## Thursday, April 15, 2010

### The measurement of time and the age of the world

The second half of Poincaré’s essay ‘The measure of time’ is the more famous because of its connection with special relativity. But I will concentrate here on the first half, where Poincaré begins with the problem that we do not and cannot have a direct intuition of the equality of successive time intervals (equality of duration of successive processes). This is not a psychological point. Two successive periods of a clock cannot be compared by placing them temporally side by side, that is why direct perception can’t verify whether they lasted equally long, Bas Van Fraassen, Scientific Representation (Oxford 2008), 130.

In the case of two sticks we can check to see whether they are equally long (at a given time) by placing them side by side; that is we can check spatial congruence (at that time) by an operation that effects spatial coincidence (at that time). We can check whether two clocks run in synchrony during a certain interval if we place them in spatial coincidence. These procedures do not suffice for checking whether two sticks distant from each other in time or space are of equal length, nor whether distant clocks are running in tandem, nor whether a clock’s rate in one time interval is the same as some clock’s rate in a disjoint time interval. But in physics, criteria for spatial and temporal congruence are needed. Poincaré is concentrating on this need, ibid. 130-31.

What measures duration is a clock, and physics needs a type or class of processes that will play the role of standard clocks. What type or class to choose? One answer might be: the ones that really measure time, that is, mark out equal intervals for processes that really take equally long. While certain philosophers or scientists might count his demand as intelligible, it must be admitted that there could be no experimental test to check on it. We cannot compare two successive processes with respect to duration except with a clock; but clocks present successive processes that are meant to be equal in duration. This is similar to Mach’s point about thermometry: whether the melting of ice always happens at the same temperature, or the volume of a substance expands in proportion to temperature increase, can be checked only with something functioning as a thermometer–and thus cannot be ascertained in order to check whether thermometers are ‘mirroring’ temperature, ibid. 131.

Poincaré wishes to reveal by these examples two problems that arise in developing a measurement procedure for duration. The first is the initial one, illustrated with the pendulum: we cannot place successive processes side by side so as to check whether their endpoints coincide in time. So there is no independent means for checking whether successive stages of a single process are of equal duration: the question makes sense only after we have accepted one such process as ‘running evenly,’ ibid. 132.

#### 1 comment:

1. Interesting. I've thought similarly with regard to producing empirical evidence. I developed a theoretical machine as a thought experiment that it might actually be possible to fabricate. A few years ago while accompanying one of my kids on an amusement park ride, I noticed how the machines were geared and produced whirling cars attached to whirling carriages attached to a larger whirling device. The relative velocity of each car through the central movements of the carriages was nil, but very high relative velocities were achieved between a car from one primary carriage to a car from an adjoining primary carriage, although secondary, tertiary, etc., carriages could be added. With each additional carriage, the relative velocity between such cars would increase exponentially. The size of each carriage and car would decrease with each additional step. As the relative velocity between cars would be engineered to approach the speed of light, laser emitters and receptors could be included between cars to register the moment each passed compared to a benchmark of predicted time index from the centermost movement to the primary carriage given its similar distance from the cars allowing for the elimination of discrepancies due to the time it takes for information to travel to a central location. The apparent paradox of time dilation should be observable at varying velocities. The question I would have is that if such a machine were possible, what form would resistance take to prevent the machine from exceeding the speed of light between cars?

I have also wondered if some residual effects of the extreme time dilation in the universe that would have be prevalent at the creation would have any residual effect and observed with wonder that a probe having accomplished a few planetary fly-bys was noted to have reported a slower than expected departure from the solar system. Could it be related? Could black matter and even red sift (physics can be such a colorful science) simply be accounted for by residual time dilation from the creation? Who knows.