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I am having a bit of trouble understanding the point of the following relativity scenario.

Imagine two freely floating rockets (side by side) of height $L$ in outer space. The rockets have a light on top that gives a flash of light every second. A person who is attached to the floor of both rockets. They see the subsequent flashes one second after another too but a bit ($L/c$) later than the light that emits them. So the time at the top flows with the same rate as the time on the floor, according to both persons. Now one rocket starts to accelerate, parallel to the other, and at the same time, the lights on the top give a flash of light. The person on the floor of the accelerating rocket receives this flash of light a bit earlier than the person in the freely floating rocket. The rocket keeps accelerating and the lights give off the second flash of light. The person in the accelerating rocket receives this second flash not the same amount earlier as the first flash (otherwise the second person would receive the flashes one second after each other too), but a higher amount earlier as the first flash because the rocket is accelerating towards the second flash.

This means the person in the accelerating rocket sees that there is less than a second passed between receiving the two flashes. The same holds for all subsequent flashes. So for the person in the accelerated rocket time goes slower.

I understand that an accelerated ship would be the same as being in a gravitational field, therefore time would move slower for the accelerated ship. Therefore, I guess less time should pass between the two flashes of light, in respect to another observer.

However, I don't see the point of the scenario posing that the ship is accelerating towards light.

Does time slow down for the ship because it's moving towards light? Or just because it's being accelerated - therefore having the same properties as a gravitational field? What is the point of this scenario?

A layman explanation would be mostly appreciated.

Qmechanic
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    See Why can't I do this to get infinite energy?. – mmesser314 Dec 28 '20 at 00:54
  • @mmesser314 thanks. It's certainly a wonderful answer, though at times a bit too complex for my understanding. Do you mind giving me your opinion as to this particular scenario in my question? It would be very appreciated. Thanks again. –  Dec 28 '20 at 01:16
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    Time slows because of gravity, and gravity is just like acceleration. That is to say, time slows because of acceleration. – mmesser314 Dec 28 '20 at 02:08
  • @mmesser314 thanks again for pointing me to your answer to the other question. It's been very enlightening. I'm just a bit confused by this part: "If you measure a longer period on Earth than the space station finds, it is because your clock is slower" -- If your clock runs slower on Earth, wouldn't you measure a shorter period, as less time would pass? I noticed you corrected this information from a previous edit of your answer. How should I interpret it? Please kindly help me understand this. –  Dec 30 '20 at 00:17
  • Thanks. I fixed the answer. – mmesser314 Dec 30 '20 at 05:16

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Does time slow down for the ship because it's moving towards light? Or just because it's being accelerated - therefore having the same properties as a gravitational field? What is the point of this scenario?

The point is to imagine what it's like in an accelerating elevator, or rocket.

These are the effects according to classical physics and relativity:

  1. Objects appear to have weight
  2. Upper clocks appear to run extra fast
  3. Lower clocks appear to run extra slow

Classical physics says that when an upper clock is brought next to lower clock they read the same time.

Relativity physics says that when an upper clock is brought next to lower clock they do not read the same time, because of the different motions of the clocks.

Classical physics says time does not slow down in the rocket.
Relativity physics says time does not slow down in the rocket.
So can we forget the time slowing down in the rocket?

stuffu
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  • Thanks. Although the very scenario in my question mentions time slowing down in the rocket, so any confusion is not entirely my fault then. I take you do not agree 100% with the scenario –  Dec 30 '20 at 03:08
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    @RobertoValente Have you checked this: https://www.feynmanlectures.caltech.edu/II_42.html Particularly this part: "So if you were sitting in the tail you would conclude that clock A was running faster than clock B. If you were to do the same thing in reverse—letting clock B emit light and observing it at clock A—you would conclude that B was running slower than A. Everything fits together and there is nothing mysterious about it all." – stuffu Dec 30 '20 at 03:36
  • Thanks! I wasn’t familiar. –  Dec 30 '20 at 03:45
  • Thanks again @stuffu, for the Feynman reference. It is exactly the scenario mentioned by the original person my question is about, but way easier to understand in the original text, so I owe you one. One last thing, do you think you could help me understand a few aspects of Umaxo's answer to my question? I believe he references the same Feyman scenario you showed me. –  Dec 30 '20 at 15:03
  • @RobertoValente I can't make head or tails of Umaxos's answer. Maybe it's wrong ;) Any question about accelerating rockets and clocks I can answer. Like "what effect does acceleration have on clocks?" Answer is here: https://en.wikipedia.org/wiki/Time_dilation#Clock_hypothesis (Answer is: None) – stuffu Dec 31 '20 at 07:58
  • Thank you, you have been very helpful. Just one last thing: I'm not sure what you mean by acceleration doesn't have any effect on clocks... when all these relativity scenarios seem to say the opposite - that acceleration and gravitational fields do have an effect on clocks. What do you mean? Thx again –  Dec 31 '20 at 13:12
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    @RobertoValente I mean that it has been tested by accelerating things - no effect on aging has been found. Also putting clocks near big masses has been tested, and an effect on ticking rate has been found. Christian Doppler found the laws that tell the apparent rates of clocks in accelerating rockets. In the Feynman reference Feynman explains Doppler's effect in an accelerating rocket. Mr Doppler did not know any relativity. – stuffu Jan 01 '21 at 18:55
  • Thanks for the help @stuffu -- Regarding the effect of acceleration on the ticking of clocks, I'm not sure you are 100% correct. Check this answer - it confirms the clocks tick at a different rate, because of the gravitational potential in the accelerated rocket. If they didn't tick differently, it would be a violation of the equivalence principle. And - as you said - clocks do tick differently in a gravitational field. Please let me know what you think. Regards! –  Jan 02 '21 at 00:52
  • Gravitational potential in an accelerating frame of an accelerating rocket is like centrifugal force potential in a rotating frame of a spinning carousel. It exists in that weird frame, but not in a normal inertial frame. Note that in my answer I said that the observer sees differences between the clocks, Doppler effect and motion time dilation were the reasons. The differences are such that equivalence principle holds. John Rennie's error is not making very clear that the answer is given in a very weird accelerating coordinate system, and maybe using that coordinate system in the first place. – stuffu Jan 02 '21 at 03:55
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The fundamental principle on which relativity (both special and general) is based is the general principle of relativity

