MadSci Network: Physics

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

‘Sorry if it’s dumb’?  No, there are no dumb questions.  Just dumb 
answers.  And I fear I’m about to give you some!

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:
but I admit I find that answer very unsatisfactory.

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:

This is part of a more comprehensive relativity FAQ:

If you want a very good written introduction to the subject, I highly 
recommend “Spacetime Physics,” written by Edwin F. Taylor and John 
Archibald Wheeler, published by W. H. Freeman and Company, ISBN 0-7167-
0336-X.  It has much of the math, but far more importantly it has clear 

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 
the universe during my  lifetime?”

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:
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 

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:

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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