why i am asking this question is that, i thought that photon takes no time to reach the earth or any other place in the universe due to length contraction. the reason for this is space wraps completly from starting to the end making the displacement zero, which is due to the value of $c$. the velocity of space around it from its reference frame.

  • $\begingroup$ Because the photon experiences neither time nor space, it does not have a reference frame on its own. If, hypothetically, an observer could move with the photon at the speed of light, his time would stand still and so he would not be able to make any measurements or observe anything. Thus he would not be an observer and so this "frame" would not be a frame of reference. More strictly, a frame involves coordinate axes, but in the hyperbolic geometry of our spacetime, all axes at the speed of light fold together into one line, so the concept of space or time coordinates is no longer meaningful. $\endgroup$ – safesphere Jul 23 '18 at 17:47
  • $\begingroup$ What depends on the relative velocity is length contraction and time dilation. These effects are different from "wrapping" or more precisely "curving" spacetime. A visual analogy of what the relative velocity does to the spacetime is gently bending a sheet of paper without crumbling it. While this affects how things look relative to each other, it doesn't really distort anything on the sheet. In contrast, gravity is equivalent to "stretching" the sheet, as if it is made of rubber. This does distort what is on the sheet and it is why we call this effect the spacetime curvature. $\endgroup$ – safesphere Jul 23 '18 at 17:57

Massless elementary particles like the photon are traveling at the speed of light in vacuum when measured locally.

Viewed from earth, though, it takes for the photon to reach earth from the sun approx 8 minutes.

Massless particles do not travel at infinite speeds, they have a finite speed, c, and since the distance is finite to, the time it will take them to reach earth is not zero, in this case it is approx. 8 minutes (when viewed from earth).

Now the misunderstanding with photons since they are massless, is that they do not have a reference frame. You could not say, let's imagine we are traveling with the photon, what would we see, how much time would pass, and questions like that.

If you really want to imagine what it can be like for the photon, you have to start doing math. What does math tell us?

Math tells us, that (if you could travel with the photon), the time elapsed between the photons emission in the sun and its absorption on earth, would be 0.

Photons, being massless, based on math, do not experience time like we do, their speed in the time dimension is 0.

In GR and in math we call this a lightlike worldline.

It is usually hard to understand, because massless particles are at one end of the scale, and in math some divisions would go to infinity regarding their speeds, and other attributes, meaning they are not countable. That is why we cannot talk about a reference frame for the photon.

It would be much easier for you if you would try to figure out, what would it be like if you would travel with a neutrino from the sun to earth.

Neutrinos have mass, and their speed is just a little less then c, but still their calculations would be relativistic, as close as you can get to speed c.

Now in that case, length contraction would cause the distance seen from the neutrino's frame, to be almost 0. Time on the neutrino's frame would pass very slowly, so for the neutrino (in the neutrino's frame), it would be much less then 8 minutes to get to earth.

This case is almost the photon's case, you see but it is still countable, so it makes you easier to understand what would happen if there was a frame for the photon.

So I will not try to answer your question in the title. "Does the space and time wraping depends on the relative velocity of frame of reference?"

Now what you are thinking of, is warping of spacetime, as you call it, that as per SR and GR is time dilation and length contraction. I just showed you that yes, relativistic speeds, like the one the neutrino is traveling at, will cause time dilation and length contraction.

  • $\begingroup$ In SR, a body with non-zero mass has a timelike worldline (in every inertial frame). A photon has a lightlike worldline. $\endgroup$ – PM 2Ring Jul 23 '18 at 19:23
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    $\begingroup$ I don't see how this answers the question in the OP - does space time warping depend on relative velocity. $\endgroup$ – enumaris Jul 23 '18 at 20:13
  • $\begingroup$ @PM2Ring yes right, you are right. $\endgroup$ – Árpád Szendrei Jul 23 '18 at 23:37
  • $\begingroup$ @enumaris he is talking about time dilation and length contraction, and I hope I answered that. $\endgroup$ – Árpád Szendrei Jul 23 '18 at 23:42
  • $\begingroup$ There are a lot of extra words, but I think this actually answers the OPs question, the key point being: "Now the misunderstanding with photons since they are massless, is that they do not have a reference frame." $\endgroup$ – Kyle Oman Jul 27 '18 at 6:45

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