How Does Time Dilation Affect Perception of Speed in Relativity?

[FrankFrankov]

Hi, forgive my ignorance on this subject, but I was wondering if you could help me understand how time slows down the faster something moves:

Here's where I have the problem:

Imagine a room with person1 sitting in a chair clapping once every minute. Now image person2 is sitting in a machine that can spin him around the room as fast as he wants up to near the speed of light. According to the theory of relativity, as person2 goes faster around the room, the slower time will pass for him, thus person1 will seem to be clapping faster, even so fast as to be a hum.

Doesn't this completely conflict with the logic that the faster you move the slower things around you seem? I.E. if I was gifted with a superhuman metabolism, where I could race around and do things much much faster than everyone else, I would perceive them as slower than me, not FASTER than me.

So why whould person2 be able to watch person1 age faster than him? Shouldn't person1 seem to be slowed down to almost a stop?

 

[JesseM]

Doesn't this completely conflict with the logic that the faster you move the slower things around you seem? I.E. if I was gifted with a superhuman metabolism, where I could race around and do things much much faster than everyone else, I would perceive them as slower than me, not FASTER than me.

It seems to me you're confusing two different meanings of "the faster you move" here--the mere fact that you are hurtling through space more quickly doesn't mean the processes in your body should be going at a faster rate. If you're in a car and you hit the accelerator, you'll be passing by marks on the road more quickly, but why would this cause your metabolism to increase?

 

[FrankFrankov]

It seems to me you're confusing two different meanings of "the faster you move" here--the mere fact that you are hurtling through space more quickly doesn't mean the processes in your body should be going at a faster rate. If you're in a car and you hit the accelerator, you'll be passing by marks on the road more quickly, but why would this cause your metabolism to increase?

Fair enough, forgive my use of "Metabolism" in that paragraph then, and replace it with: "machine that can zoom me around faster than everyone else".

The actual issue is the perceived slowness of everyone else when I'm going faster.

 

[JesseM]

Fair enough, forgive my use of "Metabolism" in that paragraph then, and replace it with: "machine that can zoom me around faster than everyone else".

OK, but are you still saying there's some reason to think a person riding a machine in a circle would see a person at the center clapping slower as opposed to faster?

The actual issue is the perceived slowness of everyone else when I'm going faster.

There are two points that might be helpful here. One is that the time dilation formula is only intended to tell you how clocks slow down in the frame of an inertial observer, that is, one who is not accelerating--acceleration can mean either changing speed or changing direction, so an observer moving in a circle is not moving inertially (all non-inertial observers can tell they're moving non-inertially because they'll feel G-forces, like the apparent 'centrifugal force' experienced by an observer moving in a circle). The time dilation formula is no longer expected to work in the frame of a non-inertial observer. For inertial observers, time dilation is fully reciprocal--if you and I are moving at constant velocity relative to one another (constant velocity=constant speed and direction), then in each of our own rest frames it will be the other person's clock which is ticking slower than our own.

The second point is that even for an inertial observer, there is a distinction in relativity between how fast you see clocks ticking vs. how fast they are actually ticking in your frame. For an inertial observer, the speed a clock is ticking in their frame depends on compensating for the fact that the light from different ticks of the clock may have been emitted at different distances from them, and therefore took a different amount of time to reach them (this is the origin of the Doppler effect). Here's a little example I gave in another thread: suppose in 2036 I see the image of a ship 26 light years away according to my ruler with its clock reading 50 years, and then 4 years later in 2040 I see an image of the same ship 20 light years away according to my ruler with its clock reading 58 years. This means I visually saw the clock advance 8 years (58 - 50) in 4 years of my time (2040 - 2036), so visually it looks like it's sped up by a factor of 2. But I can correct for the time the light from each event took to reach me and conclude that the first event actually happened at a time-coordinate of 2036 - 26 = 2010 in my frame, and the second happened at a time-coordinate of 2040 - 20 = 2020 in my frame, meaning that in my frame the clock actually took 10 years to advance 8 years from 50 to 58, so it was slowed down by a factor of 0.8 in my frame. This is what would be predicted by the time dilation formula, since if it was 26 light years away in 2010 and 20 light years away in 2020 in my frame, it traveled 6 light years in 10 years so it must have been going at 0.6c, and the time dilation formula says a clock moving at speed v will be slowed down by a factor of squareroot(1 - v^2/c^2), and squareroot(1 - 0.6^2) = squareroot(0.64) = 0.8.

