Re: Does 'time' exhibit wave properties?

On 2005-08-20, RHNL <rhnl@xxxxxxxxxxxx> wrote:
> If gravity is a wave/particle, and 'time' is a function of it's definition,
> is 'time' also a wave/particle, or simply a synthetic, linear measure.
>
> If not so, does time radiate?

This is a perfect example of an ill posed question. Let me try to
explain why.

Gravity, as we see it around us, is a force. That is, every object has
an arrow attached to it that points in the direction that gravity wants
the object to go. That's how we explain why things fall. Going up one
level of sophistication, we might wonder what determines the direction
and magnitude of this force. Many very smart people have struggled with
this question, two of the most notable ones being Newton and Einstein.
The best theory we have to date is general relativity, which is
approximated by Newtonian gravity in most everyday situations. GR says
that at every point in space, we can define a quantity (or rather a
group of quantities collectively) labeled the metric tensor. It also
says that this metric tensor field obeys equations of motion that are,
in a sense, similar to those of electromagnetism. Similarly, the
equations of GR admit wave like solutions for the metric tensor.

Time, as wee commonly think, is measured by counting the number of ticks
of a clock, a wristwatch would do for example. Everyone can carry their
one watch, and compare the time readings from time to time. It turns
out that, even without tinkering with their watches, different people
get different readings on their clocks when compared, the difference
depends on where each person has been. Again, going up one level of
sophistication, we may wonder how much the time readings change
depending on the motion of different people between two comparisons. The
best answer to this question is again general relativity. GR says that
these differences can be calculated from the values of the metric
tensor.

At this point, one might be tempted to think that since the
gravitational force and time are both related to the metric tensor, that
they must be the same. However, this is a logical fallacy, relation does
not imply identity. I hope that the extent of the difference between
time and gravitational forces is clear from the above two paragraphs.

Now, let's talk about the wave/particle business. So far the discussion
has been purely classical. However, for more than a hundred years now,
people have been noticing that certain particles have wave-like
properties (electrons), while certain waves have particle-like
properties (high energy electromagnetic radiation, gamma rays). Again,
being seekers of sophistication, we ask why that is. The question has
also puzzled a great many people, and resulted in our best answer to
date being quantum mechanics. Once waves and particles are described
quantum mechanically, their respective particle-like and wave-like
properties appear naturally. As I mentioned above, in GR, the metric
tensor is a classical field that admits wave-like solutions known as
gravitational radiation. Logically extrapolating what we know from
quantum mechanics to gravitational radiation, we conclude that
high energy gravitational radiation must possess particle-like
properties.[1]

At this point, we might be tempted to ascribe these wave/particle
properties to the gravitational force and time, since they are both
related to the metric tensor. However, this is the same logical fallacy
as before. The wave/particle properties can be attributed to the
behavior of gravitational wave solutions to the metric tensor, once
quantum theory is taken into account. But as already discussed, neither
the gravitational force nor the measurements that we call time can be
identified with the metric tensor, and hence cannot inherit its
attributes.

To sum up. There is no answer to your question, since it does not make
sense. Similarly, there is no answer to the question "What color is the
speed of a car?".

A much more sensible question would be: Given that quantum theory
predicts wave/particle properties of gravitational radiation, how could
these properties be detected with measurements of time and gravitational
forces?

Hope this helps.

Igor

[1] Of course, there are problems with applying quantum mechanics to
gravity, but they go beyond the scope of this post. It is also worth
noting that the application of quantum mechanics to weak gravitational
radiation is not particularly controversial. However, neither the
classical nor the quantum form of gravitational radiation has been
directly observed.

.

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