The Twins Paradox in Relativity

But no reference to the traveling clock experiment,

or the Global Positioning System satellites, where these effects are of practical importance.

Experimental fact is very effective at disciplining theoretical speculation.

It can be expanded to the Triplets Paradox, for example

SRT is well above me, I'm afraid. Some of the explanation of the Twins Paradox refers to the twins' clocks transmitting their time to the other twin (the clock signal is transmitted at the speed of light). Even allowing for the travelling twin's speed when approaching the speed of light, and the relativistic effect it has on each clock's perceived time, as the travelling twin's speed doesn't exceed that speed, each twin will, eventually, receive the clock time of the other.

But what happens with the Triplet Paradox where the moving triplets are accelerating away from each other? Once they've "exceeded" C in relation to each other, although they can receive the stationary triplet's clock reading (and he can receive theirs), can one moving triplet still receive the other moving triplet's clock signal? If there is such a moment when they can no longer receive each other's signal, when they finally stop moving away and start moving towards each other again, will there be a moment when they suddenly start receiving that "missing" clock signal as they catch up with it (or perhaps it catches up with them)? Will there be a specific moment when they not only receive a missing clock time, but coincidentally receive the "accurate" time as transmitted by the other moving triplet, so appear to be receiving two different clock readings at the same time?

I am not a physicist but like many of us here I have been banging my head into various technical problems so I am used to see when some claim is somewhat questionable. It's been years since I have read Einstein's papers but I remember an example he gives, that with a train and a periodically flashing light on it. Obviously if the train is moving away from the observer because of the fixed speed of light the period will seem somewhat longer to the observer. What is not addressed by this simple example is the case when the train moves towards the observer - in which case obviously the period will seem shorter to the observer. A way to think of all that in terms obvious to most of us here is that our reality is a state machine clocked (IIRC there was some minimum time defined by Max Planck, could be the clock period) by some clock; what we perceive as time is the resulting change of states. While this is a simplified and probably naive model it does explain the train-flashing-light-period dependence on direction. And it explains why clocks at the equator and on the poles run the same without involving gravity.

Actually they don't.

One of Einstein's minor errors in his 1905 paper on special relativity was to predict how much slower a clock at the equator would tick when compared to one at the pole (due to the extra rotational speed of a clock at the equator). Every now and then someone points it out... eg

They only run at the same speed when *both* the GR and SR corrections are applied simultaneously and only then at mean sea level.

It is hard to get your head round but everybody's clock ticks at a different speed. Your head ages marginally more quickly than your feet.

The best clocks in the world at NIST are now sensitive and stable enough to detect a vertical shift of about 30cm or a foot in old money.

This isn't a bad introduction by Brian Cox for BBC science series.

(you might have to spoof a UK address to see it)

That doesn't happen.

Sylvia.

I have been digging into physics just as much as it takes to do what I do so me being naive with that sort of thing is no surprise. I am vaguely aware of what your references say, I think I may have read some of these some time ago. What I don't get though is the flashing light on the train thing. Looks obvious to me that the observed period depends on the movement direction (assuming gravity is constant, i.e. it is no factor). In fact this should be easily measurable (not that I would go into it, just wondering if you or someone else has an explanation, I am not the "out there to challenge the science" type, more the "curious until things get clarified for me" sort).

If you shine your laser pointer at two points 180 degrees apart in the sky, the relative speed of the light pulses in your frame of reference is 2c. No paradox is involved.

Also, there's no simultaneity between separated objects moving at different speeds. The relativistic garage illustrates this.

Say you have a 1927 Bugatti Type 41, which is 252 inches long. Your garage is the standard 20 feed (240 inches) long, and has a very fast automatically-controlled door at each end. The doors are designed to open and close automatically to allow the car to enter and leave.

Because the Bugatti is so fast, you drive towards the open end of the garage at 0.5c. You measure the length of the garage as

240 inches * sqrt(1-0.5**2) = 207.8 inches.

The hood of the car passes through the open door, then the closed door opens before the back bumper has passed through the doorway. No collision occurs, because the second door opens before the first one closes.

Your spouse, waiting for you to come home from your drive, measures the length of the car as

252 inches * sqrt(1-0.5**2) = 218.2 inches.

The car fits into the garage, so as it enters, the first door closes before the second door opens. Once again no collision occurs, because the car is shorter than the garage.

The math works out fine in both English and metric, and no paradoxes are involved.

Cheers

Phil Hobbs

But, but... the bottom of the tires are in contact with the garage floor. Shouldn't that anchor the Bugatti and garage into the same frame?

