When moving at the speed of light time stops

[Nugatory]

What I mentioned in the last posts I learned at school and read in books. In order to be precise, before posting I adopted the information

“For photons, their life time is an instant of 0 seconds, and in their frame space is contracted to zero.”

in its sens from a physics book.

Which physics book? Sadly, there are some bad ones out there... and if you cherry-pick quotations from even (especially?) the good ones you can be misled...

The last posts of forum users showed me that the word “frame” is not admitted in this forum

Nothing wrong with using it, you just have to use it correctly.

 

[Dale]

Sorry, DaleSpam, but your mere derivation of the proper time formula from Lorentz transformation does not inhibit the possibility that the constraints the original formula is underlying do not rule the resulting formula (e.g. from the formula x = y*z/z derives x = y; both are not defined for z=0, but may be the second works also for z=0).

Can you find one example in physics to support this? Specifically, any example where a general formula has some constraint, but a specific formula derived from that general formula does not have that constraint. If not, then it seems like you are just "grasping for straws".

Note also, your purely mathematical example is not a counterexample. If x = yz/z then a plot of z=0 would be a "hole" in the function. See the discussion in example C here:
http://www.freemathhelp.com/find-limit.html

What I mentioned in the last posts I learned at school and read in books. In order to be precise, before posting I adopted the information

“For photons, their life time is an instant of 0 seconds, and in their frame space is contracted to zero.”

in its sens from a physics book. - Except the notion “frame” which I can take back. I used it because for me a “frame” was not an “inertial frame”. The last posts of forum users showed me that the word “frame” is not admitted in this forum. I hope you accept my following correction:

“The photon life time (in vacuo) is an instant of 0 seconds, the photon path is contracted to zero”.

Please provide references for these quotes. They do not sound like they came from mainstream scientific sources like textbooks or peer-reviewed papers. They sound like they may have come from pop-sci books.

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 space-time interval,

All correct so far.

life time of light is 0 seconds and the light path is zero.

What is your basis for this claim?

But science found out that light takes 8 minutes from Sun to Earth, over a distance of 8 light minutes.

Yes.

If time dilation is not applying to light, is there a “similar effect”, similar to the time dilation of special relativity (as we know it from the twin paradox)?

If you don't make the claim above then there is no effect at all. That is one reason that such a claim requires some justification, which I don't see.

 

[Nugatory]

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 space-time interval, life time of light is 0 seconds and the light path is zero.
But science found out that light takes 8 minutes from Sun to Earth, over a distance of 8 light minutes.
If time dilation is not applying to light, is there a “similar effect”, similar to the time dilation of special relativity (as we know it from the twin paradox)?

You are mixing distances in space-time with distances in space and intervals of time, and that may be where the confusion is coming from.

Consider two events: Event A is a photon leaving the surface of the sun; and event B is that photon striking a photon detector on earth.

An observer at rest relative to solar system, measuring time in minutes and distances in light-minutes would say that event A is the point in space-time (x=0,t=0); and event B is the point (x=8,t=8). That is, it took eight minutes for the photon to travel the eight light-minutes between sun and earth.

An observer on a spaceship passing through the solar system at .6c relative to the solar system would say that event A is the point (x=0,t=0) and event B is the point (x'=4,t'=4). I used the Lorentz transforms to calculate this, and there is no contradiction because the two observers are moving relative to one another so they are using different coordinate systems; the little ' symbols help us not mix them up.

It's worth noting that the choice of origin is arbitrary, and the two observers don't have to pick the same one. For example, if our first observer decided to pick the origin to be the surface of the Earth three seconds before the photon was detected, then he'd say that event A was (x=-8,t=-5) and B was (x=0,t=3). The spaceship observer could still decide that he wants to call event A (x'=0,t'=0) so B is (x=4,t'=4)... Or he could choose as the origin an event long ago and far away, so that A is at (x'=10000,t'=8371) and B is (x'=10004,t'=8375)... or anything else.

Notice the following things:
1) As far as the first observer is concerned, the emission and detection events were separated by 8 minutes or time and 8 light-minutes of distance.
2) As far as the spaceship observer is concerned, the emission and detection events were separated by 4 minutes of time and 4 light minutes of distance.
3) Both observers measured the same value for the speed of light (the obvious one light-minute per minute), even though the times and distances involved were different.
4) Both observers also get the same value for the spacetime distance between the two events, defined by $s^2=\Delta x^2-\Delta t^2$
5) Although for both observers the space and the time distances are both non-zero, the space-time distance in #4 is zero. That's the null space-time interval you referred to above, and it does not mean that either the space or the time separations must be zero.
6) Try as you might, you will not be able to find a reference frame in which the space or time distances are zero, nor in which the speed of light will come out to be anything except oene light-minute per minute.

