JesseM
Garth said:
Proper time $$\tau$$ is that time measured in the rest frame, moving and/or distant (in a gravitational field) clocks will run at a different rate, rulers will contract etc. Therefore measure the 'rate' of $$dt/d\tau, dx/\tau$$ etc.
I understand what proper time is, I was asking what you are measuring a change in with respect to proper time. Can we represent the magnitude of the 4-velocity as $$d\lambda / d\tau$$ (or $$cd\lambda / d\tau$$, perhaps), where $$d\lambda$$ is some physically meaningful quantity? If so, what would it be?
Garth said:
BTW Although time bears the same mathematical relationship to the space dimensions as the imaginary numbers do to the real, calling time ‘imaginary ict has its own problems as MTW point out in ‘Gravitation’ page 51.
Thanks, I didn't know that--I guess although the trick works nicely in SR it can't be generalized to GR.

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Garth
Gold Member
JesseM said:
Can we represent the magnitude of the 4-velocity as $$d\lambda / d\tau$$ (or $$cd\lambda / d\tau$$, perhaps), where $$d\lambda$$ is some physically meaningful quantity? If so, what would it be?
By the 'magnitude' of the 4-velocity Ua I assume you mean its norm? In which case $$\lambda$$ would simply be proper time as
UaUa = 1.

Garth

JesseM
Garth said:
By the 'magnitude' of the 4-velocity Ua I assume you mean its norm? In which case $$\lambda$$ would simply be proper time as
UaUa = 1.

Garth
Yeah, I just meant the norm (Greene also used the word 'magnitude' in his quote earlier). The norm of a 4-velocity vector $$u = (cdt / d\tau, dx / d\tau, dy / d\tau, dz / d\tau)$$ is just $$\sqrt{c^2{(dt / d\tau )}^2 - {(dx / d\tau )}^2 - {(dy / d\tau )}^2 - {(dz / d\tau )}^2}$$, correct? I suppose it's just the chain rule, but I didn't immediately see that this was the same as $$cd\tau / d\tau = c\sqrt{dt^2 - c^{-2}(dx^2 + dy^2 + dz^2)} / d\tau = \sqrt{c^2 dt^2 - dx^2 - dy^2 - dz^2 }/d\tau$$. But in this case, you are defining "speed through spacetime" as c times $$d\tau / d\tau$$, so the profound-sounding statement "everything moves through spacetime at the speed of light" reduces to the trivial statement that $$d\tau / d\tau = 1$$. It doesn't seem at all natural to me to define "speed through spacetime" in this way (and it seems especially misleading since you have defined 'speed through space' and 'speed through time' in terms of derivatives with respect to coordinate time rather than proper time). I think that if you use this explanation when describing relativity to a layman, you should at least make it clear that when you say "speed through spacetime" you really mean "the speed of light times the rate that the object's own clock is ticking as compared with itself (and this rate is of course 1 for all objects)".

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Garth
Gold Member
It would not be a major part of my lecture but another way of trying to explain the 'meaning of relativity'. I'd first ask what rate does time flow? With the obvious answer one second per second, in order to talk about time dilation you have to compare one clock against another. However if space and time are combined in space time, with one second of time equivalent to 186,000 miles then 'one second per second' can become '186,000m.p.s' or light speed.
Garth

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Hi Crosson - I'm sorry to hear that you're getting attacked personally. There is no call for that here. Welcome to the forums by the way. However I didn't see anyone accuse you of reading "The Elegant Universe". JesseM only said In fact, Brian Greene is the only author I have seen who describes relativity this way,... Unless you were thinking of PBRMEASAP? In that case it's not clear to me what he's talking about.

Second - I see that you're getting flack for the term "layman." Simply look in a dictionary for a definition when people complain about a word. From Meriam Webster

Layman - a person who does not belong to a particular profession or who is not expert in some field.

A person can be a layman in quantum field theory and an exepert in special relativity. The term "layman" is not a condescending term and should never be thought of as such. Its a relative term. Everyone is a layman in some area.

So when you ask how to explain SR to the layman then it will depend on the particular layman. If the layman is a mathematian then you might choose one way, if the layman is an electrical engineer you might choose another way, etc.

Crosson said:
I tell them: (first, explain spacetime)

"Relative to anyone else, we move through space-time at the speed of light.
In my humble opinion that is a very bad idea. In doing so you're taking a term that they know, i.e. "move" which is a displacement in space in a given time, and replaces it with something foreign. e.g. dividing a temporal interval by a temporal interval and calling that "motion." Keep in mind that you can't say that light moves through spacetime at the speed of light.

