The Twin Paradox

" So in the end in the battle between Newton and Einstein, who is right? In every day life, they both are. The speeds at which life goes by are so slow that it has only been in recent history that we have been able to detect the differences. Newton viewed space-time as being flat, unchanging and very boring, but that is not at all the case in Einstein’s world. To Einstein, space-time is very dynamic, changing depending gravity and velocity."

 Newtonian Physics vs. Special Relativity (futurism.com)

I've got to think about this some more but, my present understanding is that the watches in Uncle Ken's thought experiment do not just appear to run differently, they actually do run differently.  The formula that Uncle Ken keeps quoting (rt=d) is Newtonian physics.  I believe that time dilation operates the same in Newtonian physics as it does in Einsteinian physics, but the differences are so small as to be imperceptible for all practical purposes.  It might be easier to visualize if we look at it from an expanded cosmic perspective. 

In the classic thought experiment involving two twins, one who takes a long journey at a significant fraction of the speed of light, the traveling twin does not just appear to age more slowly than the twin who stays home, he actually does biologically age more slowly.  When he returns home his rate of aging returns to the rate of his twin, but his currant age does not revert to the current age of his twin, he will always be younger than his twin unless his twin undertakes an identical journey while he stays home this time.  

Twin paradox - Wikipedia

Speaking of links, did you even read this one?

Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to them will be measured to tick slower than a clock that is at rest in their frame of reference. This case is sometimes called special relativistic time dilation. The faster the relative velocity, the greater the time dilation between one another, with time slowing to a stop as one approaches the speed of light (299,792,458 m/s).

Time dilation - Wikipedia

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I have been reading all the articles in the "Draft" series with interest.  Some of it is familiar from stuff you posted in our old email days, but some gaps are being filled in this time, which is good.  

draft seven

 Of course I believe in everything Einstein is quoted as saying, and I don't really disagree with what Beagles is saying inasmuch as I don't understand what he is saying.  If Old Dog revs up the engine on the old widow maker he is speeding up.  Myself, standing at that bend in the road could break into a run and I would be speeding up.  But time itself never speeds up anymore than that spot in the road where Beagles is standing to observe ever speeds up.  Once again speed = distance/over time.  You cannot apply the term to time anymore than you can apply it to distance.

But maybe this is what Beagles is thinking.  Old Dog is wearing the gold watch they gave him for his many faithful years at Kinko's, and Beagles is wearing the one he got from the paper mill.  Everything seems perfectly normal to both as Old Dog roars down the road.  If they look at their watches they are going at just the right speed.  But if either one had a telescope and could look at the watch of the other it would appear to be moving slower than their own watch (because they are in motion relative to each other).  If Old Dog slows down, or if Beagles starts to run up the road, then they will notice that the other guy's watch is moving a little faster than it was relative to their own, though it will still be slower than their own.  If they both come to a complete stop then their watches will appear to the two of them to be moving at the same speed.

That's all I have this morning.  But I am appalled by how little I know about the speed of sound.   Maybe I will look that up over the weekend, but most likely not because I almost never look anything up over the weekend.

Here is that draft thing.  Old Dog is off the interweb and Beagles doesn't appear to be reading it, but I guess I will keep putting it up until the end.  You know like the cowpoke who thought the cuspidor was a water pitcher and drank it all down.  His buddy, Clem, asked him why, when he discovered it was not cold clear water, he kept drinking it, and he replied, "It was all one strand." 

 

 As I've said even though Marlene had moved me out to make room in her bed for Bob the three of us remained friends.  I'd often drop by the house on Benvenue (Have I told you that it was next door to the house where Patty Hearst got snatched?  It was), around suppertime.  Marlene had some kind of job, with the University I think.  I used to sell the Berkeley Barb on the weekends which some of the money I'd give for rent and the rest would last me more or less the rest of the week.  Bob had had a job when I first arrived, but he'd quit by now.  So he decided to become a drug dealer.

He'd been approached by a young guy on Telegraph Avenue, who wanted him to get him some dope.  Bob had a big supply of something currently popular in the area called Hog, no idea why it was called that, no idea what it was.  It fell into the category of all day drugs such as LSD, psylocibin, peyote, STP.  Sometimes it was called one, sometimes it was another. Sometimes it was organic, Man, sometimes it was lab-made, Man.  Sometimes it was 20 mikes (mgs), sometimes it was 20,000. Sometimes it was orange barrels, sometimes it was purple tabs, it came in all shapes and colors and the only clue as to what it was was what the seller told you it was, and he only knew what the guy who sold it to him told him it was. But it generally did last all day, so everybody was happy.

So Bob was going to sell this guy some Hog, and you know, use that profit to buy more, and maybe the guy would tell his friends, and maybe Bob could broaden his line and add some orange barrels and purple tabs, you know, make a go of this thing.

