Science desk
< December 1	<< Nov \| December \| Jan >>	December 3 >

Welcome to the Wikipedia Science Reference Desk Archives
The page you are currently viewing is a transcluded archive page. While you can leave answers for any questions shown below, please ask new questions on one of the current reference desk pages.

December 2

Velocity and acceleration in special relativity

I was thinking that acceleration can always cause time dilation (clocks tick slower) in special relativity but when I tried to imagine the following, I got confused.

Imagine 3 frames A, B, C such that frame A is our ancestors stationary frame, B is an intermediate frame with velocity v1 relative to A, and C is our stationary frame after our ancestors traveled to it with a precise clock. Frame C has a relative velocity v2>v1 (all are in the x direction, in empty space without gravitational effects for simplicity).

We were born in Frame C without knowing anything about our ancestors journey and we decided to visit Frame A. (Accelerating first to frame B then decelerating to frame A). In this case how come we will have another time dilation (additional slow ticking in clock) while we were just travelling back to the original (supposedly stationary frame)?

We are supposed to assume that we were stationary in frame C without knowing the truth, and so we will assume that we will have time dilation during our journey from C to A not the reverse (and if I am right then even our ancestors should not had been confident that they had time dilation unless they witnessed it). I hope you can explain where I got wrong.Almuhammedi (talk) 20:05, 2 December 2024 (UTC)[reply]

The essence of the theory of relativity is that notions such as velocity are only meaningful relative to the frame of reference of an observer. Observers using different frames will measure different values. This is not a matter of being right or wrong. It is meaningless to say that an observer is stationary in their frame of reference "without knowing the truth". They are stationary by definition. Time dilation of a moving clock can only be observed from a frame of reference relative to which the clock is moving. For an observer holding the clock, the clock is not moving, so they will not themselves observe time dilation during their journey. Only outside observers can observe this. --Lambiam 01:40, 3 December 2024 (UTC)[reply]

I introduced the 3 frames to simulate what happens to an atomic clock on a traveling plane.

Of course there is a reference relatively (stationary clock) that is supposed to show the difference.

In this case assume that our ancestors traveled with 2 atomic clocks x, y to frame C but we used only one of their clocks, x to travel to frame A and then returned back with it to frame C.

From our perspective, we considered the travelling clock (x) as the accelerated clock (as well as us) which should suffer time dilation after returning to our frame C.

However, to an external observer relatively stationary to frame A, who witnessed our ancestors travel he will understand that Clock x only reduced its speed when traveled to its original frame A and then returned to frame C which means it suffered temporary less time dilation than clock y.Almuhammedi (talk) 06:50, 3 December 2024 (UTC)[reply]

So there are two clocks at C that show the same time. One clock, y, remains at rest at C. The other clock, x, is moved from C to A and back to C. Then, on return, x will be running behind y. What happened before x's journey from C to A and back is not relevant. --Lambiam 15:14, 3 December 2024 (UTC)[reply]

What makes you so sure?

Just return both clocks to their original frame A and compare the results with a third stationary clock in frame A. I think you will see the opposite of what you you've said. Almuhammedi (talk) 16:50, 3 December 2024 (UTC)[reply]

I may have some confusion between acceleration and deceleration here which caused my wrong conclusion.Almuhammedi (talk) 17:52, 3 December 2024 (UTC)[reply]

I suggest that you read our article on the twin paradox. BTW, I think that the (sourced) statement that "[t]here is still debate as to the resolution of the twin paradox" is misleading. The twin paradox is only paradoxical in the sense that it is a counterintuitive effect predicted by the laws of both special and general relativity. The issue is that the explanations commonly provided – other than "this is what the laws tell us; do the maths yourselves" – are ad hoc explanations for special cases and do not cover all conceivable scenarios exhibiting the counterintuitive effect. --Lambiam 08:54, 4 December 2024 (UTC)[reply]

Snow questions

Two questions related to snow that I have wondered in recent times, not homework.

Why do most European countries lack snowfall data in their weather observations? Without data, snowfall cannot be specified since snowfall is not same as change of snow depth from one day to next.
Can Lake Geneva, Lake Constance and Balaton ever produce lake-effect snow? --40bus (talk) 21:58, 2 December 2024 (UTC)[reply]

@40bus 1. Presumably because in a temperate climate it's almost impossible to measure. What falls as snow on higher ground (which may or may not settle as snow) may fall as sleet or rain on lower ground, or it will turn to water or ice in the rain-gauge. Shantavira|^{feed me} 10:01, 3 December 2024 (UTC)[reply]

But US, Canada and Japan have continental climate (at least in some areas), so why then they measure? And is snowfall deducible from precipitation value so that 5 mm of precipitation equals 5 cm of snowfall? --40bus (talk) 10:54, 3 December 2024 (UTC)[reply]

