The discussion revolves around the concept of time dilation in the context of special relativity, particularly focusing on the implications of traveling at or near the speed of light. Participants explore various scenarios involving time measurement for observers on Earth versus those traveling in space.
Participants express differing views on the implications of traveling at the speed of light and the nature of time experienced by massless particles. There is no consensus on the application of time measurements across different frames of reference, particularly concerning photons.
Some participants highlight the limitations of definitions and assumptions when discussing time measurements in the context of massless particles, indicating that the discussion may depend on specific interpretations of relativity.
It's impossible for any observer to reach the speed of light in relativity. But suppose someone is on a ship which moves away from the Earth at some speed v that's smaller than c (c is the speed of light), and then turns around and returns to Earth at the same speed v. In this case, if the person on Earth has aged by some amount T between the time the ship left and returned, then the person on the ship will only have aged by a smaller amount [tex]T * \sqrt{1 - v^2/c^2}[/tex]. For example, if the person on Earth aged 10 years, and the ship was moving at 0.8c (80% the speed of light), then the person on the ship will have only aged by [tex]10*\sqrt{1 - 0.8^2}[/tex] = [tex]10*\sqrt{0.36}[/tex] = 10*0.6 = 6 years.fire100_anand said:If two persons are wearing the same watch showing the same time say 5 Am...one person remains in Earth and the other person goes to space at the speed of light ...After one hour the watch on person on Earth will show..what will be the time on the watch worn by the person who went to space...please explain time dilation
slider142 said:As an alternative reply, if one uses continuity, one can argue that objects traveling at the speed of light do not experience any passage of time, so omitting the impossibility of a massive object accelerating to the speed of light, they will read their time as 5AM, no matter what time the person left back on Earth reads.
robphy said:Can you use continuity?
If so, can you show this explicitly?
Given two events P and Q, it is not at all necessary for one to be in the future light cone of the other (the interval may be space-like, not time-like. Indeed, the third possibility is that the events are light-like, which is the case since they are connected by the worldline of a photon). Photons, as measured from our reference frame, have future and past events with respect to our reference frame. As we know from our study of relativity, simultaneity is relative to each reference frame. It may just be the case that all events are simultaneous as measured from the frame of a photon.robphy said:You see, it seems to me that:
given two distinct events P and Q on a photon's worldline,
either P is to the future of Q, or vice versa.
So, I question whether time-measurements by massive particles (and conclusions drawn from them) can be applied in the massless case.
Yup.slider142 said:Given two events P and Q, it is not at all necessary for one to be in the future light cone of the other (the interval may be space-like, not time-like. Indeed, the third possibility is that the events are light-like, which is the case since they are connected by the worldline of a photon).
slider142 said:Photons, as measured from our reference frame, have future and past events with respect to our reference frame.
slider142 said:As we know from our study of relativity, simultaneity is relative to each reference frame. It may just be the case that all events are simultaneous as measured from the frame of a photon.
Indeed, the idea of measurements *in* the frame of a photon is rather silly, but the interpretation of time in that frame is so common that it would be an omission to leave it unmentioned. :)