Why ct instead of t

[Jacques]

Relativity use ct for the time dimension . Why ?

Why not use simply t for the forth dimension ?

I understand that ct bring te dimension of time to a dimension of space. But why do we need to do that ?

Thanks for your answer

[Tom Mattson]

Higher level books on relativity do use t for the 4th dimension. ct is used in elementary treatments because students are still used to old systems of units (SI, English, what-have-you) that necessitate a conversion factor c with the dimensions of velocity.

[s pepperchin]

It depends on the equation you're looking at, the units for ct is meters or some other unit of length. so are you using length or time?

[Jacques]

OK thanks for your answer. I was wondering about that because forgetting that some parameter in an equation have unit of time may lead to something completely erronous. It is important to carry the unit in the equations specialy if you use normalized unit. For example taking the speed of ligth to be 1, it's easy to forget that it is a speed.

Thanks again

[Tom Mattson]

The reason that c isn't carried around in the upper level textbooks is that there is no reason that you couldn't think of time as a distance. 1 second of time is about 3*10⁸ m of distance traveled for a light pulse. This is explained in Taylor and Wheeler's Spacetime Physics, which is meant for sophomores or juniors (post Halliday and Resnick).

[Jacques]

there is no reason that you couldn't think of time as a distance.

Why think time as a distance ?

[5614]

Because it is the distance moved in the 4th dimension.

[Tom Mattson]

Once you understand relativity, you turn that question on its head: Why not treat time in the same way as distance?

 

Using different units for time and distance obscures the symmetry of relativity, which puts space and time on the same footing. In that book I told you about it is explained that the factor [imath]c[/imath] is just a conversion factor between space units and time units and that it is no more significant than the conversion factor "5280 feet = 1 mile".

[Jacques]

So the distance between two tic-tac of my clock is 300,000 km !

For me it's 0 km distance and 1 second apart.

I understand that using ct make space-time symetric, but don't we lost the distintion between space and time ?

[Tom Mattson]

So the distance between two tic-tac of my clock is 300' date='000 km !

[/quote']

 

Something like that.

 

For me it's 0 km distance and 1 second apart.

 

That's fine, but it's not a convenient point of view when doing modern physics.

 

I understand that using ct make space-time symetric, but don't we lost the distintion between space and time ?

 

The distinction I've been describing is something we want to be rid of, because it arises from nothing more than a choice of units and is therefore artificial. But there is still a very important distinction that remains. The basic invariant of SR is [imath]x^2+y^2+z^2-t^2[/imath]. The difference between the spatial coordinates and the time coordinate is that minus sign. That distinction between space and time is preserved in the metric, and it cannot be dispensed with.

[5614]

[edit] - the quote was added, Tom Mattson hadn't replied when I started replying.

but don't we lost the distintion between space and time ?

That is the idea!

 

Just as going forward (1st dimension) is very similar to going sideways (2nd dimension) and going up (3rd dimension) is also very similar going forward in time (4th dimension) is again similar.

 

I've heard people asking 'if you lived in a 2D world could you possibly imagine a 3rd dimension?'. I don't know the answer and it sure takes a bit of imagination for us to imagine the 4th dimension but just because it is not simple and is not something we can consciously move about in does not mean it cannot be treated as a 'normal' dimension (ie. like the 1st, 2nd, 3rd).

[sunspot]

Most people are used to time being a measure of changes of state. This is one definition of time. The distance analogy is another definition that better fits into the implications of relativity. If one looks at special relativity and how the laws of physics are the same in all references, or just changes in mass, distance and time relativity can alter all the laws of physics between references, then the definition of time needs to be even more than just an aspect of distance. The implication is that time is a type of potential. One can see this in energy which is expressed as wavelength (distance) and frequency (time). Energy defines distance but also contains a potential that coordinates with this distance and gives it an energy punch. In other words, a length of distance doesn't do much on its own, but coordinate frequency with this distance, and it can cause a change of state.

[Jacques]

Thanks for your answers.

But doesn't we lost something ?

For example it make speed a pure number without units.

s=space

t=time

speed=s/t or in relativity speed= s/s

[5614]

We lose a distinction between space and time, in a sense yes. But we do not lose distinction between dimensions.

 

Just like you wouldn't confuse vertical and horizontal components of a velocity, so you wouldn't confuse the 3rd and 4th dimensions.

[Tom Mattson]

Thanks for your answers.

But doesn't we lost something ?

For example it make speed a pure number without units.

s=space

t=time

speed=s/t or in relativity speed= s/s

 

Speed is still s/t, but in the so-called "natural units" of SR speed becomes a dimensionless number between 0 and 1.

