# When moving at the speed of light time stops

Nugatory
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However, I do not understand the following (please correct me if I’m wrong with these conclusions):
Photons are composing light, so light is submitted to a null path, meaning that time of light is 0 seconds and the light path in space is zero (see #55 and 58).
Post 55 and 58 are referring to proper time and proper distance; that's the s in $s^2=\Delta x^2-\Delta t^2$, not the Δx or Δt.

[edit: corrected a typo in the space-time interval formula]

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Post 55 and 58 are referring to proper time and proper distance; that's the s in $s^2=\Delta x^2+\Delta t^2$, not the Δx or Δt.
Before I answer I’d like to make sure that you are really talking about s2=Δx2+Δt2 or if this is an error and you want to return to your above-mentioned formula s2=Δx2-Δt2. Which one do you mean?

Nugatory
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Before I answer I’d like to make sure that you are really talking about s2=Δx2+Δt2 or if this is an error and you want to return to your above-mentioned formula s2=Δx2-Δt2. Which one do you mean?
You're right, that's supposed to be a minus sign.

Dale
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Photons are composing light, so light is submitted to a null path
Yes.

meaning that life time of light is 0 seconds and the light path in space is zero (see #55 and 58).
No. This is not what null path means. Look at the forumla. A null path, $\Delta s^2 = 0$, clearly means that the time along the path, $\Delta t$, is equal to the distance along the path, $\Delta x$, in any inertial frame (in units where c=1). It does not imply that both are 0. Here, the time is 8 minutes and the distance is 8 light-minutes.

Post 55 and 58 are referring to proper time and proper distance; that's the s in $s^2=\Delta x^2-\Delta t^2$, not the Δx or Δt.
Answer: No, PAllen is talking about null spacetime interval, but he also describes something else. In#58 he is talking about a spacelike path and a timelike path, his two integration formulas giving 0 for proper length and proper time. So my question in #74 is justified.

PAllen
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Answer: No, PAllen is talking about null spacetime interval, but he also describes something else. In#58 he is talking about a spacelike path and a timelike path, his two integration formulas giving 0 for proper length and proper time. So my question in #74 is justified.
Proper length is simply spacetime interval along a spacelike path. Proper time is simply spacetime interval along a timelike path. My integration formulas are just a convenient re-expression of the metric valid in a global inertial coordinate system in SR (I gave separate formulas only because for a spacelike path you typically want to integrate along a spatial coordinate, and for a timelike path along a time coordinate). I corrected my earlier argument that it might make sense to say proper time is zero along a light path on prodding by Dalespam and Gwellsjr. Instead, the better interpretation of the different types of spacetime paths is:

- spacelike means you can consider the path to be like a measuring tape path using some general 'simultaneity' convention. In the special case of a spacelike geodesic, you have a ruler in some inertial frame.

- timelike means it is a possible path of a clock.

- null means it can neither be a clock nor a measuring tape. It does not mean it can be both a zero length tape and a frozen clock. It means it is radiation path, or massless particle path - which cannot be treated as either a clock path or a tape measure.

I corrected my earlier argument...
Thank you for this important answer, but I must admit that I cannot understand very much.

Also it seems to me that it is off my subject. Space-time interval is concerning Lorentz transformation, and it is difficult or even impossible to develop statements about photons on this base. So you did not talk as you wanted about application of √(1-v^2/c^2) (proper time formula/ Lorentz contraction formula)?

For me the question is not at all meaningless because I am actually working on a model for wave-particle duality of light which shall be based on SR, and I have to find the right expression concerning the space-time path of light (proper time formula/ Lorentz contraction formula).

Nugatory
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For me the question is not at all meaningless because I am actually working on a model for wave-particle duality of light which shall be based on SR, and I have to find the right expression concerning the space-time path of light (proper time formula/ Lorentz contraction formula).
Hmmm.... I have to caution you that, based on the questions you're asking, you're building on a fairly shaky mathematical foundation here. It's not enough to identify the formulas, you have to understand their derivation. Without that, the most likely outcome is that you'll come up with a model that is less accurate and useful than the (astoundingly successful) relativistic model of wave-particle duality that we already have.

If you are serious about understanding SR, you might want to consider spending several serious months working your way through a reasonably math-oriented textbook. You will get a LOT of help from posters here if you find yourself stuck.

One can describe light as a plane-wave using the usual wave equation

ψ(t,x) = exp[i(ωt + kx)]

provided ω=k.

Dale
Mentor
it is difficult or even impossible to develop statements about photons on this base.
Actually, it is fairly easy to develop statements about photons on the basis of the space-time interval. Furthermore, statements that you develop based on the spacetime interval have the advantage that they are frame-invariant.

For example: the spacetime interval of light is 0. From the formula we have:
$ds^2=-c^2 dt^2 + dx^2 + dy^2 + dz^2$
setting ds=0 and rearranging we get
$c^2 dt^2 = dx^2 + dy^2 + dz^2$
which is the equation of a sphere with radius c dt. So light expands out in a sphere at speed c in all inertial frames. This is the second postulate of relativity.

PAllen