Time dilation and the human body

[Ricb]

TL;DR Summary

aging at light speed

As your velocity increases time in your frame of reference slows down with respect to other frames of reference until, at the speed of light, time essentially stands still. Hypothetically, I am travelling at the speed of light and, therefore, for me, time stands still. I am travelling to a star system that is 40 light years away. Does my body clock stand still or will my body still age even though time compared to the outside universe stands still?

 

[Dale]

It is not possible for a massive object to travel at the speed of light.

If you are traveling just under the speed of light in an inertial frame then you will age slowly in that frame.

 

[russ_watters]

Does my body clock stand still or will my body still age even though time compared to the outside universe stands still?

Your body clock is a clock. It behaves like other clocks.

 

[Ibix]

As your velocity increases time in your frame of reference slows down with respect to other frames of reference until, at the speed of light, time essentially stands still.

The first part is more or less true as far as it goes. Note that there are a lot of traps for the unwary with this line of thinking. The bit about the speed of light is incorrect, however. It is not possible to define time (specifically proper time, which is what you are talking about) for things moving at light speed.

Hypothetically, I am travelling at the speed of light and, therefore, for me, time stands still.

This is impossible. "Has non-zero mass and travels slower than light" and "has zero mass and travels at the speed of light" both turn out to be tautologies in relativity, so you cannot travel at the speed of light even in principle. And, as noted above, "time stands still" isn't accurate.

I am travelling to a star system that is 40 light years away. Does my body clock stand still or will my body still age even though time compared to the outside universe stands still?

Replacing your assumption of light speed with "near light speed relative to the star systems", Russ' answer is correct: your body is a clock like any other. Given sufficient fuel (which is a horrifyingly large amount, on the order of millions of tons per kilo of payload even with the most efficient rocket possible) and resistance to acceleration, you can make the journey in arbitrarily short time by your own experience.

 

[Orodruin]

As your velocity increases time in your frame of reference slows down with respect to other frames of reference until, at the speed of light, time essentially stands still.

Just to avoid a very common pitfall: Other reference frames will see you age slower. However, you will still feel and age exactly the same in your own rest frame. By symmetry, you will see other reference frames moving at some speed and hence they will be time dilated relative to you. There is no universal rest frame that decides which frames are moving or not.

 

[Janus]

To add a bit to what already has been said: While you, in your frame of reference, will not age any slower, It will take less time by your clock to reach that planet than it would according to someone on Earth. Let's say that you are moving at 99.99% of c relative to the Earth and this distant planet. According to the Earth, you will take just a smidge over 40 yrs to reach the planet, while aging only a bit over 0.57 years. You will also agree that you aged 0.57 years, but not because you aged slower. There is another aspect of Relativity besides time dilation in play: length contraction. Because both Earth and the planet are moving at 99.99% of c relative to you, they, and the distance between them undergo length contraction as measured from your frame of reference. As a result, the distance between them is only 0.57 light years according to your measurement, which only takes 0.57 years to cross at 99.99% of c.

 

[Orodruin]

which only takes 0.57 years to cross at 99.99% of c.

… which is what Earth and the planet are doing in the traveller’s rest frame. Obviously, the traveller is at rest in this frame and therefore not moving.

 

[phinds]

TL;DR Summary: aging at light speed

As your velocity increases time in your frame of reference slows down with respect to other frames of reference until, at the speed of light, time essentially stands still. Hypothetically, I am travelling at the speed of light and, therefore, for me, time stands still. I am travelling to a star system that is 40 light years away. Does my body clock stand still or will my body still age even though time compared to the outside universe stands still?

I suggest you learn the difference between time dilation and differential aging. As others have pointed out, you clearly have a serious misconception about these concepts.

 

[jbriggs444]

I suggest you learn the difference between time dilation and differential aging. As others have pointed out, you clearly have a serious misconception about these concepts.

This is just a quick explanation of the distinction between "time dilation" and "differential aging".

Time dilation is when you compare the wrist watch on someone's wrist against an array of clocks, all of which are synchronized and at rest in some chosen inertial frame. This array of clocks can be thought of as a coordinate system. If the person with the wrist watch is moving, one can observe that the wrist watch is advancing slowly compared to the sequence of readings on the clocks that it passes by.

That is to say that "proper time", the reading on the wrist watch, is advancing more slowly than "coordinate time", the readings on the local clocks.

Differential aging is when you have two people with wrist watches. They toodle around town on different paths at different speeds then meet up for dinner. One can observe that the elapsed time recorded on the two watches may be different when they get together again.

That is to say that the "proper time" elapsed on different trajectories between the same start event and the same end event can vary depending on the trajectory.

The number one gotcha that trips up students of special relativity is the relativity of simultaneity. When you synchronize an array of clocks to construct a coordinate system, it turns out that the synchronization will depend on the chosen standard of rest. There is a systematic skewing that takes place depending on the relative velocity between two inertial reference frames. Leading clocks lag.

 

[DaveC426913]

There is another aspect of Relativity besides time dilation in play: length contraction. Because both Earth and the planet are moving at 99.99% of c relative to you, they, and the distance between them undergo length contraction as measured from your frame of reference. As a result, the distance between them is only 0.57 light years according to your measurement, which only takes 0.57 years to cross at 99.99% of c.

[Oops. What he said...]

And the observer in the travelling spaceship will measure the distance from Earth to the target planet to be much less than 40 light years. .57 light years, in fact - which is why he can get there in such a short time.

Furthermore, he will observe everything (on average) to be greatly compressed in the direction parallel to his path - including the diameter of the target planet and Earth, both of which will appear like compressed discs - 8000 miles wide but less than 100 miles (1/(40/.57)ths of 8000) thick - the former hurtling flat-face-on toward him, and the latter hurtling flat-face-on away from him.