Does the twin paradox hold true for particles as well?

[Adrian07]

Personally I don't believe that paradox's can exist in nature, it just means something has been missed.
Senario - we will use a velocity where 1 year in space = 10 years on earth. The Earth will be our control clock. The space traveller just has to be able to see the earth, in orbit if this does not cause to many problems.
The person on Earth and the traveller both have counters which they use to count the number of Earth's rotations, and clocks showing the passage of time. After the 10 years have passed on Earth the traveller comes back to earth.
Both counters must agree on the number of Earth's rotations and both people must agree that the Earth has orbited the sun 10 times. The clocks however will show 10 years passed on Earth and ! in space. Is the traveller 9 years younger or has he been robbed of 9 years, he has after all seen the Earth orbit the sun 10 times in his 1 year.

 

[ghwellsjr]

Personally I don't believe that paradox's can exist in nature, it just means something has been missed.
Senario - we will use a velocity where 1 year in space = 10 years on earth. The Earth will be our control clock. The space traveller just has to be able to see the earth, in orbit if this does not cause to many problems.
The person on Earth and the traveller both have counters which they use to count the number of Earth's rotations, and clocks showing the passage of time. After the 10 years have passed on Earth the traveller comes back to earth.
Both counters must agree on the number of Earth's rotations and both people must agree that the Earth has orbited the sun 10 times. The clocks however will show 10 years passed on Earth and ! in space. Is the traveller 9 years younger or has he been robbed of 9 years, he has after all seen the Earth orbit the sun 10 times in his 1 year.

He has not been robbed. He is actually 9 years younger.

 

[Dale]

Is the traveller 9 years younger or has he been robbed of 9 years

What does that even mean?

 

[jtbell]

He is actually 9 years younger.

If the two are identical twins, and the stay-at-home twin's hair has turned gray during the trip, the traveler's hair will still be black/brown/blond/whatever.

 

[Nugatory]

Both counters must agree on the number of Earth's rotations and both people must agree that the Earth has orbited the sun 10 times. The clocks however will show 10 years passed on Earth and 1 in space. Is the traveller 9 years younger or has he been robbed of 9 years, he has after all seen the Earth orbit the sun 10 times in his 1 year.

Groundie's wristwatch ticks off 24 hours as the Earth rotates once around its axis, 8766 hours as the Earth orbits once around the sun.

Traveler's wristwatch ticks off 2.4 hours as the Earth rotates once around its axis, and 876.6 hours as the Earth orbits once around the sun.

All their biological processes, including aging, will proceed according to the time measured by their wristwatches. If the twins have similar metabolisms and Groundie usually eats three meals during 12 daylight hours and then sleeps through the 12-hour long night as the Earth rotates once on its axis... Traveller will likely also eat three meals in twelve hours, then sleep for twelve hours, even though the Earth will have rotated on its axis several times during his 24-hour period.

Assuming that both twins live to ripe old age of 70, their wristwatches will tick off a total of 613620 hours between birth and death, no matter what the Earth and the sun are doing. Once they've rejoined on earth, Traveler will live on for nine years after Groundie has died of old age.

So no, Traveller hasn't been "robbed" of anything.

 

[Adrian07]

Both twins agree that 10 years have passed. How can you be sure that 1 has aged 10 years and 1 only 1 year. Without clocks they must agree that time has also passed at the same rate for both. Why should physical processes slow down simply because you are moving faster.( I am of the opinion that 1 twin will age slower but that is no reason not to question it) I suppose the fundamental question is why does time slow down, we can describe it mathematically but that does not answer the question.

 

[Dale]

How can you be sure that 1 has aged 10 years and 1 only 1 year.

Because experiments confirm it. Relativistic muon travelers outlive their stay at home twin muons exactly as predicted by SR.

Why should physical processes slow down simply because you are moving faster.

Because the laws of physics are invariant under boosts and because the speed of light is also invariant under boosts. Those two postulates are the reason "why" for all of the strange relativistic effects.