[Jacques]

Speed is still s/t, but in the so-called "natural units" of SR speed becomes a dimensionless number between 0 and 1.

Thanks again for your answer and time !

Still not confortable with that, but I must live with it if I want to go deeper in my learning of SR.

[5614]

Still not confortable with that, but I must live with it if I want to go deeper in my learning of SR.

Whilst it is probably safer to properly understand something before moving onto more complex problems there are occasions when that is false. For example now, if you can just accept it as true and then move on learning SR then later it may become obviously correct. However you can only ever reach that stage of it being "obviously correct" if you just accept it for now.

 

Post any other SR problems you run across because, well, firstly so you can get your problems solved(!) but also because I like SR and SFN is where I learn a lot of physics, if someone posts a thread on SR then it's quite possible I will learn some SR, which is good!

[s pepperchin]

Speed is still s/t, but in the so-called "natural units" of SR speed becomes a dimensionless number between 0 and 1.

 

I think a better way to say it is that we look at all velocities as fractions of c.

[Norman Albers]

Use it just because it is a mess if you don't! It would be nice to have multiple dimensions (first definition) of the same analytic dimension (second definition). I am dealing with that right now in my electron model. I am a pure theorist who deals with pure b******t. It is fair to ask me to put dimensions into my geometric models which were done with none. When you ask me to produce a number, at the very end, expect me to be in a panic for a few days. If you are good you can just pour rubber cement on the paper, and c's and k's stick where they should like glitter. I am having to be a little more thorough.

[□h=-16πT]

Thanks again for your answer and time !

Still not confortable with that' date=' but I must live with it if I want to go deeper in my learning of SR.[/quote']

 

If we're dealing with a theory in which c plays a fundamental role, why not absorb this constant into the background of the theory itsellf, so to speak, by simply redefining the units? If you're not comfortable with it, just think of it as a mathematical simplification, we're just being pragmatic: it gets to be a pain in the arse in long calculations, in any branch of physics , if we have to keep writing out the same constant that really doesn't affect the manner or progression of the calculation itself, except until we want a numerical value, where we can just easily convert back to SI. In GR geometrised units are used, where G=c=1, and in quantum physics its often convention to take units where h-bar=1 or h-bar=c=1.

[Norman Albers]

Plus or minus the panic. The glitter trick works well if there is, say, only one 'k'. Where I have a wave packet falling off exponentially, there are 'k' and 'a'. Selective glue application is called for. In my papers you'll see I am always defining away constants. Please, PURE B******T, simply for convenience. Feynman has some fun here, defining 'unworldliness' by saying the D'alembertian of 'unworldliness' is zero. We have achieved ultimate elegance but said not much. HEY, JACQUES, remember in Hesse' Magister Ludi they end up at the Magic Theater where the price of admission is: your mind. Yes we have lost something, it will mess up your mind, and you will love it because that's why you came, no?

[Norman Albers]

We are literally beings of light, and I am not talking wu-wu stuff either. You must face headon the fact that when you chase light, you change and you see Doppler-shifted frequencies and measure, still, 'c'. I think we are about to see this more completely. Space and time are thoroughly resliced by motion and by gravitation. Rather than repeat, go see my post in Philosophy, Time Not Universal, where we got into simultaneity. Like quantum mechanics you just have to do it and hang out with it until your old mind falls away.

[dkv]

The response has been varying.The concept of ct is not yet clear..

Any distance travelled is also travelled 0n theTime Dimesnion also.

But how much?

This answer you get is by multiplying c with time.

Isnt that simple?

[Severian]

Imagine that the world had lines painted on it, some going east-west and others going north-south. (And imagine that your measurements of distance are small enough that we can neglect the curvature of the Earth.)

 

Now let's say we measured any north-south distance in metres while we measured any east-west distance in feet. Everything would be consistant, and we would have no problems - but we would need to be careful when measuring a distance that we look at its orientation.

 

Now some bright spark will realize that an object which is length x metres when laid north-south is a length y feet when laid east-west where y=a*x (a is about 3, I forget exactly) and this holds for any size object!

 

He will then go on to hyposesize that the laws of physics are independent of which direction you are facing. He will suggest not using separate distance scales but measuring east-west distances in metres too! (And for the next hundred years, spotty teenagers and sad pseudoscientists will post nonsensicle arguments in web fora claiming he was wrong...)

 

Time and distance are much like this. Einstein realized that the laws of physics are the same in any spac-time direction. You can rotate away from the time axis and into the space axis (this is a Lorentz transformation). The factor 'c' is just to compensate for our stupid units (like 'a' was in my analogy).

[Jacques]

Severian you are telling me that In relativity space and time are the same thing ???