Is a day longer than 24 hours on top of Mount Everest?

Question

If I had two identical watches and placed one at sea level and one on top of Everest, would they keep the same time?

Answer 1

The simple answer is no. It would actually be shorter.

In simple newtonian mechanics an object on the top of everest and an object at ground level will take the same amount of time to circle the earth (ie one day) and return to their initial positions. However the object on top of everest will be moving faster. Take a large revolving door for example. If two people enter the door and one goes to the middle of the door (by the pivot) and the other goes next to the edge of the door, the person at the edge will have to move faster than the guy at the middle to keep up.

However, in reality newtonian mechanics is only an estimate. It is Einstein's theory of relativity that brings about the most accurate timings. Using Time dilation methods it can be shown that the object on top of everest will have an ever so slightly shorter day because it is moving faster.

Answer 2

for all intents and perpoises no they will not be the same. IF you want to be very picky, and you have very very very accrurate atomic clocks, then yes they will read differant times.

The gravity on the top of mt everest will be slightly less than at sea level, thus you will have to make a small relitivistic correction.

Also because it is farther away from the surface of the earth it will be moving a little faster as well, so you will have to make another very small relitivistic correction.

There was an experiment where they put an atomic clock on to a plane and flew it around for a while to try to measure time dialation, and they did come up with a small change ... but I do not think the clocks would be acurate enouph to get a change on the top of mt everest.

Answer 3

Since a watch can be either mechanical or electrical and each measures 'time' using a different principle, I think that, theoretically you might find differences between a pendulum, a balance wheel and a crystal and an atomic controlled clock.

This highlights the fact that our measurement of time is essentially artificial and depends on our observations of things behaving in a regular manner.

In fact the day length of 24 hours is an average over the year if one measures a day as being from midday to midday (one revolution of the earth on it's axis in relation to the sun, such that the sun is at the same latitude. This not only varies over a year by from approximately -15 minutes to +18 minutes but it is also increasing slowly.

I think that what you are getting at is that the watch on Mount Everest is moving faster than the watch at sea level but on average I don't think this is the case. One has to consider the total speed of the earth in relation to some fixed point. Not only is the earth rotating on its axis, but it is also rotating round the sun which itself has a motion through the galaxy which in turn has a motion in relation to other galaxies. Can one even say that it stops there - that there is a point somewhere in the Universe which is absolutely motionless?

If one adds all of these motions - the speed of which may fractionally affect the time shown by two watches at different points, the net result would be practically the same for both watches, so the answer to the question would be that there might be minimal variations due to rotational motion (just as a point on the wheel of a car changes in speed in relation to the road from 0 to twice the speed of the vehicle) but the average speed of the watches is the same, so the time they show will be essentially the same.

There is a point in an argument such as this where practicality and theory have to part amicably. What matters for a theoretical scientist is absolutely of no importance to someone involved in, for example, tracking an expedition on Mount Everest, or to a goatherd in the Himalayan foothills. The point at which the argument becomes academic is different for each, so one can never say that one conclusion is 'wrong' and another is 'right' if both are saying essentially the same thing in more or less accurate terms.

Answer 4

OK,

A day is defined as the time it takes for the earth to make a full rotation.

However, you travel at a faster positional speed the further away from the core of the Earth you go.

In special relativity, the faster you travel, the slower time becomes. The difference in speed between sea-level and Everest is minute and any time difference could only be measured using a caesium clock.

But, the difference would be there.
The day on top of Everest would be longer by a very small fraction of a second

Answer 5

Well, air pressure and temperature might affect the movement of your watch, depending on what type it was.

But in relation to the distance from the Earth to the sun, the distance between sea level and the top of Everest is miniscule. Everest orbits the sun right along with the rest of the planet, so the time would be the same.

Answer 6

Occasionally, a leap second is added on to the 24th hour of December 31st or June 30th and sometimes both. So if Everest and the sea-level measurement-point are either side of the International Date Line, carefully-chosen 24-hour periods would be 1 seond difference in length, but not because of altitude.

Answer 7

Actually, the watch on Everest is further from the center of rotation ... in a higher "orbit" around the center of the Earth ... so it travels further in the same amount of time.
The faster you travel, the slower time travels. The watch on Everest (if it were very very very accurate) would show slightly LESS time elapsed than the one at sea level.

Answer 8

Consider this - the earth rotates once every 24 hours. If you are at sea level or on Mount Everest you still rotate once every 24 hours.

However, I think Einstein may have been on to something.

Answer 9

The length of a day is determined by the rotation rate of the earth, so whether you are down a hole or on top of a ladder, it's always EXACTLY the same length.

HOWEVER

your linear speed through space is greater (relatively) the further you are from your axis of rotation. Your axis of rotation is a line, by the way, not a point, so latitude is what matters. Your linear speed one foot to the left of the north pole is bugger all, but your linear speed at the equator is much greater. On top of a mountain near the equator is greater still (but not by much).

Relativity should (I think) mean that time should run slightly slower at the equator as a result of this. But maybe it doesn't work quite like that when things are spinning rather than moving in a "straight" line.

Any proper physicists know the answer to this?

Answer 10

No. they will have about the same time. Its just the same as asking if they dont have 24 hours a day in the higher latitudes. If your watches are accurate to the milisecond or more, they may have small differences, but it will not be due to the differences in altitude, theoretically.

Anyway, the earths rotation does not take exactly 24 hours. It takes about 23 hours 59 minutes 45 seconds or somewhere along that line.