Understanding the Lorentz Factor: A Simple Explanation on Simple.wikipedia.org

[daytripper]

Hello everyone.
So naturally, as I'm sure everyone else here does, I believe in the education of the general public. I recently became aware of a site called www.simple.wikipedia.org[/URL]. This is a wikipedia for people who want a simple explanation of things (along with children, people who speak english as a second language, etc.). When I learned about this, I naturally surfed around and found that there was no article on my favorite topic of SR. The Lorentz factor. So I took it upon myself to write down my understanding of it, in the hopes that it might intrigue someone who doesn't have the mathematical foundation necessary to read the real wikipedia article on this subject. I ran the risk of misinforming someone, but I don't think it'd be entirely too detrimental.

My request: could someone who is more experience with this topic proofread what I've written and make sure that I'm not leading people amuck? Here's a link to the article. Thank you.
[PLAIN]http://simple.wikipedia.org/wiki/Lorentz_factor"

-DT

 

[Nabeshin]

Twin B wouldn't notice that time had slowed at all. To him, if he looked out a window, it would seem like the universe sped up. So time is relative.

Isn't this incorrect? In B's reference frame the world is moving past him at -.9c so he observes time dilation of the outside world just the same as A. The problem arises because he isn't in an inertial frame.

 

[daytripper]

Ahhh... yea, when I wrote that I was a little shaky on that sentence exactly. It's been months since I really sat down and studied this stuff. Though my initial instinct (that the universe was moving with respect to him) was correct, I couldn't resolve the problem you spoke of, so I assumed I was wrong. I'll change that.

 

[Ich]

I couldn't resolve the problem you spoke of, so I assumed I was wrong. I'll change that.

Now, that's the crux with the lorentz factor. If he sees the universe "tick slower", we obviously get a paradox, because upon return, the universe definitely has aged more.
There is no resolution with that single factor. What happens is: If B compares his clock at anyone time with the respective nearest clock that is at rest in A's frame, these actually read increasingly more time than B's own clock. In this sense, the universe "ticks faster", and that's how time dilatation is defined.
If you exchange "A" and "B" in the above sentence, it is still valid. This is not a contradiction, because both sentences describe different measurement setups.
Now, how to include that in an article about the "Lorentz factor", I have no idea.

 

[Sam Park]

My request: could someone who is more experience with this topic proofread what I've written and make sure that I'm not leading people amuck? Here's a link to the article. Thank you.
http://simple.wikipedia.org/wiki/Lorentz_factor"

The description of time dilation and the twin paradox is backwards. It says "when twin B got back to earth, he would be many years older than twin A", but in fact he would be many years younger. The numerical calculation is also backwards.

There are quite a few other things wrong with that page. For example, the comment about "what's wrong with classical relativity" doesn't make sense, and the comment about "the universe changes so the speed of light doesn't change" is not a very apt description. Also, talking about things not getting heavier as they are accelerated is a bit askew, because kinetic energy actually does gravitate (like every other form of energy), but this involves general relativity.

 

[Nabeshin]

Meh. I don't think any of this stuff (twin paradox, time dilation, length contraction, mass increase) belongs in an article about Lorentz factors anyways. Maybe in an article about Lorentz transformations, but in my opinion all that needs to be in the Lorentz factor is a description of what the Lorentz factor does and how it relates to the Lorentz transformations.

 

[daytripper]

The description of time dilation and the twin paradox is backwards. It says "when twin B got back to earth, he would be many years older than twin A", but in fact he would be many years younger. The numerical calculation is also backwards.

wow. I am far less qualified to write that page that I originally believed. Oh, and so far as the mess up on the twin paradox... no clue how that one slipped past me. haha. that is incredibly incorrect. I'll fix that as soon as I can but... wow, that is wrong. edit: fixed.

There are quite a few other things wrong with that page. For example, the comment about "what's wrong with classical relativity" doesn't make sense,

I don't understand how the part about Classical Relativity is off, though. If classical relativity applied to all things, including light, then there would be a problem with causality. We would see an event before it occurred because we trace back the time of the event the same way we trace back diverging photons to locate an object.

and the comment about "the universe changes so the speed of light doesn't change" is not a very apt description. Also, talking about things not getting heavier as they are accelerated is a bit askew, because kinetic energy actually does gravitate (like every other form of energy), but this involves general relativity.

My statement about the universe compensating for speed to make light constant is not true and pretty much implies some sort of intelligence to the universe, so perhaps that whole concept should be reworded but I don't really know how. I'm using it as a sort of metaphor, I suppose... it's just the best way I could think to explain why (how?) this stuff happens. Change it if you'd like, though. It is a wiki.

Meh. I don't think any of this stuff (twin paradox, time dilation, length contraction, mass increase) belongs in an article about Lorentz factors anyways. Maybe in an article about Lorentz transformations, but in my opinion all that needs to be in the Lorentz factor is a description of what the Lorentz factor does and how it relates to the Lorentz transformations.

I realize that a lot of this isn't entirely relevant to the Lorentz factor but my key goal in writing that was to interest people in the topic. After all, it's not exactly the "real" wikipedia and I figure too much information is better than none. Plus, if you would like to type up a layman's explanation of a linear transformation, go ahead, but that's just more overhead for the reader.

thanks again for the corrections

 

[Sam Park]

If classical relativity applied to all things, including light, then there would be a problem with causality. We would see an event before it occurred because we trace back the time of the event the same way we trace back diverging photons to locate an object.

The speed of a baseball thrown at a pedestrian from a moving car is approximately equal to the sum of the car's speed and the speed of the ball relative to the car, but this doesn't imply that the pedestrian will get hit by the baseball before it is thrown.

 

[Nabeshin]

The speed of a baseball thrown at a pedestrian from a moving car is approximately equal to the sum of the car's speed and the speed of the ball relative to the car, but this doesn't imply that the pedestrian will get hit by the baseball before it is thrown.

But in a different reference frame someone will see the pedestrian not get hit by the ball (or some other disagreement in observations), which is in essence a violation of causality.

 

[Sam Park]

But in a different reference frame someone will see the pedestrian not get hit by the ball (or some other disagreement in observations), which is in essence a violation of causality.

No, you're confusing classical physics with special relativity. The original poster is saying that in classical physics someone can get hit by a baseball before it is thrown (or equivalently, hit by a "classical light pulse" before it is emitted). This is not true. Classical physics has absolute simultaneity and causality, and changing frames of reference makes no difference. So his purported explanation of what's wrong with classical physics is invalid.

It isn't possible to invalidate Galilean relativity by reasoning of that kind, because Galilean relativity is a limiting case of Lorentzian relativity. We decide between them based on observation, not based on logical sylogisms. (There actually are rational reasons, apart from experience, for believing that nature would choose Lorentzian over Galilean relativity, but those reasons wouldn't be good candidates for "simple wiki" articles.)

 

[daytripper]

I only have a second. But I've decided to delete the part of the article concerning the car. Either I didn't remember the story correctly or the story was wrong (or both). But either way, it's gone.