 

[Moonraker]

You are mixing distances in space-time with distances in space and intervals of time, and that may be where the confusion is coming from.

Yes, thank you for your explanations! ”null space-time interval” is wrong in this context, indeed. I did not adopt correctly the terms of the posts #55 and 58. Here is my correct question (modifications bold):

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 life time of light is 0 seconds and the light path in space is zero (see #55 and 58).
But science found out that light takes 8 minutes from Sun to Earth, over a distance of 8 light minutes.
If time dilation is not applying to light, is there a “similar effect”, similar to the time dilation of special relativity (as we know it from the twin paradox)?

 

[kweba]

If when you're moving at the speed of light time freezes, why then does it take light 8 minutes to reach the Earth from the sun?

The trick here is that in Special Relativity (which is the theory that encompasses Time Dilation), TIME is NOT universal, unlike in the previous Newtonian/Classical sense and model of space and time, where Time is independent. In SR, TIME is dependent on each object and observer in the universe.

To illustrate this, it's like saying every object in the universe has its own clock that ticks on its own rate. Some clocks tick faster, and some tick slower, than others.

So with light moving at the speed of light, TIME freezes in its own point of view. This is called "a frame of reference". Time freezes only within that light. In a sense, the light does not "age" and does not experience/feel time. (Refer to the Twin Paradox below.)

But for the rest of us (things and people especially here on Earth) who move at relatively slow everyday-speeds, time does not freeze (not even slowing down by that much for that matter), and so we experience "the passage of time".

It is us, the people, the things, and everything on Earth, who experience that 8 minutes before the light from the sun reaches us here on Earth, in our own reference frame.

Einstein himself had provided a beautiful illustration on Time Dilation with regards to reference frames: the ever famous "Twin Paradox"

To summarize the twin paradox, there are twin brothers. One brother is left at home, while the other brother is an astronaut in a space shuttle moving close or at the speed of light (to indicate a really fast velocity). When the astronaut brother returns home after some long period of time, he found that, in a way, he was still the same than his twin brother who have aged a lot more than him. So in essence, time have passed at different rates between the two twins, and that the astronaut twin remained "young".

For more info on the Twin Paradox, here's a link on wikipedia.

Note: I humbly admit I'm not an expert on this, so I would like to apologize, especially for the others, if I may have posted some wrong and misunderstood facts. Thank you.

 

[Nugatory]

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]

 

[Moonraker]

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]

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]

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.

 

[Moonraker]

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]

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.

 

[Moonraker]

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]

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.

 

[Mentz114]

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

ψ(t,x) = exp[i(ωt + kx)]

provided ω=k.

 

[Dale]

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]

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)?

Spacetime interval is independent of Lorentz transformation. Spacetime interval is an invariant property of a spacetime path (when speaking of interval between two events in SR, implicitly you imagine a geodesic path between them). It is independent of coordinate system, reference frame, or observer. Lorentz transform is the particular form coordinate transformation between different inertial frames with standard coordinates, when there is also no translation or rotation.

The last sentence of your comment quoted above shows the confusion of separating a formula from its meaning. Length contraction and time dilation are very different things, and both are different from what I was referring to, even though they happen to have the same formula in inertial frames. Length contraction refers to disagreement between frames on measured distance between two objects (or ends of one object), each frame needing to do a series of operations to accomplish such a measurement, using their own, conflicting, simultaneity determination. Time dilation refers to the ratio of a moving clock rate to time rate in some inertial reference frame (sticking to the simple SR case). Time dilation for the same clock will differ between different inertial frames. What I was referring to was computing the proper time along a specific clock path, using some inertial frame. This will come out the same in every inertial frame (in one frame, the dilation may be greater on average, but then the coordinate time will be greater, so the integrated total will be the same; that's what it means to say proper time = time measured on some specific clock between two identifiable events in its history, is invariant. )

When I threw out the idea of trying to call the zero interval along a null path its proper time, it was correctly pointed out that I was proposing there was some type of clock that could follow along a light path - that's what proper time means. I accepted that my suggestion wasn't meaningful.