Is light time dilated?

[Vorpal]

I guess in my mind the only correct observation/measurement is a universal one that considers all observers simultaneously.

But that's the source of the so-called paradox: different observers would consider different events simultaneous.

This would create a paradox however with self-observed proper times conflicting with other-observed dilated times when they are in the same inertial frame.

Here's a simple geometrical picture one can draw on a piece of paper: have an angle, and imagine two observers starting from the vertex and going along the rays of the angle, marking distance traveled. Let's call the first "t-axis" and the second "T-axis", and the angle between them θ.

t      T   t      T
|_____/    |\    /   Two different identifications
|____/     | \  /    between t-axis and T-axis lead
|___/      |\ \/     to opposing relationships:
|__/       | \/       t/T = cos θ vs. T/t = cos θ
|_/        |\/      (A) Ident. perpendicular to t-axis
|/         |/       (B) Ident. perpendicular to T-axis
A          B

STR is exactly the same way, with the "distance traveled" being proper time, except that the minus sign in the metric makes the trigonometry hyperbolic (γ = cosh θ). A insists on a particular notion of simultaneity, while B insists on another. Their duality of observing the other as dilated is not a contradiction because they're actually measuring completely different intervals.

 

[Singularitarian]

Let's take a step back. Special relativity is all about the space-time metric:
ds² = dx² + dy² + dz² - (c dt)²To transform from one inertial reference frame to another, we must preserve ds². The class of continuous transformations which do this are called Lorentz transformations. When we apply these transformations to an object, we can derive things like length contraction and time dilation, which are consequences of the Lorentz transformations. The Lorentz transformations are usually formulated in terms of a relative velocity between our initial reference frame and our final reference frame, and so are the length contraction and time dilation formulas. If we plug in c to our time dilation formula, it looks like time stops.

But we've actually skipped a step. What happens if we plug in c to our Lorentz transformations directly, and THEN see what we get? Well, we encounter a problem: if you try plugging in c for your relative velocities for the Lorentz transformations, you get a divide by zero. Which is undefined. So we cannot use the Lorentz transformations to change to a reference frame moving at the speed of light, and so the length contraction/time dilation equations derived from that are just not valid. Now, there are a number of ways of looking at that, but I think the simplest way to handle it is to simply conclude that a frame moving at c is not a valid inertial reference frame. This doesn't mean that nothing can move at c, it means that you cannot adopt it as a reference frame. So the question of what happens to time in the reference frame of the photon becomes meaningless.

But that's because there is no time, its hard to define any true frame. If everything around it is moving at the speed of light, then it is true distance disappears from the equations. From here, you can even justify it has no specific location, if there is no true distance from its frame. If failing to distinguish a frame, then the photon is not adiquately assigned a description, for the Lorentz Tranformformations must be consequentially true for a photon, if Einsteins special Relativity is to hold, unless you are of course, challenging his theory?

 

[Vorpal]

But that's because there is no time, its hard to define any true frame. If everything around it is moving at the speed of light, then it is true distance disappears from the equations. From here, you can even justify it has no specific location, if there is no true distance from its frame.

Why? It's not as if the universe is obligated to conform to a positive-definite metric structure. It'd be far stranger if that was the case, since then time and space would be indistinguishable (one gets exactly the same thing in Galilean spacetime--the null curves are different, but they're still there).

If failing to distinguish a frame, ...

I'm not sure how sticking to its principles and still being both logically and empirically consistent constitutes a failure. If the photon had a reference frame, that would be a direct contradiction to the postulate that lightspeed is invariant in all reference frames.

... then the photon is not adiquately assigned a description, for the Lorentz Tranformformations must be consequentially true for a photon, if Einsteins special Relativity is to hold, unless you are of course, challenging his theory?

The general Lorentz transformation can be applied for a photon; the full Lorentz group has more than enough crap in it to deal with this. What you're thinking of as "Lorentz transformation" is really a special case of the hyperbolic (timelike) part of the Lorentz group. There are also elliptic (spacelike) transformations, which have as a special case ordinary rotations in space, and parabolic (lightlike) transformations which 'rotate around' a lightlike vector in an analogous way.

 

[Singularitarian]

It still moves along a null-trajectory, and experiences no time, according to relativity.

Case closed.

 

[Reality Check]

It still moves along a null-trajectory, and experiences no time, according to relativity.

Case closed.

It still moves along a trajectory and experiences time, according to relativity.
A null geodesic ("null-trajectory"?) is still a path through spacetime.

Case closed

 

[Singularitarian]

It still moves along a trajectory and experiences time, according to relativity.

