockets are placed in space, away from any gravitational fields, so that they are pointed to one another, on a straight line. The rockets are far away from each other and we shall call the left one A and the right one B. Midway between rockets A and B we place a source of light we shall call S, capable of emitting blue or red light, each simultaneously to left and right, toward rockets A and B.

Rockets A and B, together with S form a single inertial frame of reference S for now (in other words, they are all stationary to one another).

Now we send blue light simultaneously from our source S toward rockets A and B. This starts the thrusters and the rockets burn their fuel, therefore being accelerated toward one another, on a collision course. The rockets burn all their fuel and each reaches constant velocity v in relation to our stationary frame of reference S, but in opposite direction. The speed at which the rockets are travelling is "normal" speed (i.e. not nearly close to the speed of light, but something a normal rocket could do).

After the burn is completed, we send red light simultaneously from our source S in the direction of rockets, therefore resetting the counters of our clocks. Now we have a system of three inertial reference frames, A - for rocket A, B - for rocket B and S - for our source of light S, in linear motion in relation to one another. And we have our clocks on rockets A and B synchronised, as observed from S.

Just before the collision occurs (i.e. when rockets A and B are in immediate vicinity of light source S) and if the trip of rockets is sufficiently long, we shall have the following situation in relation to clocks, as observed from different frames of reference, due to time dilation as per special theory of relativity:

* clock A displays N as observed from reference frame A

* clock A displays M (different from N) as observed from reference frame B

* clock A displays L (different from N and M) as observed from reference frame S

And due to symmetry of motion and identical construction of clocks:

* clock B displays N as observed from reference frame B

* clock B displays M (different from N) as observed from reference frame A

* clock B displays L (different from N and M) as observed from reference frame S

In comparison, such a system would show N on both clocks as observed from any frame of reference using only Newton's mechanics.

The conclusion of the experiment is wrong. At the point of collision, Both clock A and B will show the same number, according to SRT also. But both A and B will claim the clocks were not synchronized, as according to each, light took less time to reach the other because the other frame was moving towards the light source. So the other frame was reset (long) before this (applies to both A and B), but it still counts same number of ticks till the collision, supporting the hypothesis that "moving clocks run slow".

You can do the numbers, they will match exactly. I am also critic of RT and have tried many such paradoxes but these paradoxes no longer remain so when you put it in equations.

Which should be the case. If it were so easy to find inconsistencies in theory of relativity through simple thought experiments, someone would have done so long ago and gained the Nobel prize in the process. At least mathematically the theory is airtight.

Hi PhysicsDude,

This "twin paradox" is only of passing interest to me as my initial article refers to Nordenson's more fundamental critique.

But even in this paradox, isn't it remarkably strange that at the moment when all clocks are in close vicinity of each other (just prior to the collision), they are showing times which are paradoxical.

Because, from A's point of view:

Clock in A: N

Clock in B: M

From B's point of view:

Clock in A: M

Clock in B: N

From S's point of view:

Clock in A: L

Clock in B: L

(L, M, N are all different)

How can a clock's time change in close vicinity of three observers (all in different reference frames)?

I believe Srid's explanation is correct. A and B and S will see the same numbers on the dial, they will differ in the synchronizations of the dials, and hence the time that has elapsed between the events.

I think I see Sriram's point.

He is correctly saying, I believe, that the onset of inertia of A and B (when the red flash reaches each) is simultaneous wrt S, but is not simultaneous wrt A or B.

I would suggest caution.....

These things are very tricky to explain in layman's terms...... maths is its own language and translating it would without a solid grounding in that subject is almost impossible....

We can think about it and feel a little smarter about ourselves but thats about it....

Hi Harmanjit.I found the links at your http://harmanjit.googlepages.com/ have broken. Have you copied the articles there to this blog?

I am interested in spiritual subjects, like spiritual freedom.

Except AFT, what online resources do you recommend?

I read your article about Goenka's Vipassana and then came here.

Very nice to found your articles.

@kenneth

That website (harmanjit.googlepages.com) was just an experiment, and I only created a skeleton.

Regarding my recommendations for online reading, I enjoy many things, and the list of those feeds is displayed at the side of my blog.

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