### Re: how much time has passed for a photon since it was emitted

Date: Fri Jan 2 13:32:34 2004
Posted By: Guy Beadie, Staff, Optical sciences, Naval Research Lab
Area of science: Physics
ID: 1069201367.Ph
Message:
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‘Sorry if it’s dumb’?  No, there are no dumb questions.  Just dumb

Q: “So,how much time has passed for a photon emitted let's say 1000 years
ago, earth time?”

A: None.  Zero seconds.  A photon emitted 1000 years ago is just as ‘old’
as a photon emitted at the birth of the universe.

That, at least, is the standard story.  See:
http:
http:
http:
htt

I’ll give my interpretation of the answer, based on the following
postulate for the behavior of light: the speed of light measured in any
frame of reference is always the same – the speed of light.  In other
words, a photon will travel at the speed of light in no matter what
reference frame you view it.

Think about that.  It means that there is no reference frame in which
light isn’t traveling at the speed of light, and therefore no reference
frame in which one could look at how a photon ‘at rest’ experiences time.
You can imagine and calculate for inertial frames passing by at speeds
very close to the speed of light, but none AT the speed of light.  This
means that the question of how old a photon is in its ‘rest-frame’ is
meaningless: there is no such frame.

The stock answer of ‘zero’ comes from looking at the limiting behavior of
particles traveling at speeds that approach that of light.  The time
experienced by these particles when traveling over a fixed distance
becomes shorter and shorter until, if their speed is EXTRAPOLATED to c, it
becomes zero.

The postulate I quoted serves as a foundation of special relativity.  See:
http://ww
w2.corepower.com:8080/~relfaq/speed_of_light.html

This is part of a more comprehensive relativity FAQ:
http://www2.c
orepower.com:8080/~relfaq/relativity.html

If you want a very good written introduction to the subject, I highly
recommend “Spacetime Physics,” written by Edwin F. Taylor and John
0336-X.  It has much of the math, but far more importantly it has clear
explanations.

Q: “Or, just to put it another way, if I somehow manage to travel at
99.999999% of  the speed of light, would I be able to reach the edge of

A: Not quite, but you’ve got the idea – if the universe were static and
bounded.  This is the path you take to explore reference frames that
approach the speed of light.  Check out:
http://www.astronomycaf
They define a ‘warp factor’ such that ‘warp 2’ would be traveling 99% of
the speed of light, ‘warp 3’ traveling at 99.9% of the speed of light,
etc.  Your example is at warp 8.  At this speed you could travel a
distance of 7071 light years, as viewed by the earth, in just 1 year of
your time.  The center of our galaxy (according to the site) is 26,000
light years away, so you could get there in under four years.

The ‘edge’ of what we can see is supposed to be ~15 billion light years
out, so traveling at warp 8 isn’t going to get you there any time soon.
You can get there in 67 years of your time if you travel at ‘warp 17’,
while it will take only 2.4 days at ‘warp 25’.

More problematically, however, the universe isn’t static, nor necessarily
bounded.  The principles of special relativity hold only in the limit
of “inertial reference frames.”  When considering the universe, that
condition is violated.  I’m not an expert, so I’ll just mention a couple
of the issues that are relevant.

It’s an open question as to whether the universe will always be expanding
or whether it will start to contract, but if it’s always expanding then
some portions of space will always be just a little ahead of you.

Furthermore, a hazy memory of Hawking’s book “A Brief History of Time”
tells me that if you really were able to travel straight through the
universe you’d wind up right back where you started, so there isn’t really
an ‘edge’ of the universe to travel to.  Questions along these lines
should go to a cosmologist, and I certainly don’t claim to be one.

Q: “A friend (physics graduate) says something about the fact that even
objects standing still in the 3D space are actually traveling at the speed
of light on the time axis in a complex 4D space and then some other
stuff...”

A:  Your friend may be referring to the fact that an object sitting still
in space nonetheless has a trajectory in time.  It does.  That does not
mean, however, that it is traveling at the speed of light!  The proper
manner in which to describe the trajectory of an object, within the
confines of special relativity, is to include four values at each point:
three values for position (X,Y,Z) and a value for the time (T).
Trajectories are found by determining the path of these variables for a
single object moving through spacetime.  All the fun stuff in special
relativity comes from the fact that distances along these trajectories are
measured in a far different way than what you’d expect.  For more details,
see the earlier reference for special relativity:
http://www2.c
orepower.com:8080/~relfaq/relativity.html

Your friend may also have been trying to communicate some of the cosmology
issues I alluded to earlier: the universe isn’t sitting still, so even
light might not be able to travel fully throughout its extent.

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