Case closed

Ahem, do you read nothing i say?


Quoted from Gribbin´s "Schrodinger´s kittens":
The Lorentz transformations tell us that time stands still for an object moving at the speed of light. From the point of view of the photon, of course, it is everything else that is rushing past at the speed of light. And under such extreme conditions, the Lorentz-Fitzgerald contraction reduces the distances between all objects to zero. You can either say that time does not exists for an electromagnetic wave, so that it is everywhere along its path (everywhere in the Universe) at once; or you can say the distance does not exist for an electromagnetic wave, so that it "touches" everything in the Universe at once. ''

 

[Reality Check]

Ahem, do you read nothing i say?


Quoted from Gribbin´s "Schrodinger´s kittens":
The Lorentz transformations tell us that time stands still for an object moving at the speed of light. From the point of view of the photon, of course, it is everything else that is rushing past at the speed of light. And under such extreme conditions, the Lorentz-Fitzgerald contraction reduces the distances between all objects to zero. You can either say that time does not exists for an electromagnetic wave, so that it is everywhere along its path (everywhere in the Universe) at once; or you can say the distance does not exist for an electromagnetic wave, so that it "touches" everything in the Universe at once. ''

That author is hopefully dumbing things down for his audience.

He does not mention that a photon does not have a "point of view". It is not an observer. It cannot observe anything such as the passing of time. You can add an hypothetical observer (as in Einstiens thought experiment of travelling at the speed of light beside a light ray)
From the point of view of the observer, their clock keeps on ticking away.

 

[Singularitarian]

No this author is absolutely correct, so are many other authors with PhD's who have said the same thing for years.

 

[Singularitarian]

Again, a photon does not have a specific point of view because time is infinitely stretched from its perspective.

 

[Reality Check]

Again, a photon does not have a specific point of view because time is infinitely stretched from its perspective.

Again, a photon does not have a specific point of view because it is not an observer.

Consider a hunk of rock traveling at 0.5c - what is its point of view? Is it admiring the pretty stars? Is it calculating its velocity?
NO - you need an observer to do this.

 

[ynot]

Again, a photon does not have a specific point of view because it is not an observer.

Consider a hunk of rock traveling at 0.5c - what is its point of view? Is it admiring the pretty stars? Is it calculating its velocity?
NO - you need an observer to do this.

[FONT=Verdana, sans-serif]What has an observer or observation got to do with relativity? How does how or whether a thing is observed or not change the reality of that thing? Isn't the use of the word “observer” only being used to define a frame?[/FONT]

 

[Reality Check]

[FONT=Verdana, sans-serif]What has an observer or observation got to do with relativity? How does how or whether a thing is observed or not change the reality of that thing? Isn't the use of the word “observer” only being used to define a frame?[/FONT]

Special Relativity is basically the mathematics of transformations between the frames of references (which are assigned by observers). That is where the Lorentz transformation comes from and thus the observation of time dilation and length contraction. To apply SR you need at least 2 different reference frames. I think that you can have a single observer to assign the 2 different reference frames.

No observers means no frames of reference. No frames of reference means that relativity definitely cannot be applied.

 

[Singularitarian]

Again, a photon does not have a specific point of view because it is not an observer.

Consider a hunk of rock traveling at 0.5c - what is its point of view? Is it admiring the pretty stars? Is it calculating its velocity?
NO - you need an observer to do this.

If someone said to you, what is the difference between the time frame of a muon and that of a photon, you would say nothing, because there is no frame?

That is not true at all. Accoring to how one wishes to measure them, a muon still experiences time, whereas a photon must not.

Argue this, and i won't be part of this discussion anymore. It should have ended upon the word ''yes. Time is infinitely ditorted.''

 

[ynot]

[FONT=Verdana, sans-serif]

Special Relativity is basically the mathematics of transformations between the frames of references (which are assigned by observers). That is where the Lorentz transformation comes from and thus the observation of time dilation and length contraction. To apply SR you need at least 2 different reference frames. I think that you can have a single observer to assign the 2 different reference frames.

No observers means no frames of reference. No frames of reference means that relativity definitely cannot be applied.

Does Relativity work for a blind observer?
[/FONT]

 

[Reality Check]

[FONT=Verdana, sans-serif]Does Relativity work for a blind observer? [/FONT]

Yes but in Braille !

I thought of another way to explain that a clock traveling at the speed of light still ticks. So if a photon somehow had a clock attached to it (or had a "point of view" that could measure time) then time would pass for it.
This does not need SR - just one of its postulates:
"Light in vacuum propagates with the speed c (a fixed constant) in terms of any system of inertial coordinates, regardless of the state of motion of the light source".