 

[Adrian07]

Just to make sure I understand what is being said.
Of course a time dilation factor of 10 also means a length contraction by a factor of 10.
So following what has been said while he's in motion our space traveller shrinks to 6in high and has a heart rate of 7 beats per min

 

[phinds]

Just to make sure I understand what is being said.
Of course a time dilation factor of 10 also means a length contraction by a factor of 10.
So following what has been said while he's in motion our space traveller shrinks to 6in high and has a heart rate of 7 beats per min

These effects are observational. That is, they are what WE see in OUR frame of reference. In HIS frame of reference, he sees nothing amiss.

 

[DrGreg]

Just to make sure I understand what is being said.
Of course a time dilation factor of 10 also means a length contraction by a factor of 10.
So following what has been said while he's in motion our space traveller shrinks to 6in high and has a heart rate of 7 beats per min

Here's an analogy from non-relativistic geometry:

1. 1000 m northeast is equivalent to 707 m north plus 707 m east
2. 1000 m north is equivalent to 707 m northeast plus 707 m northwest

So according to (1), 1000 m northeast equates to 707 m north, but according to (2), 707 m northeast equates to 1000 m north. But nothing has actually contracted or dilated, you're just comparing things in different directions.

Something similar (but not identical -- dilation and contraction are the other way round) is going on in relativity. Think

north/south = Earth time
east/west = Earth distance
northeast/southwest = ship time
southeast/northwest = ship distance​

 

[Nugatory]

Both twins agree that 10 years have passed. How can you be sure that 1 has aged 10 years and 1 only 1 year. Without clocks they must agree that time has also passed at the same rate for both.

Bear with me through this paragraph, which sound as if I'm just repeating what you've already been told but actually is making an important point...
We could count the amount number of gray hairs each twin is developing. Or right before the traveler takes off into orbit, we could we could give each twin a Great Dane puppy; the average lifespan of a Great Dane is only about 61000 hours (no matter how many sunsets and sunrises the poor dog gets to see) so Groundie's dog will be dead and buried when Traveler returns with his healthy young adult dog. Or we could give them each a sample of a radioactive material with a half-life of one year (which means a half-life of 8766 hours, not one orbit of the Earth around the sun); when the twins rejoin Traveler's sample will be decayed by one-half while Groundie's sample will be decayed by a factor of 1024.

The point of the above is that there is no such thing as "without clocks". A clock is just something that changes in an observable way with the passage of time. And if we're experiencing the passage of time, then something must be changing in a way that we can observe, so we have a clock.

Some clocks are more useful than other clocks, but generally the only clocks that will work for you are ones that are more or less moving along with you. Thus the rotation of the Earth about its axis and its orbit about the sun are excellent clocks for those of us who live on the surface of the earth. They're less useful for your relativistic orbiting traveler, although he can still use them to calculate what he'll see when he returns to the earth. They are completely useless to someone outside our solar system.

Why should physical processes slow down simply because you are moving faster. I suppose the fundamental question is why does time slow down, we can describe it mathematically but that does not answer the question.

Physics isn't very good at these "why" questions. It's all about "what" and "how" and "what will happen if...".

 

[harrylin]

Both twins agree that 10 years have passed. How can you be sure that 1 has aged 10 years and 1 only 1 year. Without clocks they must agree that time has also passed at the same rate for both. Why should physical processes slow down simply because you are moving faster.( I am of the opinion that 1 twin will age slower but that is no reason not to question it) I suppose the fundamental question is why does time slow down, we can describe it mathematically but that does not answer the question.

SR doesn't give an answer about the "why". Different people give different answers, and I doubt that ever can be proven who is right. Fact is that whatever is causing it cannot be seen. The original answer (motion through the ether) is not accepted by most people, and a popular alternative explanation is motion through spacetime. Another answer (from a totally different perspective, and thus possible to combine with other answers) is "because the laws of physics are like that". Even more popular perhaps is "shut up and calculate".