In my opinion, a scientific theory shouldbe as sensible and accessible as possible to everyone.
Then never explain it in those terms. There is no reason why one would want to hear something like that. It gives them nothing. If the person is a layman then that comment will have no meaning to them. It sure has no meaning to me other than a fancy way to say that U has a magnitude of 1. Note that there is no U for a photon though.

I dislike books that play up SR as some mystical time space weirdness. If any one has a better way to explain SR, or a way to explain length contraction in a nutshell, I would like to hear it.
Its difficult to get something more fundamental than the usual basics. They are still the best that I know of. The light clock is a great way to explain time dilation.

I've taken time to do things like this myself. E.g. see
http://www.geocities.com/physics_world/sr/sr.htm

Especially
http://www.geocities.com/physics_world/sr/light_clock.htm
http://www.geocities.com/physics_world/sr/lorentz_contraction.htm

Again, welcome to the board. I hope your experiences here are more rewarding than in this thread.

Pete

JesseM
Garth said:
It would not be a major part of my lecture but another way of trying to explain the 'meaning of relativity'. I'd first ask what rate does time flow? With the obvious answer one second per second, in order to talk about time dilation you have to compare one clock against another. However if space and time are combined in space time, with one second of time equivalent to 186,000 miles then 'one second per second' can become '186,000m.p.s' or light speed.
Garth
But $$d\tau / d\tau$$ is not equal to the velocity c, it's equal to the dimensionless number 1. Anyway, I don't see how the notion of spacetime implies that "one second of time is equivalent to 186,000 miles" unless you use the "time = imaginary distance" convention I mentioned earlier...if you measure time and space in different units, then although you are free to pick a unit system where 1 second and 1 light-second have the same numerical value in that unit system, you are also free to pick a unit system where they don't, I don't think there'd be any unit-independent physical truth expressed by the statement "one second of time is equivalent to 186,000 miles".

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JesseM - back to you on that reference - The Title of the Book is "Stephen Hawking" by Kitty Ferguson 1991 Cambridge U Press and some other publishers also - at page 100, the notion movement through time and then space is discussed with the aid of a drawing.

Chronos
Gold Member
JesseM said:
But $$d\tau / d\tau$$ is not equal to the velocity c, it's equal to the dimensionless number 1. Anyway, I don't see how the notion of spacetime implies that "one second of time is equivalent to 186,000 miles" unless you use the "time = imaginary distance" convention I mentioned earlier...if you measure time and space in different units, then although you are free to pick a unit system where 1 second and 1 light-second have the same value in that unit system, you are also free to pick a unit system where they don't, I don't think there'd be any unit-independent physical truth expressed by the statement "one second of time is equivalent to 186,000 miles".
The notion of spacetime implies nothing until you introduce a coordinate system. Once you do choose a coordinate system and assign units of measure to any one vector, you automatically impose that measurement system upon all other coordinates [dimensionless numbers].

JesseM
yogi said:
JesseM - back to you on that reference - The Title of the Book is "Stephen Hawking" by Kitty Ferguson 1991 Cambridge U Press and some other publishers also - at page 100, the notion movement through time and then space is discussed with the aid of a drawing.
So was the explanation of relativity in terms of "speed through spacetime" Kitty Ferguson's own way of explaining it, or was she recounting something that Hawking had said?

JesseM - the book is a sort of interview - part of his life and partly his ideas - there are quotes and chapters on various subjects - I can't say if she embellished upon what was communicated - but the book has been around for a long while - apparently not the one that is being complained about - and if hawking didn't like it he has had 14 years to discredited or qualify what was said.

Brian Greene reprises this explanation of SR in "Fabric of the Cosmos." Before using Bart and Lisa Simpson as characters in an imaginary experiment, he says essentially what you said, Crosson, although with some distinctions.

He emphasizes that, because everything moves through space-time at a constant speed, the name for relativity is somewhat misleading. And that in fact Einstein originally wanted to call it "invariance theory." This may be something to interest the layman (although, in my case it has only confused me to the point of wanting to become a physicist just to understand everything... and considering I'm in my senior year of economics, it's not exactly productive to be considering a career change)!

Also, he says that a parked car has devoted all of its constant motion to motion through time. But, when it starts to move it has transferred some of that motion to space and now time will slow down for it, as it has taken some of its motion away from moving through time.

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