Time Dilation: 10.5B Years at Light Speed?

[BobbyTMS]

If the light from the farthest stars that we can see have traveled at the speed of light for 10.5 billion years to reach us, wouldn’t the star or anything around it at the time the light left it be much older than the 10.5 billion years it took to travel to us? From what I have read, 1 year at close to the speed of light is equal to 3.9 here on Earth. So, if the light has traveled for 10.5 billion years at the speed of light, then is it fair to say, whatever matter existed at its place of origin when it left 10.5 billion years ago has aged 10.5 billion x 3.9, making it 40.9 billion years old?

thanks for any help

 

[JesseM]

If a clock is moving at 0.966568c (c is the speed of light) relative to us, then we will measure it to be slowed down by a factor of 3.9. In general, if a clock is moving at speed v relative to us, we will measure it to be slowed down by a factor of $$\frac{1}{\sqrt{1 - v^2 / c^2 }}$$. However, you've got it backwards--if something has been slowed down by a factor of 3.9 in our frame, that means that in 10.5 billion years of our time it would have aged by less than 10.5 billion years, i.e. 10.5 billion / 3.9 = 2.7 years.

But all of these numbers are based on the coordinate systems of the "special" theory of relativity which ignores gravity, as opposed to the "general" theory which says that gravity is caused by the curvature of spacetime, and that the gravity of the entire universe can be thought of as causing space itself to expand. In general relativity you can use a cosmological coordinate system where all the galaxies are aging at the same rate even though they are moving apart thanks to the expansion of space. For more information you might go here:

http://www.sciam.com/article.cfm?articleID=0009F0CA-C523-1213-852383414B7F0147

Ned Wright's cosmology tutorial

And for an introduction to general relativity, this site is pretty good.

 

[andrewj]

can the speed of light slow down over time

 

[mathman]

can the speed of light slow down over time

Currently there is no evidence for this. However, it is a possibility - astrophysicists are looking at it

 

[russ_watters]

If a clock is moving at 0.966568c (c is the speed of light) relative to us, then we will measure it to be slowed down by a factor of 3.9...

...but light is not a clock and doesn't 'experience time', so 10.5 billion light years is just 10.5 billion years at the speed of light.

 

[rbj]

can the speed of light slow down over time

Currently there is no evidence for this. However, it is a possibility - astrophysicists are looking at it

there is serious dispute about not only the possibility of it, but about the meaningfulness of it.

Duff: Comment on time-variation of fundamental constants and Duff, Okun, and Veneziano: Trialogue on the number of fundamental constants (The operationally indistinguishable world of Mr. Tompkins)

and here is what John Barrow said about it (The Constants of Nature: From Alpha to Omega, the numbers that the deepest secrets of the Universe):

[An] important lesson we learn from the way that pure numbers like $\alpha$ define the world is what it really means for worlds to be different. The pure number we call the fine structure constant and denote by $\alpha$ is a combination of the electron charge, e, the speed of light, c, and Planck's constant, h. At first we might be tempted to think that a world in which the speed of light was slower would be a different world. But this would be a mistake. If c, h, and e were all changed so that the values they have in metric (or any other) units were different when we looked them up in our tables of physical constants, but the value of $\alpha$ remained the same, this new world would be ''observationally indistinguishable'' from our world. The only thing that counts in the definition of worlds are the values of the dimensionless constants of Nature. If all masses were doubled in value [including the Planck mass m_P ] you cannot tell because all the pure numbers defined by the ratios of any pair of masses are unchanged.

really, if all of the dimensionless universal parameters remain unchanged, what possible meaning could it be if c or G or some other dimensionful parameter changed? how would it be measured? what would be different (from our observation)? how would we know?

 

[JesseM]

...but light a clock and doesn't 'experience time', so 10.5 billion light years is just 10.5 billion years at the speed of light.

The first part of your sentence is confusing, what do you mean by "light a clock and doesn't experience time"? If you just meant to say that light itself doesn't experience time (rather than talking about a light clock or something), I suppose this is true, but I thought the question was about how much the galaxy that emitted the light would have aged--looking back I may have misunderstood, I guess I was imagining that the OP was asking about the galaxies aging less because they are moving quickly relative to us as shown by redshift, but perhaps the post was actually talking about how much the light itself has aged, which doesn't really make sense since the proper time between events on a light beam's worldline is always 0.

To help clear up the confusion about time dilation that the poster may be suffering from, we could make things a little easier by imagining that a planet 60 light years away wants to send a message by firing a rocket at some sublight speed, say 0.6c. It's true that a clock on the rocket itself will be slowed down, in this case by a factor of 1.25. However, the speed by which clocks on the rocket slow down is irrelevant to the question of how long it takes the rocket to reach us in our frame; if the distance is 60 light years and the speed is 0.6c, then the time will be 60/0.6 = 100 years in our frame, the time dilation doesn't affect this number.

 

[russ_watters]

The first part of your sentence is confusing, what do you mean by "light a clock and doesn't experience time"? If you just meant to say that light itself doesn't experience time (rather than talking about a light clock or something),

Yes, it was a typo - fixed now.

I suppose this is true, but I thought the question was about how much the galaxy that emitted the light would have aged--looking back I may have misunderstood, I guess I was imagining that the OP was asking about the galaxies aging less because they are moving quickly relative to us as shown by redshift, but perhaps the post was actually talking about how much the light itself has aged, which doesn't really make sense since the proper time between events on a light beam's worldline is always 0.

It looked to me like the OP was asking if light itself experiences time dilation, not the moving galaxies.