But it turned out the guy didn't want Hog.  He wanted pot.  This was a bit of a problem, Bob only had his personal stash.  If he sold that he'd have to go right out and buy some more, and he wouldn't be making all that much money.  But you know when you're new in a business you have to make sacrifices, do things that are inconvenient.

We were all three of us sitting around in Marlene's bedroom before Bob was to go out to make his sale.  He was a little nervous.  Suddenly he dashed out to the bathroom and shaved.  "Just want to look good in my mug shot," he joked.

Bob was a jokester.  That was why, after he had been gone too long, and then the phone rang and he said he was in jail, Marlene didn't believe him.  Wait, I had an idea.  A month ago, when I had been phoning from the jail I noticed someone had written something peculiar on the wall behind the phone, what was it.  Bob knew exactly what it was.  Marlene went to the bank to get the bail money again.

What happened was Bob was supposed to meet the guy at this corner.  He had the pot in a baggie in his jacket pocket, and he had his hand on the baggie.  If anything happened, and most surely it wouldn't, he could just ditch the baggie into some nearby bush.  No possession, no foul.  They couldn't do anything to him. 

But the guy wasn't there.  He loitered a little but the guy still wasn't there.  There was this car though cruising along, and it had these six big guys in it, none of them looked like hippies.  But he had his hand on the bag, his eye on the bush.

"Hey you!" one of the guys yelled jumping out of the car and pointing at Bob.  Bob's hands shot straight up into the air.  The baggie remained in his pocket.

The guy, the customer, turned out to be some high school kid.  The cops had busted him and decided to use him to fish for somebody higher on the food chain.  Not that Bob was that much higher on the food chain.  I don't know why they didn't use him to fish up.  Maybe they got bored.  His folks were kind of well off and I expect they got him a good lawyer, that's more likely why they didn't fish up.

In the end he paid a fine, did no time, and it was a factor, when examining his total record, in getting him out of the draft.

Okay

 I watched the video again, and I think that Uncle Ken is right about the cyclist and the loiterer.  The part we are interested in begins about 12 minutes into the video, so you only need to watch the last six minutes or so. That said, I am still right about time dilation.  The reason I couldn't find it last night is that I was looking under General Relativity and I should have been looking under Special Relativity.  I could look that up, but I have already posted a link on the subject, although Uncle Ken seems reluctant to acknowledge it.  Here it is again in case he missed it:

Special relativity indicates that, for an observer in an inertial frame of reference, a clock that is moving relative to them will be measured to tick slower than a clock that is at rest in their frame of reference. This case is sometimes called special relativistic time dilation. The faster the relative velocity, the greater the time dilation between one another, with time slowing to a stop as one approaches the speed of light (299,792,458 m/s).

Time dilation - Wikipedia

It doesn't say anything about time speeding up as we slow down but, logically, it should because "What goes up must come down".  Einstein must have overlooked this, which is why I proposed the Beaglesonian Corollary.

The Cimrman Corollary, on the other hand, is just a joke that I included to lighten the mood.  Like the guy in the video said, "If you take this stuff too seriously it will drive you nuts.", or words to that effect.

the cyclist and the loiterer

 I am loitering on the side of the road with a  flashlight.  Beagles is standing half a mile further down the road.  From up the road comes Old Dog on his motorcycle.  Just as he passes me he flashes his headlight and at exactly the same time I blink on my flashlight.  The light from my flashlight and from Old Dog's headlight will hit Beagles at the same time.  

I think that is what Beagles is thinking of when he spoke of light from different distances reaching a point at the same time.  He is thinking of something counter intuitive and this certainly is.  One would think that the light from Old Dog's headlight would be moving towards Beagles at the speed of light plus the speed of the motorcycle, but of course that would be impossible.

The thing about the speed of light being constant is that it looks constant to every viewer who all have different viewpoints because they are generally moving relative to each other.  In this instance Beagles and I are moving at the same speed (from the rotation of the earth etc.), but Old Dog is moving at a different speed than us, so Beagles sees him differently.  A body moving at a different speed, appears to be moving slower than a body at rest relative to the observer so Old Dog will appear to Beagles to be moving slower (likewise Beagles will appear to be moving slower to Old Dog), and that will work to make his light appear at the same time as mine.

I think.

That's the best I can do for the nonce without doing any research.  I was going to include a horn among the instruments and have us both blow them as Old Dog roars past me, thinking the sound of Old Dog's horn will arrive sooner, but doing a little research I am not so sure.  There is such a thing as the speed of sound and I am not sure why sound should have a constant speed.  Isn't sound just stuff bumping into other stuff?  Isn't that the way with waves in the sea, and don't they all travel at different speeds?

I don't know.