  • Local laws of physics are the same irrespective of the reference matter which a particular observer uses to quantify them.

It follows immediately from the general principle that time for an observer never slows down. One should therefore ignore misleading accounts which talk of time slowing down as though it were a real effect. What actually happens is an apparent affect. It looks to one observer as though time for a different observer is slower. This is true whether on is thinking of special relativy (no gravity) or general relativity (where gravity is involved).

The particular example you quote is doubly misleading, because it seeks to draw a conclusion from the rate at which the flashes are seen. That is wrong. The conclusion (apparent time dilation) should be drawn from the calculation of when the flashes took place, not from when they are seen.

To keep things as simple as possible I have explained it with these diagrams in The Large and the Small

enter image description here

enter image description here

enter image description here

Using an accelerated observer does make things a little more complicated, but first one needs to understand that in all circumstances time dilation is an illusion, which strictly violates the fundamental general principal of relativity.

unders

Charles Francis
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  • First, thank you very much for taking the time to answer. Can you clarify this part: "The conclusion (apparent time dilation) should be drawn from the calculation of when the flashes took place, not from when they are drawn" -- what do you mean by "drawn" in this case? –  Dec 30 '20 at 19:55
  • The original scenario in my question seems to belong originally to Feynman. You can find it here: https://www.feynmanlectures.caltech.edu/II_42.html -- link provided by @stuffu -- Just look for the spaceship illustrations at the middle of the page. Do you think it's not a good analogy for understanding time dilation? Could you expand on your opinion? Thank you very much. –  Dec 30 '20 at 20:15
  • Sorry, my fingers typed the wrong word. Sometimes they are not connected to my brain. I meant seen. – Charles Francis Dec 30 '20 at 20:15
  • I thought so. Thank you again. If you could address my last comment above regarding Feynman analogy, I'd be really glad. Thanks. –  Dec 30 '20 at 20:27
  • Feynman is explaining in a different way the effect seen in fig 5.6. For an accelerated reference frame, such as the rocket, and equivalently for a frame stationary wrt to the Earth's surface, clocks at different positions run at different rates relative to each other. This is a geometrical effect. It can be seen as analogous to the comparison in apparent speed on a Mercator projection of two ships traveling due East at the same true speed t, one on the Equator, one at latitude 060. – Charles Francis Dec 31 '20 at 16:16
  • Thanks. Let me see if I understand your last comment: the speed of both ships on the Mercator projection would be the same. However, on the globe, the ship on the Equator would have moved a longer distance. Is that correct? –  Dec 31 '20 at 17:44
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    I intended it the other way round, but the principle is the same. – Charles Francis Dec 31 '20 at 17:57
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The other answers are related to your original question. As I read the Feynmann text mentioned later, my answer is different.

The original question compares the clock of an accelerated rocket to a not accelerated one. That can not be concluded from that experience, because time always runs slower for an accelerated rocket. And the quoted text suggest that it depends on approaching or receding from a light source. That is not right because in that case we could say either than time runs slower or runs faster in the accelerated frame.

What is described in the Feynmann text is different. Inside an accelerated rocket, clock at different positions ticks differently. The clock at the top runs faster than the clock at the bottom. Now 2 clocks at different positions at the same accelerated frame are being compared.

And now things get stranger: time dilation is related to the acceleration. So if the bottom clock of the rocket run slower that the top one, that means that the botton part has a bigger acceleration! But how if the ship keeps the same length? You can read about Rindler coordinates in the wikipedia, from where I quote a passage below:

Note that Rindler observers with smaller constant x coordinate are accelerating harder to keep up. This may seem surprising because in Newtonian physics, observers who maintain constant relative distance must share the same acceleration. But in relativistic physics, we see that the trailing endpoint of a rod which is accelerated by some external force (parallel to its symmetry axis) must accelerate a bit harder than the leading endpoint, or else it must ultimately break

Just to keep things in the right perspective, it is important to remark that this effect for a length of some meters, and an acceleration $g$ for example is completely negligible.

Claudio Saspinski
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  • Thank you for the excellent answer, which brought interesting information which was new to me. Just clear this up for me, when you say: "it depends on approaching or receding from a light source. That is not right because in that case we could say either than time runs slower or runs faster in the accelerated frame" -- you mean time runs faster or slower in respect to the source of light, correct? It wasn't clear. Thanks again. –  Dec 30 '20 at 23:32
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    I mean that the last line in the quote of your question: "So for the person in the accelerated rocket time goes slower". It seems that if the rocket was accelerating to the opposite direction the conclusion would be: ""So for the person in the accelerated rocket time goes faster". And that would be wrong. – Claudio Saspinski Dec 31 '20 at 01:11