# B Time dilation and relative motion

Consider the example of flashing light in spaceship. The observer in the spaceshipe and the observer in the earth measure different times. Both observers could argue that the clock of the other tick slower(motion is relative). But is anyone right ? I mean the one will measure proper time (spaceship observer) and the other will measure a bigger time. But according to the spaceship observer the observer in Earth must measure smaller time. How is it possible ?

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#### Orodruin

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Your description of the setup is far too hand-wavy to offer you a relevant answer.

#### Ibix

Both observers could argue that the clock of the other tick slower(motion is relative).
Yes.
I mean the one will measure proper time (spaceship observer) and the other will measure a bigger time.
Both measure their own proper time. Who measures the longer time depends on what exactly you are measuring.
How is it possible ?
It's rather difficult to determine who you think is measuring what. However, almost always the answer to these questions is the relativity of simultaneity. The two observers don't generally agree exactly what is meant by the start of the experiment. Or, if they do, the details of agreeing it resolve the problem.

#### FactChecker

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They are both right. Suppose each has set up a full set of what he thinks are correct lights (clocks, timers, whatever) forward and backward. They are going in opposite directions with respect to each other, so they are comparing different sets of lights. Suppose the spaceship is moving to the right. As time goes on, the Earth "stationary" reference frame is observing the spaceman farther and farther ahead to the right where he will be. But the spaceship reference frame is observing the Earthling farther and farther behind the spaceship. So they are not comparing the same sets of lights as time goes on and they can both think that the other person's lights are blinking slow.

Another way that they are both right is that they both can do physics, including experiments with light, time, and distance, and get correct results as though they were stationary.

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#### Mister T

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Both observers could argue that the clock of the other tick slower(motion is relative)
That's an oversimplified and consequently often misunderstood description. Suppose the two clocks are moving relative to each other and share the same position once and only once. At all other times they are separated and you have the difficulty of determining what the reading is on a distant clock. You cannot understand the symmetry of time dilation without sorting out this difficulty. Look at a topic called the relativity of simultaneity.

#### David Lewis

As time goes on, the Earth "stationary" reference frame is observing the spaceman farther and farther ahead to the right where he will be.
Since the distance is increasing between blinks, they would need to compensate for light travel times to calculate the blink rate.

#### Nugatory

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Since the distance is increasing between blinks, they would need to compensate for light travel times to calculate the blink rate.
Indeed they do, and that is the Doppler effect. When they are approaching one another, both will receive flashes from the other's light more often than their own light flashes; and when they are moving away from one another, both will receive flashes from the other's light less often than their own light flashes.

Time dilation only becomes evident when they subtract out the light travel time, and then both conclude that the other one is emitting flashes less often than their own. To make sense of this we have to, as @Mister T says above, consider the relativity of simultaneity.

(I expect that David Lewis understands this just fine - this comment is directed to OP and others reading thgis thread).

#### FactChecker

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Since the distance is increasing between blinks, they would need to compensate for light travel times to calculate the blink rate.
Whether the blinks are seen by a single observer back at fixed location 0 (and light travel times calculated) or a set of Einstein-synchronized clocks are used to record events along the way seems like a detail that is not central to the arguement.

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#### Mister T

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Whether the blinks are seen by a single observer back at fixed location 0 (and light travel times calculated) or a set of Einstein-synchronized clocks are used to record events along the way seems like a detail that is not central to the arguement.
But you need that set of synchonized clocks to calculate those light travel times.

#### FactChecker

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But you need that set of synchonized clocks to calculate those light travel times.
Or you need to know the distance.

#### Lynch101

Consider the example of flashing light in spaceship. The observer in the spaceshipe and the observer in the earth measure different times. Both observers could argue that the clock of the other tick slower(motion is relative). But is anyone right ? I mean the one will measure proper time (spaceship observer) and the other will measure a bigger time. But according to the spaceship observer the observer in Earth must measure smaller time. How is it possible ?
You might find this video helpful: Simultaneity and Time Dilation

Starting out trying to wrap your head around Special Relativity (SR) it can be helpful to remember that SR is counter-intuitive, that is, it overturns many of our "common sense" ideas about how nature is or how it should be. This can make it challenging to assimilate - if you're coming at it from a lay background - bcos nearly every element of the theory will be met with cognitive resistance.

For that reason, it might be more helpful to try to suspend your intuitive ideas and, instead of trying to make SR fit with your existing model of understanding, try to approach it with an attitude of trying to understand what SR says. This, of course, is not an easy thing to do, but if you can remind yourself of this idea then you can circumvent the cognitive resistance more easily and arrive at a better under standing of what SR says.

#### FactChecker

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I agree that one must spend a lot of time before the basic principles of SR become more intuitive. However, the original question -- "How can both observers think that the other is slower?" is a logical question. Some explanation is necessary before that can be accepted at all, let alone become intuitive.

#### Lynch101

I'm not sure if this will be a help or a hinderance, but hopefully it will be helpful. If I were better able to illustrate it, it would help, but unfortunately I can't. Hopefully, the explanation is enough to help you picture it.

If you look at the image (from the yt video) you've got Albert on the left and Henry on the right: on the right you will see what Henry (on the train) "sees". For him, the photon in his light clock travels the perpendicular distance between the mirrors. On the left you will see what Albert (on the platform) "sees". He "sees" the photon travel a longer, diagonal path.

What you might not see from this picture is that the longer, diagonal path is also the distance that the photon in Albert's light clock travels. So, if you could see his light clock, the photon would go from one mirror to the other, get reflected, and travel part of the way back.

Now, if you imagine things from the perspective of Henry on the train. Again, he will "see" the photon in his clock travel the perpendicular distance between the mirrors. He will also "see" Albert's photon travel the diagonal path. The key difference is, however, Henry won't "see" Albert's photon travel the full diagonal path, from tick to tock. He will only "see" it travel a distance equal to the distance the photon in his clock travels.

If we think in terms of units of time, where tick-tock (from bottom mirror to the top mirror) represents one unit of time:

from Albert's perspective, when Albert's clock has counted "one and a bit" units of time (tick-tock-and a bit) Henry's clock will only have counted one unit of time. From Henry's perspective, when Henry's clock has counted one unit of time, Albert's clock will not yet have measured one full unit of time.

Hence, for Albert, Henry's clock runs slower while for Henry, Albert's clock runs slower.

#### Lynch101

I agree that one must spend a lot of time before the basic principles of SR become more intuitive. However, the original question -- "How can both observers think that the other is slower?" is a logical question. Some explanation is necessary before that can be accepted at all, let alone become intuitive.
Agreed. I was just working on that post. I'm not sure how clear the wording is though. More illustrations would be helpful.

"Time dilation and relative motion"

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