Speed of Light

Willem said:
What does it mean to say an object travels at the speed of light through time?
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About the same as saying "an object travels at the speed of light through distance". In other words it doesn't mean much of anything.
 
Willem said:
Speed-in-time = -c.t_B/t_B = -c m/s.
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Ah, I see you've edited your post ten minutes after I posted my reply, without informing me.

But you still need to answer the question: what is "t_B"? Also, why is there all of a sudden a minus sign? And what happened to the need for a second clock?

However, none of it matters, because, as I said in my previous post: you've now answered your own OP. You've derived speed = c, which is exactly what you were asking about, so now you know what it means. I'm glad to have helped you figure it out!:)
 
origin said:
About the same as saying "an object travels at the speed of light through distance". In other words it doesn't mean much of anything.
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I do admit I've been charitably interpreting it, but perhaps, because his source for the statement is still absent, that was too optimistic of me.
 
Willem said:
What does it mean to say an object travels at the speed of light through time?
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To make sense of how things work in special relativity, Minkowski came up with the concept of the invariant space-time interval, which formally puts time on an equal footing with space. Well not quite - there is a conversion factor c and a minus sign involved for the time interval, but otherwise it's treated like a 'normal' dimension rather than a parameter. it leads to hyperbolic geometry rather than the familiar elliptic Euclidean geometry.
Read the intro here, then just the upper left definition for space-time 4-vector:
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/vec4.html
Below linked YouTube vid may further help:
 
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sweetpea said:
I just had a look into a Brian Greene book.
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Which one?

Brian said:
Here's the leap: Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed-that of light. This is a strange idea; we are used to the notion that objects travel at speeds considerably less than that of light. …... …We are presently talking about the object's combined speed through all four dimensions... ...and it is the object's speed in this generalised sense that is equal to that of light.
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I'm not aware of any such "proclamation" by Einstein. Without more context, I'm not even sure what Brian Greene is talking about here. What is a "speed through spacetime" anyway? How does he define that, and how is it different from the usual "speed through space"?

If I had to guess, I'd venture the opinion that maybe Brian is thinking about the velocity 4-vector or something (because the "time" component of that vector is the speed of light, c), but there's no way to tell from just this quote.
 
James R said:
Which one?
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' The Elegant Universe.' Paperback page 50.
James R said:
I'm not aware of any such "proclamation" by Einstein. Without more context, I'm not even sure what Brian Greene is talking about here. What is a "speed through spacetime" anyway? How does he define that, and how is it different from the usual "speed through space"?
If I had to guess, I'd venture the opinion that maybe Brian is thinking about the velocity 4-vector or something (because the "time" component of that vector is the speed of light, c), but there's no way to tell from just this quote.
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Yes, I think he is describing the 4-vector, the posts from others above point to this as well.
Here's a longer quote centered on my last book quote:
Since this view proclaims that space and time are simply different examples of diemensions, can we speak of an object's speed through time in a manner resembling the concept of its speed through space? We can.
A big clue for how to do this comes from a central piece of information we have already encounted. When an object moves through space relative to us, its clock runs slow compared to ours. That is, the speed of its motion through time slows down.
Here's the leap: Einstein proclaimed that all objects in the universe are always traveling through spacetime at one fixed speed- that of light. This is a strange idea; we are used to the notion that objects travel at speeds considerbly less that of light. We have repleatedly emphasized this as the reason relativistic effects are so unfamiliar in the everyday world. All of this is true. We are presently talking about an object's combined speed through all four dimensions- three space and one time- and it is the speed in this generalized sense that is equal to that of light.
To understand this more fully and to reveal its importance, we note that like the impractical single-speed car discussed above, this one fixed speed can be shared between the different dimensions-different space and time dimensions, that is.
If an object is sitting still (relative to us) and consequently does not move through space at all, then in analogy to the first runs of the car, all of the object's motion is used to travel through one dimension-in this case the time dimension.
Morever, all objects that are at rest relative to us and each othetr move through time -they age- at exactly the same rate or speed. If an object does move through space, however, this means that some of the previous motion through time must be diverted.
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I seem to make sense of it. At first I think I was confusing myself thinking how does this tie-in with the world line idea, which is just the static line or ''static path'' of all events of the object/car in spacetime. I was saying to myself-- ''you don't move along a world line''. Had to get the idea of a world line out of my head.
I hope you got the book, because I'm not going to type out the whole chapter.
 