This is obvious enough. I refer to the case where the laser pointer is moving towards us; no RTT involved, we just measure the period at which it flashes. Since the light speed is always c and every next flash will have less distance to travel until it reaches us it seems obvious we will see a period shorter than it is for an observer moving together with the pointer. And vice versa, if the pointer moves away from us each next flash will have more distance to travel at c to reach us so the period we will see will be longer than at the pointer (the latter being the example Einstein gives in some of the papers, IIRC). Should not be too hard to test experimentally nowadays (the direction dependence, that is). At the moment I can't see how the period of an approaching pointer will be longer for the observer. I'll better switch to doing something useful, it is not that I don't have enough to do :-).

And the pistons are going up and down pretty good too. ;)

Just stick with the front and rear bumpers for present purposes.

Cheers

Phil Hobbs

Now I want to tweak the car and garage lengths, and the speed, so that the car goes thru unscathed in one frame but gets smashed in the other. Is it possible?

Umm, sorry? "before"? Is that a slip? Did you mean "as the back bumper passes through the doorway?

Very cool illustration BTW. I want to use it, but want to make sure I have it correct first.

Clifford Heath.

No, the point is that seen from a point in the car's reference frame, the events happen *in a different order* from what you'd see in the garage's frame.

I picked the Bugatti because I'm a fan, and looked up the standard length of a garage on the net--the fact that it worked out well with a speed of c/2 was fortuitous. (I'm very far from the first to use that general sort of illustration, of course, but it's a fun one.)

Cheers

Phil Hobbs

Nope. When a collision occurs, it's because the two objects moving at different speeds are trying to be in the same place at once. If there's no difference in position, you can have simultaneity, same as if there's no difference in speed.

Cheers

Phil Hobbs

Oh ok, I get it.

My grandfather had a Type 40 for a while - it's now restored and living in a garage 15km from here. But his really interesting car that I'd like to find more about was a Lea-Francis "Hyper" - the first supercharged British production car. He used to race that at the Albert Park track and the Philip Island track, which are both current or previous F1 tracks. I don't think he ever entered F1, but I have a number of photos he took while flag marshalling at Phillip Island in 1933.

Clifford Heath.

<snipped>

One extra thing - the (very fast) train's time is dilated, so if both stationary you (ie, waiting in the station) and the driver are both flashing at 1Hz, he'll send fewer flashes than you.

Is that right?

Fun!

Cheers

Phil Hobbs

Yep... pretty much all wrong....

.

Well...... An actually correct account of the solution to the "Twins Paradox" is here:

It explains the situation without accelerations, or frame switching. Yep. Trust me, this is the real deal...:-)

-- Kevin Aylward

SuperSpice

Often quoted, but wrong. Its not how SR works.

In Special Relativity, clocks do not tick at different rates

Its a fundamental axiom of special relativity that "the laws of physics are indepandant of inertial motion". This means, according to special relativity, clocks must always tick at the same rate.

SR explains the apparent measurement of clock ticks reading slow by "time travel". One travels through time at different t rates. Its a subtitle, but important distinction.

Special Relativity holds that for example, one can cover time at a rate of say, 100 secs/sec

Consider Dr.Who in his Tardis. He is traveling into the future , his own ageing and clok ticks stay the same , for him, but he gets to the future before someone else. If Dr. Who sent pulses as he is traveling, as he is observe red to be traveling into the future, the received clock pulses would be received as if slower .

The analogy is that there are many routes from London to Edinburgh. The odometer will read different distances, but it always clocks up distance at the same rate.

Clocks actually slowing down is a feature of the Lorentz Ether Theory, known prior to the invention of SR and which Special Relativity claims to be superior to.

The elephant in the room is that if the SR model is correct, then it leads to the "Block Universe", that is, intrinsic to SR is that the future already exists for everyone. This is in direct contradiction to Quantum Mechanics, which holds that the future is intrinsically non deterministic.

Of note, is that QFT, is, essentially, and Ether theory in denial:

Professor (UK head of department) of Physics at Cambridge, David Tong (Adams prize winner) has a YouTube general audience lecture on QFT:

0:31 - "...What are we made of...what are the fundamental building blocks of nature...?" 19:30 - "... so there is spread something throughout this room, something we call the electron field..its like a fluid that fills ..the entire universe..and the ripples of this electron fluid..the waves of this fluid get tied into little bundles of energy, by the rules of quantum mechanics..and these bundles of energy are what we call the particle the electron....and the same is true for every kind of particle in the universe..."

Kevin Aylward

SuperSpice