PS. see for example this thread for such a discussion: https://www.physicsforums.com/showthread.php?t=595021

 

[Dale]

I have a slightly different take than harrylin, although my thoughts have changed over time. I think that it is OK to say that a theory answers "why" questions about its derived results. What it cannot answer "why" questions about are (1) its own postulates/assumptions and (2) anything that cannot be derived from those postulates/assumptions. That is because the answer to any "why" question that it can answer is the postulates/assumptions.

So "why is there time dilation, relativity of simultaneity, or length contraction" can all be answered "because the laws of physics are frame invariant and because c is frame invariant", which is the only "why" answer that SR can give for anything.

 

[Adrian07]

Reading the above thread suggests that time is not fully understood and so is limiting a complete understanding of relativity.
I wonder if it is because we cannot help [n thinking of time in the same way as space although distance can be described in terms of time and c.
Getting back to the above discussion and putting things simply earthbound takes the short rout through space and the long rout through time. Traveller takes the long rout through space (he obviously moves a much greater distance) and shortcut through time, both reaching the same destination at the same time.
If the laws of physics are the same in all frames can physical processes change according to which rout taken, you cannot get something for nothing. Is there possibly something unknown that balances the slower aging process.
Something that is not taken into account is the total energy used by each twin, the traveling twin requires a huge amount of additional energy to move, if this was somehow added to the lifespan of the earthbound twin say in terms of energy used per year would things balance out.
In other words are the mathematics complete when comparing the twins.

 

[harrylin]

I have a slightly different take than harrylin, although my thoughts have changed over time. I think that it is OK to say that a theory answers "why" questions about its derived results. What it cannot answer "why" questions about are (1) its own postulates/assumptions and (2) anything that cannot be derived from those postulates/assumptions. That is because the answer to any "why" question that it can answer is the postulates/assumptions.

So "why is there time dilation, relativity of simultaneity, or length contraction" can all be answered "because the laws of physics are frame invariant and because c is frame invariant", which is the only "why" answer that SR can give for anything.

That answer (laws of physics) was basically included in my nutshell summary; but thanks for the elaboration.

 

[harrylin]

[..] If the laws of physics are the same in all frames can physical processes change according to which rout taken, you cannot get something for nothing. Is there possibly something unknown that balances the slower aging process.
Something that is not taken into account is the total energy used by each twin, the traveling twin requires a huge amount of additional energy to move, if this was somehow added to the lifespan of the earthbound twin say in terms of energy used per year would things balance out.
In other words are the mathematics complete when comparing the twins.

I'm afraid that I don't fully follow you; but perhaps I answer your question by stating that SR has been re-derived from Maxwell's electrodynamics and the conservation of momentum and energy. Maxwell's electrodynamics implies the second postulate, and everything together implies the first postulate. Conservation of energy is certainly a known part of it all.

 

[Dale]

If the laws of physics are the same in all frames can physical processes change according to which rout taken

Certainly. As long as the law of physics says that the route-based process changes occur in the same way in all frames.

Is there possibly something unknown that balances the slower aging process.

Not according to the best experimental evidence available.

 

[Nugatory]

Getting back to the above discussion and putting things simply earthbound takes the short route through space and the long route through time. Traveller takes the long route through space (he obviously moves a much greater distance) and shortcut through time, both reaching the same destination at the same time.

That's not an altogether bad way of thinking it, as long as you remember that it's a qualitative hand-waving description and don't push it too far. As always, if you want to be exact, you have to learn the math.

Is there possibly something unknown that balances the slower aging process?

We can't do any experiments with actual twins because we don't have spaceships capable of moving people at relativistic velocities for months or years. But subatomic particles are small enough to accelerate to relativistic velocities easily, and short-lived enough to measure thousands of lifespans. And we almost routinely observe slow-moving particles dying of old age long before their faster-moving twins (DaleSpam mentioned the muon experiments back in #7 of this thread).

So I have to ask... Why are you looking so hard for some unknown thing that might balance the slower aging process? The experiments we can do have told us that slower aging really does happen.