Time dilation and lorentz transformation

[nn542]

i have a quick question, that is

according to the lorentz transformation, the moving frame will have the longer time than the frame in the rest.

so is that means if I'm on a moving car for my whole life, my time will greater than those who are in the rest relative to the earth?

 

[phinds]

i have a quick question, that is

according to the lorentz transformation, the moving frame will have the longer time than the frame in the rest.

so is that means if I'm on a moving car for my whole life, my time will greater than those who are in the rest relative to the earth?

You have it backwards. If I stand still my whole life and my twin brother drives around in a car his whole life, when we finally meet up to choose our burial plot he will be something like a microsecond younger than me. If he speeds around in a really fast spaceship, he might be noticeably younger than me.

 

[ghwellsjr]

Time Dilation means it takes longer for someone who is moving with respect to a frame that someone who is stationary in the frame.

 

[bobc2]

Time Dilation means it takes longer for someone who is moving with respect to a frame that someone who is stationary in the frame.

What? That's a little confusing, ghwellsjr. Why not use a block universe Loedel space-time diagram--it becomes clear that each sees the other's clock ticking more slowly (time dilation). And you get a two-fer--length contraction comes along for free in the diagram.

 

[Agerhell]

i have a quick question, that is

according to the lorentz transformation, the moving frame will have the longer time than the frame in the rest.

so is that means if I'm on a moving car for my whole life, my time will greater than those who are in the rest relative to the earth?

Actually, the fact that we are living on a spinning Earth complicates things. If you keep going west for your whole life your clock will actually tick faster the faster you go. If you go east your clock will tick slower. So in an earth-bound scenario, you will have to take the rotating Earth into account.

 

[phinds]

Actually, the fact that we are living on a spinning Earth complicates things. If you keep going west for your whole life your clock will actually tick faster the faster you go. If you go east your clock will tick slower. So in an earth-bound scenario, you will have to take the rotating Earth into account.

No, if you are comparing someone traveling on Earth relative to someone stationary on Earth the rotation is irrelevant and that is the scenario the OP posited.

I think my original post is the answer to exactly what the OP asked.

 

[PeterDonis]

if you are comparing someone traveling on Earth relative to someone stationary on Earth the rotation is irrelevant and that is the scenario the OP posited.

This is true only as long as none of the travelers go all the way around the Earth. (I agree that the OP probably intended the scenario to be restricted that way.) But if one traveler goes westward all the way around the Earth, he *will* experience slightly more elapsed time than someone who remains stationary on the rotating Earth, when the two meet up again. This is just a version of the Hafele-Keating experiment with no altitude change.

 

[ghwellsjr]

Time Dilation means it takes longer for someone who is moving with respect to a frame that someone who is stationary in the frame.

What? That's a little confusing, ghwellsjr. Why not use a block universe Loedel space-time diagram--it becomes clear that each sees the other's clock ticking more slowly (time dilation). And you get a two-fer--length contraction comes along for free in the diagram.

The OP is not confused that Time Dilation happens for a moving observer. He realizes that dilation means expansion, not contraction (like is true for lengths). He is confused by how time dilation results in a moving observer aging more slowly than a stationary one.

I did not mean to detract from phind's excellent answer, only to point out that it takes longer for the moving observer to reach the point where he needs to choose a burial plot than it takes for a stationary observer. This is the sense in which time dilates (expands, gets bigger, takes longer) for the moving observer. Seconds take longer, minutes take longer, it takes longer to get to your next birthday, everything takes longer.

 

[mfb]

No, if you are comparing someone traveling on Earth relative to someone stationary on Earth the rotation is irrelevant and that is the scenario the OP posited.

Stationary on the ground is not stationary on Earth - and in particular, it is not an inertial system. You can age quicker relative to someone standing on the ground, if you (partially) cancel the rotation, by staying at the poles or always moving westwards with the appropriate velocity.

 

[PeterDonis]

You can age quicker relative to someone standing on the ground, if you (partially) cancel the rotation, by staying at the poles or always moving westwards with the appropriate velocity.

I agree about always moving westwards, *if* you hold latitude constant; but someone standing still at the poles ages at the same rate as someone standing still on the equator ("standing still" means at rest with respect to the Earth's surface in their vicinity). The Earth's surface is an equipotential surface (at least, it is if we idealize it as an oblate spheroid of rotation); that means it is a surface that equalizes the rate of time flow, taking the rotation into account.

From the standpoint of an inertial frame, someone on the Equator is moving relative to the poles, making their clock run slower, but they are also at a higher altitude because of the Earth's equatorial bulge, making their clock run faster. The Earth's surface (in the idealized case) is shaped so that the two effects exactly cancel.

 

[mfb]

You are right, I forgot to include GR.

 

[phinds]

Both Peter and mfb pointed out things that I DID overlook --- the all westward/eastward travel and the use of the poles. I wish I could say I was just trying to avoid complications but no, I really did just overlook them.