Near the speed of light time slows down but not at everyday speeds?

[Nick tringali]

Hello, just some general questions I have been thinking about
1. So as you approach the speed of light time slows down, but why not at everyday speeds like walking around? I know people are going to say time slowing down only matters at extremely high speeds. However, shouldn't time dilation effect all speeds not just very fast ones even if it is by a number that is so small? In my mind, there has to be an amount of time slowing down, even if it is so small, that occurs at everyday speeds. If time dilation doesn't occur at slow speeds and only fast ones, why is that the case, is there like a threshold speed? Can you calculate time dilation for someone driving there car at 20 miles per hour? Let me know if this question makes sense.

 

[Ibix]

1. So as you approach the speed of light time slows down, but why not at everyday speeds like walking around?

It does slow down (well - that's not really what happens at any speed, but it's a close enough description for the purposes of this question). If you and I synchronise our watches and then you walk to the other side of the room and back at speed $v$ then my watch will show elapsed time $T$ and yours will show elapsed time $\sqrt{1-\frac{v^2}{c^2}}T$. If you jog, (and if my mental arithmetic is reliable) that'll come out to around five hundred billionths of a nanosecond difference per second you spend jogging, which is why you probably haven't noticed.

 

[hmmm27]

The question makes plenty of sense : the answer is that time dilation isn't a linear function of velocity : graph

 

[PeroK]

Hello, just some general questions I have been thinking about
1. So as you approach the speed of light time slows down, but why not at everyday speeds like walking around? I know people are going to say time slowing down only matters at extremely high speeds. However, shouldn't time dilation effect all speeds not just very fast ones even if it is by a number that is so small? In my mind, there has to be an amount of time slowing down, even if it is so small, that occurs at everyday speeds. If time dilation doesn't occur at slow speeds and only fast ones, why is that the case, is there like a threshold speed? Can you calculate time dilation for someone driving there car at 20 miles per hour? Let me know if this question makes sense.

There is no such thing as approaching the speed of light, only approaching the speed of light relative to some reference frame. Motion is relative, not absolute.

The situation is complicated by gravity on the surface of the Earth, but in an inertial scenario (no forces and no gravity) velocity-based time-dilation is reciprocal. If you are moving relative to someone else, then you both measure the other's time as dilated by the same amount. If you are approaching the speed of light relative to them, then they are approaching the speed of light relative to you.

 

[BWV]

I calculated one time that my lifetime of commuting had added another few seconds to my lifespan, but was disappointed it was not enough to justify taking up cigarette smoking

 

[kuruman]

Time dilation can be calculated at any speed. All you need to find is the gamma factor,$$\gamma=\frac 1 {\sqrt {1 - \frac {v^2} {c^2}}} .$$ For slow speeds such as 20 miles per hour or 9 m/s calculating the gamma factor by plugging in the formula becomes problematic because it is very close close to 1 since $$\frac{v^2}{c^2}=\dfrac{1}{10000000000000000}=10^{-16}.$$A series expansion comes to the rescue at this point. To an extremely good approximation we can write $$\gamma=\frac 1 {\sqrt {1 - \frac {v^2} {c^2}}}\approx 1+\frac {v^2} {2c^2}=1+5\times 10^{-17}.$$ This says that if your twin brother travels at 20 miles per hour for a year as measured by his clock, you will age by 1 year and an additional $\frac {v^2} {2c^2}=1.4\times 10^{-8}~\mathrm{s}=14~\mathrm{ns}.$

 

[Nick tringali]

Thank you all.

 

[Ibix]

I calculated one time that my lifetime of commuting had added another few seconds to my lifespan, but was disappointed it was not enough to justify taking up cigarette smoking

Much as I like this comment, I ought to point out that commuting has no effect on your lifespan - you still only experience your three-score years and ten. From your perspective, your stay-at-home twin ages slightly faster than you.

(Note that the scenario discussed here is different from the symmetric I-see-your-clock-tick-slow-you-see-mine-tick-slow behaviour for inertial motion. This is fine because at least one of you is not in inertial motion.)

 

[BWV]

Much as I like this comment, I ought to point out that commuting has no effect on your lifespan - you still only experience your three-score years and ten. From your perspective, your stay-at-home twin ages slightly faster than you.

(Note that the scenario discussed here is different from the symmetric I-see-your-clock-tick-slow-you-see-mine-tick-slow behaviour for inertial motion. This is fine because at least one of you is not in inertial motion.)

You must not be married, this was all from the standpoint of my spouse