Expert: Philip Stahl - 12/25/2004

Question
I thought about the light we see from stars and many stars it takes millions and some billions of light years for the light to reach earth and we get an age of the universe from seeing  this light but isn't that misconcieving considering theory of relativity for the light it didn't take this long. At light speed time stays still so for the light it didn't take any time to reach the earth. So from this view it seems the age of the universe is wrong. It's like the subatomic particles, like muons that are going near light speed in the atmosphere that reach earth. In the lab they disengrate in seconds, yet they reach the ground from the atmosphere  because of relativistic effects. Wouldn't the same be true about light.

Answer
Hello.

There are several problems with your assumptions:

i)Light lacks mass, so is not subject to the (special) relativistic reformulations placed upon mass-particles such as muons. That includes time dilation effects. (Time measured in reference frame of traveling object much less than stationary object or observer)

Thus, light travels at velocity c = 186,000 miles/sec and sustains that in a vacuum. It also sustains that velocity relative to any other bodies in space- a property which we call “the constancy of the speed of light”.

Einstein formulated this proposition as follows:

THE SPEED OF LIGHT IS ALWAYS FOUND TO HAVE THE SAME VALUE, NO MATTER WHAT THE MOTION OF THE SOURCE OR THE OBSERVER.

To put this in concrete terms: If you are traveling in a rocket ship that's going 100 miles per second, and you send out a beam of light from your ship – the speed of that beam of light remains at: c

NOT c + 100!

Or (c – 100) if sent in the reverse direction.

ii)Light traveling across the vacuum of space doesn't mean time “stands still”.  Rather, light propagating takes time (governed by the value of c) to reach anyone in another part of the universe, once it leaves a light source.

Example: we observe the star Alpha Centauri which is 4.3 light years distant. This means that its light has taken 4.3 YEARS to reach our eyes. This is 4.3 years whether measured from our frame of reference, or from the light waves - which as I said undergo NO time constriction effects. (Assuming it doesn't pass any massive, gravitating bodies!)

At any given moment you look at this star, therefore, you are not seeing it as it is at the instant of your watch- but as it was 4.3 years ago (e.g. if you observed tonight, you'd see it as it was in the latter part of 1999)

If you look at the galaxy of Andromeda (M-31) which is 2.2 million light years away, you are seeing it as it was 2.2. MILLION YEARS AGO, not as it is this instant.

Thus, there is NO way you can observe a celestial object and see its light at this instant- though it may seem that way. The reason is that the light from any of these objects can still travel no faster than c, or 186,000 miles a second.

Even the light from the Sun takes the time it takes to travel 93 million miles across space. Or – about 8.3 minutes! Thus any light or radiant energy you feel or see from the Sun is already 8.3 minutes old by the time you feel it!

iii) Measuring the age of the universe, is not as simple a matter – however- of noting the time taken for the light of its most distant objects (say quasars) to reach us

This is because another phenomenon enters, which we refer to as the “expansion of the universe”.

In expansion, the light (as spectral lines) from a distant object – say quasar – is shifted by some amount, we call it z. The shift is caused by the source (object) receding from us, the speed of recession corresponding to the shift.

The speed of recession v = cz

where z denotes the shift of the light (spectral lines) for the object, and c = speed of light as before.

For example, if z = 0.3 for some object, then:

v = 0.3 c

In other words, the object is moving away from us at a speed of three-tenths the velocity of light.

we can also write, more generally:

v = H D

where H is “Hubble's constant” and D is the distance of the object.

Generally, what we do is to plot a graph of v (velocity of recession) against D (distance) for a variety of distant objects with differing red shifts, z:




v
^
!
!
!
!
!
!
!----------------------------------> D


The graph (not shown above) will be a diagonal straight line up and to the right, and the slope or gradient of the line yields H:

E.g.  H  = (v2 – v1)/ (D2 – D1)  = slope of line


The Hubble constant H also sets the age for the universe. (Provided we assume the expansion rate for the universe is constant)

That is:

T (age) = 1/H

the reciprocal of the Hubble constant. (The mathematical details are a bit excessive to go into here, but if you request them in a follow-up question, I can show how it is obtained).


As you can see from the above, finding the age of the universe is not as straightforward as you had believed.