relativity time dilation questions

Changing the rest frame isn't just a matter of labelling, because your time and distance measurements depend on what frame they're made in. Even the time ordering of events can change.

The classical example of the latter is the relativistic garage. Say you have a garage with a door at each end. The garage is 20 feet long, and you have a very fast limo that's 30 feet long in its rest frame. If you're standing next to the garage as the limo approaches at 0.9c, you'll measure its length as 30*sqrt(1-.9**2) = 13 feet long, so it will easily fit in the garage (albeit briefly), and you can (conceptually) close both doors at once.

If you were driving the car, you'd see the car as 30 feet long, and the garage as 20*sqrt(1-.9**2) = 8.7 feet long--far too short to fit the whole car. But in that frame, the doors don't close simultaneously--the second one opens again before the first one closes.

Cheers

Phil Hobbs

What Phil said, Space time Physics by Taylor and Wheeler is a great intro to special relativity. (You can find it as a free PDF on the web)

George H.

Yeah, I really should have spent some time getting my head around Special Relativity back when I could do the math...

One thing that always bothered me was regarding the red shift and speed of light. If objects at the furthest point in the universe are receding from us at close to C then we too are receding from them at the same speed. Therefore the speed of light in our neighbourhood is determined by the base line which is already close to C. Which means the actual speed of light could be much faster IF you could figure out what the base reference point was.

How on earth do you get a base reference point then? Certainly the rubber sheet doesn't answer this.

I'm sure I'm missing something and to be quite honest have done no research on the matter as busy with my regular life and businesses...

I guess I better track down that book by Taylor & Wheeler.

And Archive.org rides to the rescue once again:

Just wasting time - sorry!

John :-#)#

There is no base reference point. Both the star at the edge of the universe and we, agree that we are moving away from each other at some speed. You can pick either one as your reference frame to measure things from.

That's it. George H.

I was going to say, great example but what always gets me is: When the car stops and both observers are in the same frame, then who has aged more?

But then I thought of another question about the example. If you are inside the garage and the first door is receding and the second is approaching, then it makes sense that you would see the first close after the second. But if you're riding in the trunk (or just more than

Time runs slower for the person traveling near light speed. (We measure the lifetime of muons (2 u sec) that are created in the upper atmosphere. (cosmic ray collisions.) If you look at the muon flux as a function of height, there is very little change... because the 'clock' on the muons is running much slower. If they decayed in 2 u sec. regardless of speed, then you'd have 1/2 left after ~600 m (c * 2 u sec.) But almost all of them make it to the Earths surface for us to observe.)

It's mostly just that the door closings happen at different times. (not simultaneously.) Try reading some of the Taylor/ Wheeler book.

George H.

Dear Jamie, there are two types of time dilation : apparent time dilation an observer sees on a receding clock and the real type of time dilation happens during acceleration.

The first type is an illusion, so it works both ways. the second type is molecular wavefunctions being balanced in each proton with the inertial effects of acceleration of that proton electron pair.

ahmmm.... why post in this group. There is a relativity newsgroup...

-- Kevin Aylward

According to standard Special Relativity, whilst pop accounts typical explain it this way, it is incorrect.

According to SR, time does not run slow for the object moving relatively. The accepted description is that the object takes a "longer path in space-time". For example, traveling a straight path from LA to San Francisco will take X miles. Traveling via Reno, will take longer. The odometer reads different, not because its calibration changes with the straight line distance, but because it took a longer path. A clock is equivalent to the odometer .

-- Kevin Aylward

Great thought experiment. Say the garage doors can open and close very qui ckly. The second door (furthest away from the approaching limo) is already closed. The first door is already open. The car reaches the garage and u pon the end of the car clearing the first door sends a signal to open the s econd door. I suppose the issue is that the open signal can't travel faste r than c, so it does not arrive in time to open the second door... but, if it could travel instantly... would the door be opened in time? What woul d the observer at the garage see? What would the driver see? Would the ca r plow through the door?

Rick C.

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The aging is not caused by the relative speed since both observers see time slow for the other one. The aging is faster for the one who does not accelerate. The one who endures the acceleration has less time pass.

So to get the two into the same speed frame, which one accelerates to make that happen?

I don't think it has to do with the direction of motion.

Rick C.

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Just to be clear, it is not that the muon clock runs fast or slow, the muon clock *appears* to us to run slow. The muon sees the clock running at normal speed and anyone going in the same direction at the same speed will also see that.

Rick C.

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Ahh OK... I really only have a pop-sci understanding anyway.

I guess you can also say the muon (traveling near light speed) sees a shorter distance to the surface of the earth. (That's how I would describe it when 'travelling' with the muon.)

George H.

That's a form of the 'twin paradox'. If I take a relativistic spacecraft and fly a year out from Earth and then back again, I'll have aged less than you. But that isn't a paradox at all, because our histories are not comparable--I've accelerated to and from relativistic speed three times and you haven't.

The car doesn't collide with the doors in either reference frame. Simultaneity doesn't apply in relativity.

Cheers

Phil Hobbs

You'd be better off sticking to oscillators. ;)

Cheers

Phil Hobbs

It's just a thought experiment. A 3000-kg limo moving at 0.9c would have a kinetic energy of

KE = 3000 kg * (3e8 m/s)**2 * (1/sqrt(1-0.9**2) -1) = 3.5E20 J, a little matter of 83,600 megatons (*). Just the gammas from the impact fusion of air molecules would fry you if you were anywhere nearby, never mind the blast wave.

Cheers

Phil Hobbs

(*) A megaton is defined as 1E15 calories, or 4.18E15 joules.

Hi,

Ok that makes more sense! Gravity (acceleration field) is the ultimate time anchor! Thanks!

So lets see if the online calculator makes sense, if acceleration is the only thing that will change the absolute time difference between two objects:

Two examples:

1. For a journey from Earth, accelerating to 0.999C over a 0.5 light year distance, then decelerating over a 0.5 light year distance, and heading back towards earth: accelerating to 0.999C over a 0.5 light year distance, then decelerating over a 0.5 light year distance. (total trip distance 2 light years)

1. For a journey from Earth, accelerating to 0.999C over a 0.5 light year distance, then coasting for a 1 light year distance, then decelerating over a 0.5 light year distance, and heading back towards earth: accelerating to 0.999C over a 0.5 light year distance, then coasting for a 1 light year distance, then decelerating over a 0.5 light year distance. (total trip distance 4 light years)

The acceleration for both trips is equal, the only difference is the two light years of coasting. That coasting time should have a clock rate that is at the same rate as an earth clock, so the two trips should give the same time dilation when the earth and spaceship clock are compared back on earth. Is that correct?

The online calculator, doesn't seem to agree with this, it has inputs for a percentage of c, and distance in light years.

cheers, Jamie

Looking for an absolute answer.

It turns out that your question is ill-defined, because it contains the false implicit assumption that you can define the instant when both observers start measuring, so as to determine later how much they aged, even though the two observers are spatially separated.

Sylvia.