So one thing I have said, I think is true, but I am not sure, and the other I have to admit I don't know anything about.  Not a very good average I am afraid, but I have stretched my mind out about and I always enjoy that.

One Would Think

"If you click on your flashlight two observers at different distances, and all traveling at about the same speed relative to each other, will see the light at different times.  The closer guy will see it before the more distant guy, because the speed of light will be constant for both guys."

I thought so too, but I have heard from several sources that they both see the light at the same time.  I think the video we were talking about had something in there about it but, as you say, you can't quote a video like you can quote the printed word.  I believe it was another video from the Teaching Company (great courses on tape) where I first encountered this problem.  I've got it on a DVD somewhere, but it would be very time consuming to find it and locate the exact quote on it, and then I wouldn't have any way to post it.  I tried to find it on Wiki tonight, but was unable.  I think my best bet would be to watch the video again and note how far into it the information appears, if indeed it does appear.  Other than that, I'll just have to keep my eye out and make a note of it the next time it pops up.

"Having perfect knowledge of every atom, including its speed, it is possible to recreate a brand new Mercedes from that pile of metal."  

That "perfect knowledge" thing sounds interesting.  Where would I get some of that?  The only thing that immediately comes to mind is a Biblical quote from First Corinthians, Chapter 13:

"For our prophesy is imperfect and our knowledge is imperfect but, when the Perfect comes, the imperfect will pass away."

relatively speaking

 I am not disputing anything Einstein said.  Like you, I don't understand all the details.  What I can't figure out is your concept of time.  If you click on your flashlight two observers at different distances, and all traveling at about the same speed relative to each other, will see the light at different times.  The closer guy will see it before the more distant guy, because the speed of light will be constant for both guys.

The speed of light is 186,282 miles per second.  If one of the guys is 186,282 miles further away from the flashlight than the other guy he will see the flash one second later than the other guy.  Mercury receives the light of the sun about five minutes before we Earthlings see it.

As I said I don't fully understand the theory, and as you have admitted neither do you, so we are both arguing our respective interpretations of it, and so it's kind of pointless.  On the other hand it stretches the mind does it not?

I didn't say that the same people would recur in each cycle of the big bang.  I said:  Actually the big crunch does not think that the universe will come back the same way every time, but we have eternity here so we can rest assured that it will come to those identical times where I am typing the post an infinite number of times, so, you know, same difference. 

But melting down that scrap metal, let's make it a brand new Mercedes, is an interesting case. The way modern day physicists understand the universe is that matter can never be created or destroyed.  It can be converted to energy, but then that energy can be converted right back to the same amount of matter at any time.

They also believe that information can never be lost.  Having perfect knowledge of every atom, including its speed, it is possible to recreate a brand new Mercedes from that pile of metal.  One of the odd things about time is that mathematically it works just as well going backwards as it does going forwards, and working things out backwards, having perfect knowledge, you can work out how it became that lump of metal, and you can work out what that lump was before it got melted down.  

That was the problem with black holes.  It was previously thought that when matter fell into a black hole all information about what it was before that event was lost.  But now I believe it has turned out that black holes will eventually dissipate and when they do that the information will be retrieved.

I am on pretty shaky ground on that last paragraph, but I think I am correct, but I won't do the research at the current time.

I am glad to hear that the Old Dog is still kicking, and that at some future time he will achieve internet and will be conversing with us.  He sort of breaks up these little spats between the two of us.  Sometimes it is nice to think of something cooling like an ice cream machine.

Believe it or Not

"I could never figure out what you are saying about time.  There is no such thing as the speed of time as I explained though I am sure that I have not convinced you." 

You don't have to convince me, you have to convince the vast majority of the scientific community that believes in Einstein's Theory of Relativity.  Like I said, I take no position on the theory's validity because I don't understand the math.  Newtonian physics is good enough for me because it works on Planet Earth, which is where I spend most of my time.  I don't understand all the math in Newtonian physics either, but I am familiar enough with the general principles that, if a tree falls in the forest, I know enough to get out of its way.  

Point of clarification:  Are you disputing what Einstein said about time, or are you disputing my understanding of what he said?  I readily admit that my understanding of it is incomplete.  I thought I was onto something with this time thing, but maybe not.  Specifically, do you accept the premise that the speed of light is absolute and constant to all observers regardless of their position and state of motion?  Do you also accept the premise that two observers of the same light source will see it at the same time regardless of their respective distances from that source?  If so, how can that happen without the two observers existing in different points of time?  

All that stuff about the ultimate fate of the Universe is theoretical as well.  If any of the cyclical theories is true, what's to say that the same individual humans keep reappearing during each cycle?  If you melt down a bunch of scrap iron and re-cast it, none of the original metal objects will be recognizable in the finished product.  Why would this be any different?