 

[Anthea Lawn]

Your example is also a little complicated by having the observer travel round in a circle which means that his distance from the clapping person is actually the same at all times. This is a different scenario to the observer traveling in a straight line (eg in the infamous railway carriage often used as an analogy in relativity textbooks). A further complication (which I'll not get into here) is that while the observer is maintaining a constant *speed*, his *velocity* is continually changing (as velocity is a vector quantity)

 

[FrankFrankov]

I read what you guys are saying, but I still don't understand it. I do understand the idea about how person2's brain has no reason to think person1 is acting slower than him, that makes sense.

So person1 wouldn't be clapping faster as person2 goes faster? Is this because person2 is always the same distance from person1? What's the reasoning behind this other than it simply "breaks the equation"?

The way I see it, (probably wrong - but I want to understand the concept, not the math) if person2 were to instead traveling inertly away from person1, then returning to see that person1 has aged, wouldn't the return trip be a negative number, cancelling out the leaving trip? Essentially putting us in the same boat as the circling person2?

Isn't this quite convenient that we can never OBSERVE something age before our eyes?

 

[Jonathan Scott]

I read what you guys are saying, but I still don't understand it. I do understand the idea about how person2's brain has no reason to think person1 is acting slower than him, that makes sense.

So person1 wouldn't be clapping faster as person2 goes faster? Is this because person2 is always the same distance from person1? What's the reasoning behind this other than it simply "breaks the equation"?

The way I see it, (probably wrong - but I want to understand the concept, not the math) if person2 were to instead traveling inertly away from person1, then returning to see that person1 has aged, wouldn't the return trip be a negative number, cancelling out the leaving trip? Essentially putting us in the same boat as the circling person2?

Isn't this quite convenient that we can never OBSERVE something age before our eyes?

In this case, the one going round would indeed see the person in the middle clapping faster by the expected time dilation rate based on their speed, and the one in the middle would see the one going round to have a slower time rate.

 

[JesseM]

So person1 wouldn't be clapping faster as person2 goes faster? Is this because person2 is always the same distance from person1? What's the reasoning behind this other than it simply "breaks the equation"?

No, person1 would be clapping faster as person2 sees things visually, sorry I wasn't clear on that. My point about inertial vs. non-inertial observers is that since person2 is moving non-inertially, the time dilation formula doesn't work from his perspective (i.e. person2 can't say that since person1 is moving relative to him, that means person1's clapping rate is slowed down rather than sped up in his frame). If person2 was instead moving in a straight line at constant speed relative to person1, then each would measure the other one's clapping to be slowed down relative to their own (though as I said, there's a difference between what each one measures in their frame and what they actually see, but what they see would still be reciprocal--if they were moving apart they would each see each other clapping slower, if they were approaching one another they would each see the other clapping faster).

The way I see it, (probably wrong - but I want to understand the concept, not the math) if person2 were to instead traveling inertly away from person1, then returning to see that person1 has aged, wouldn't the return trip be a negative number, cancelling out the leaving trip? Essentially putting us in the same boat as the circling person2?

If person2 turns around, then person2 is no longer moving inertially. Person1 is moving inertially, so the time dilation formula works fine in her frame--since person2 is moving at high speed both when traveling away and traveling back in her frame, person2's clock will be running slow on both phases of the trip in her frame, so person2 will have aged less in total when they meet.

Isn't this quite convenient that we can never OBSERVE something age before our eyes?

But you do--if you look at the numbers in my example, I saw you age 8 years in 4 years of my own time, for example.

 

[FrankFrankov]

got it. thanks guys.