Consider an observer with a clock that consists of a photon bouncing between 2 mirrors. The photon will always travel at the speed c in the observer's reference frame according to the postulate. Thus the clock will always tick, even if the observer is traveling at the speed c.
Now throw away the observer (or blind them!). What happens to the clock?
I think that the clock continues to tick.

 

[theneedtoknow]

Yes but in Braille !

I thought of another way to explain that a clock traveling at the speed of light still ticks. So if a photon somehow had a clock attached to it (or had a "point of view" that could measure time) then time would pass for it.
This does not need SR - just one of its postulates:
"Light in vacuum propagates with the speed c (a fixed constant) in terms of any system of inertial coordinates, regardless of the state of motion of the light source".

Consider an observer with a clock that consists of a photon bouncing between 2 mirrors. The photon will always travel at the speed c in the observer's reference frame according to the postulate. Thus the clock will always tick, even if the observer is traveling at the speed c.
Now throw away the observer (or blind them!). What happens to the clock?
I think that the clock continues to tick.

You are absolutely right...not much more to add , but this guy seems to think that the time dilation we measure of an object ACTUALLY applies to the point of view of an observer moving WITH the object...so just because we would measure time as infinitely stretched (not passing), then our observation must somehow force the photon to not experience it (even though all moving refference frames experience time as normal in their own frame)

 

[sol invictus]

No observers means no frames of reference. No frames of reference means that relativity definitely cannot be applied.

That's not true. A "frame of reference" in this context simply means a coordinate system. One doesn't need an observer to discuss what the relation is between two coordinate systems. And come to think of it, I don't actually see any reason why one can't imagine an intelligent observer made out of massless radiation, and therefore moving at the speed of light.

As for the topic of this thread, perhaps it would help to think of things like this. When we speak of "the reference frame of something", we mean the reference frame in which that thing is at rest. Technically, that means the choice of coordinates in which the object has zero velocity - which in turn means it is "moving" in time, but not in space. Its worldline is extended only in time.

For something moving at the speed of light, no such frame exists. But something very similar does exist - a frame in which again the worldline is extended only in one coordinate, not in any of the others (so it's "moving" only in that one coordinate). The difference is that that coordinate is null, rather than timelike - but that's the only difference.

 

[edd]

Accoring to how one wishes to measure them, a muon still experiences time, whereas a photon must not.

I'm still waiting for an explanation for this:

Take a clock, or almost anything that oscillates reliably and can therefore function to some degree in a clocklike manner. Accelerate it and observe that as it goes nearer the speed of light it oscillates slower and slower, and see how if it were to go at the speed of light it would apparently stop. We can agree on that much.

Then tell me why I had to use the word 'almost' just then, because the most accurate clocks in existence rely on something for which this isn't true - the photon. The photon, which when emitted in a particular manner from a particular kind of caesium gives us the very definition of a second, as it oscillates 9,192,631,770 times in that period.

I don't know how you exactly define a photon's "experience" of time, but it seems to me that a photon doesn't do an awful lot other than oscillate, and therefore can't be said to be 'frozen' in the same way that a clock accelerated to lightspeed would be.

 

[sol invictus]

I don't know how you exactly define a photon's "experience" of time, but it seems to me that a photon doesn't do an awful lot other than oscillate, and therefore can't be said to be 'frozen' in the same way that a clock accelerated to lightspeed would be.

I agree. And not only can the photon oscillate, it can interact with other particles as it moves along, although only if they were emitted by something ahead of the photon (because anything behind can never catch up).

In fact one useful trick in physics is to use "lightcone gauge", meaning to use a lightlike direction, such as the one a photon moves in, as time. That works perfectly well (although it has some quirks).

 

[Thabiguy]

Take a clock, or almost anything that oscillates reliably...

Perhaps it should be pointed out that photons oscillate quite differently from the way a clock or some other process oscillates.

If you move very fast relative to a clock, you will always observe that it slows down. However, if you move very fast relative to a photon source, you can observe the photon to oscillate faster (if you move towards it). That's because unlike a clock, which just measures time, the oscillation of a photon also depends on its wavelength, which intrinsically changes as you accelerate. (In a way, you can interpret the oscillation of a photon as a measure of distance travelled rather than time; if you mark the "nodes" of oscillation, you will find that they correspond to a grid which is regular in the rest frame of the emitter.)

It's a necessary consequence of special relativity. A photon cannot undergo any detectable changes that would depend only on the time it has been travelling - that would allow experiments with inconsistent results.