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When an object travels at the speed of sound it creates a "sonic boom": it creates sound. Therefore I must assume that when an object travels at the speed of light, it creates light: it bursts into flames. :)
 
TheFrogger said:
When an object travels at the speed of sound it creates a "sonic boom": it creates sound. Therefore I must assume that when an object travels at the speed of light, it creates light: it bursts into flames. :)
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A sonic boom is created by the shockwave produced when an object travels faster than sound.

There is an analogous phenomenon when a particle travels through an optically dense medium faster than the phase velocity of light for that medium. This is called Cerenkov (or Cherenkov) radiation: https://en.wikipedia.org/wiki/Cherenkov_radiation
 
I read "Tim and Tobias" a few times. :D

Not because it was difficult (it was black band, the highest) but because I enjoyed it.
 
TheFrogger said:
When an object travels at the speed of sound it creates a "sonic boom": it creates sound. Therefore I must assume that when an object travels at the speed of light, it creates light: it bursts into flames. :)
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No object - by which I mean something that has mass - can ever travel at the speed of light (in vacuum).

As exchemist said, objects can sometimes travel faster than the speed of light in some kind of medium, in which case they produce a sort of "light boom" (Cherenkov radiation) akin to the sonic boom produced by objects travelling fast than the speed of sound in a medium.
 
sweetpea said:
' The Elegant Universe.' Paperback page 50.
Yes, I think he is describing the 4-vector, the posts from others above point to this as well.
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I still can't tell for sure from the extra stuff you quoted. It's frustrating because what I really want to know is the maths he is using to conclude that his "speed through spacetime" is c. I have read the book - a long time ago - but don't own a copy.

DaveC426913 said:
One of my top two non-fic books.

My brain had stretch marks after reading it. (And I read it about 5 times.)
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I found it a frustrating read, for exactly the same reason that I've given here. It is very light on maths and heavy on hand-wavy descriptions. I understand that it was written for a popular audience, but I was keen to actually get a better working understanding of string theory, not descriptions by analogy.

This is not to diss Brian Greene. I've seen him talk in various forums - not necessarily just about physics - and he's a good communicator who says sensible things.

I guess that book wasn't really written with people like me in mind.
 
James R said:
I guess that book wasn't really written with people like me in mind.
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Agree. I was written with people like me in mind - an armchair science-wannnabe without the post-sec math chops.

I found it brain-stretching because of the ability to intuit the concepts - got me a long way toward being able to conceptualize 4+ dimensions.

It also allowed me to understand, in very concise terms, exactly how GR and QM are incompatible - where the infinities actually arise. I can now describe the basics in just a couple of paragraphs. Wonderful to have some personal mysteries solved and tied with a bow.

(For the same reason you don't read pop-sci books, I don't watch pop-sci shows. They're barely more than fluff, and I've already read the book they're based on.)
 
Please post on topic.
"Tim and Tobias" was challenging, but not too taxing. It was a black-band book, which meant it was at the highest-level available, but the pictures kept the storyline moving along at a brisk pace. :)
 
TheFrogger said:
"Tim and Tobias" was challenging, but not too taxing. It was a black-band book, which meant it was at the highest-level available, but the pictures kept the storyline moving along at a brisk pace. :)
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You still haven't explained what a black-band book is, or what these levels are.

I'm going to take a shot in the dark and guess that these are for grade school children's books, and the difficulty ratings thereof.
 
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