No, not accurately. Snow comes in many different consistencies and levels of moisture, from tiny dry flakes to huge wet masses that fall as almost pre-made snowballs. Our (Canada) weather forecasts include estimates for amounts of snow to land, but they're hilariously inaccurate for the simple reason that snow, unlike liquid water, can pile up and drift. We had a dumping of snow this past weekend and the thickness of snow on one varied quite a bit just across the width of my driveway. So, should the record show the 15 cm in my front yard, the 10 cm in my driveway or the 8 cm in my neighbour's driveway? Depending on the type of snow falling, that ratio would change as well. Matt Deres (talk) 18:15, 3 December 2024 (UTC)[reply]

"Hilariously inaccurate" seems a gross exaggeration to me. The measurement should indicate the average depth of new snow over an area large enough that the variations between your front yard, your driveway, and the next driveway are irrelevant. --142.112.149.206 (talk) 09:17, 4 December 2024 (UTC)[reply]

Spoken like someone unfamiliar with snow. It's not really a knock on the forecasters; it's just the nature of the material. To measure rainfall, it's not so complicated: rain may get blown about, but it typically only lands once. Not so with snow. It lands, gets picked up, lands, gets picked, and so on. If you picked a spot in your yard to measure, you'd find the level going up and down as the day transpired. So, from 6pm to midnight you'd get 10 cm of accumulation, then from midnight to 6am you'd get -3 cm of accumulation. Rain also doesn't "pile up" in areas. It lands unevenly, of course, but that hardly matters because it drains and gets absorbed. Snow piles up in chaotic ways, depending on the wind, the nature of the snow, and the terrain. Some of the worst whiteout conditions occur when there's no precipitation at all. Matt Deres (talk) 20:21, 4 December 2024 (UTC)[reply]

True, but irrelevant to reporting or predicting the amount of snow that falls. Which I was shoveling today, by the way. You accuse the forecast of inaccuracy because it does not report what you want it to, that's all. --142.112.149.206 (talk) 06:23, 5 December 2024 (UTC)[reply]

I'm not accusing them of anything; just reporting the plain fact that there's no accurate way of measuring it. If we could easily see accumulations of rain, we'd recognize that they too are broad estimates. Snow is worse, as I've detailed above. We just don't have a methodology for measuring snowfall that accounts for the fact that the amount that came out of the clouds bears little resemblance to what builds up on the ground. Matt Deres (talk) 16:11, 6 December 2024 (UTC)[reply]

The Dutch weather office collects hourly snowfall data at some (not all) staffed weather stations, most of them at airfields, but apparently not at the more common unstaffed weather stations or the even more common precipitation stations. Maybe it's hard to measure automatically.

Snow can fall in temperatures slightly above freezing, rain can fall slightly below freezing, so the combination of precipitation and frost doesn't tell you about snow. Usually the snow melts within hours. On most days with frost, it only freezes part of the day; we used get about 50 freeze-thaw cycles per year in the east of the country, fewer along the sea, but I think that has halved in recent years. PiusImpavidus (talk) 14:54, 3 December 2024 (UTC)[reply]

Re your question 2 - According to our article that you linked above "a fetch of at least 100 km (60 mi) is required to produce lake-effect precipitation". Lake Geneva, the largest lake in Europe, is only 95 km (59 mi) along its longest side (it's crescent-shaped, so the longest straight line would be somewhat shorter), so it seems unlikely (FYI: "fetch" is the distance that an air mass travels over a body of water). Alansplodge (talk) 21:15, 4 December 2024 (UTC)[reply]

What's more, any lake effect would be overwhelmed by the effect of the surrounding mountains. This would also be the case for Lake Constance. Lake Balaton has no surrounding mountains, but is only 75 km long and so shallow that it can cool quickly, reducing the lake effect. There are several larger lakes in the north-east of Europe (Vänern, Vättern, Ladoga, Onega).

BTW, interesting etymology. Lake Geneva, a name appearing only in the 16th century, is named after the English exonym for the city of Genève, derived from Latin Genava and originally Celtic Genawa (compare the Italian city of Genova). The older local name of the lake is Léman, from a (Celtic?) word for lake, or pleonastically Lac Léman (already Lacus Lemanus in Roman times). Lake Constance, a name in use since the 15th century, is named after the German city of Konstanz, in English known by its French exonym Constance, derived from Latin Constantia, probably after emperor Constantius. Locally, the lake is since the 6th century known as something like Bodensee. Names from Roman times are known, but no longer in use. PiusImpavidus (talk) 11:22, 5 December 2024 (UTC)[reply]