Do photons experience instant lifetimes?

[SeventhSigma]

Do photons experience "instant" lifetimes?

So we know that, for instance, the Andromeda Galaxy is about 2 million lightyears away. That means that from an observer on Earth, we would watch a photon take 2 million years to actually reach that galaxy.

But if we're the photon itself, would it actually feel "instant"? According to the gamma factor in t = T*(1-v^2/c^2)^.5, when you move at c, t = 0, which means that no matter how long a stationary observer has to "wait" for us to cross a particular distance, we experience it as instant -- is this correct?

Would the light from the Big Bang, therefore, experience instant life followed by instant death at the end of our universe assuming it does not change its speed at any point?

 

[ghwellsjr]

If you do a search on photon lifetime on this forum you will find hundreds of threads that discuss this issue. Why don't you check the responses and then post a summary?

 

[bcrowell]

FAQ: What does the world look like in a frame of reference moving at the speed of light?

This question has a long and honorable history. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers.

The most straightforward argument is based on the positivist idea that concepts only mean something if you can define how to measure them operationally. If we accept this philosophical stance (which is by no means compatible with every concept we ever discuss in physics), then we need to be able to physically realize this frame in terms of an observer and measuring devices. But we can't. It would take an infinite amount of energy to accelerate Einstein and his motorcycle to the speed of light.

Since arguments from positivism can often kill off perfectly interesting and reasonable concepts, we might ask whether there are other reasons not to allow such frames. There are. One of the most basic geometrical ideas is intersection. In relativity, we expect that even if different observers disagree about many things, they agree about intersections of world-lines. Either the particles collided or they didn't. The arrow either hit the bull's-eye or it didn't. So although general relativity is far more permissive than Newtonian mechanics about changes of coordinates, there is a restriction that they should be smooth, one-to-one functions. If there was something like a Lorentz transformation for v=c, it wouldn't be one-to-one, so it wouldn't be mathematically compatible with the structure of relativity. (An easy way to see that it can't be one-to-one is that the length contraction would reduce a finite distance to a point.)

What if a system of interacting, massless particles was conscious, and could make observations? The argument given in the preceding paragraph proves that this isn't possible, but let's be more explicit. There are two possibilities. The velocity V of the system's center of mass either moves at c, or it doesn't. If V=c, then all the particles are moving along parallel lines, and therefore they aren't interacting, can't perform computations, and can't be conscious. (This is also consistent with the fact that the proper time s of a particle moving at c is constant, ds=0.) If V is less than c, then the observer's frame of reference isn't moving at c. Either way, we don't get an observer moving at c.

 

[SeventhSigma]

Alright -- what about something arbitrarily less than c (say multiple orders of magnitude deep within a fraction of a percent lower than c)

 

[henry_m]

Alright -- what about something arbitrarily less than c (say multiple orders of magnitude deep within a fraction of a percent lower than c)

Then that something could get to Andromeda in an arbitrarily small amount of proper time (i.e. time according to the object) as described by the equation in your first post.

In principle, someone could travel to Andromeda close to the speed of light, take a quick photo of the milky way, and do the return journey, having only aged slightly. Unfortunately for our intrepid photographer, 4 million years will have passed on Earth when he get's home so he might be a bit lonely.

This is the famous twins' 'paradox', the inverted commas being because this is not really a paradox, just perhaps a bit counterintuitive. And it's been tested!

 

[SeventhSigma]

Can someone explain how to understand Lorentz Transformations and worldlines? I see all this talk of things being timelike/spacelike and concepts of "invariance" in a great many discussions -- and I don't understand how it all works. Is there an easy example?

 

[Naty1]

That last post is just too big a set of questions...
Try reading here
http://en.wikipedia.org/wiki/Lorentz_transformation

and
http://en.wikipedia.org/wiki/World_line

the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime.

See specifically the illustration for "world lines in special relativity". It takes a little while to get used to the picture at first but time spent thinking about it clarifies a lot of pieces in relativity. Note this is an inertial reference frame, observer at the origin.

Light like cones are traced out by light speed particles...those moving at speed "c".
One thing I found useful was the nomenclature for "time like" referring to the light cone region closer to the vertical time axis than the two dimensional horizontal space plane in space time diagrams where the lightcone slope is the usual 45 degrees. "space like" is the region outside where activities are closer to the space plane. So the former describes particle speeds less than c, the cone shape itself particles at speed at c, and the latter [spacelike, outside the cone] can't affect particles at the origin because they are too distant in space and time.

In Newtonian (classical) physics where signals are instantaneous, not limited to speed "c"... everything happens instantaneously...distant signals can " reach out and touch someone" (at the origin) no matter how far away.

 

[SeventhSigma]

I've read these but found them to be a bit confusing and dense. Are there easy examples of each?

 

[SeventhSigma]

Is a worldline similar to this sort of image?

http://www.universetoday.com/wp-content/uploads/2007/10/2007-1015inflation.jpg

But doesn't a "light cone" imply merely 2-dimensional crosssections describing how far light can travel at a particular point in time? Wouldn't it need to be a fusion of spheres?

 

[Naty1]

Try here for examples of world lines:

http://en.wikipedia.org/wiki/World_line

 

[Naty1]

yes, similar...but start with simple examples:

Can you graph the formula d = vt?

Thats the "world line" of a body in one dimensional space and time moving at steady velocity v.

How about d = 1/2at².

[The cone I referenced above in Wikipedia extends this to two space dimensions and time.]

That's the world line or a body under going uniform acceleration in one dimensional space...and time.


Try here for examples of world lines:

http://en.wikipedia.org/wiki/World_line

 

[GrayGhost]

I've read these but found them to be a bit confusing and dense. Are there easy examples of each?

I'd recommend starting at this Wiki link ...

http://en.wikipedia.org/wiki/Minkowski_diagram"​

It refers to most the other related links (when necessary), including the worldline link reference (in para 2)

Here's the figure (in that Wiki page) of most interest to you ...

http://en.wikipedia.org/wiki/File:Minkowski_diagram_-_3_systems.png"​

I wouldn't worry much of the other figures at first.

GrayGhost

 

[Dale]

Most of the time people have been exposed to worldlines without even knowing it. If you have ever plotted position as a function of time then you have drawn a worldline. The only difference being that for some reason for worldlines the tradition changed to plotting time on the vertical axis and distance on the horizontal axis.