How does time "slow down" when you reach c?

[LazerFazer]

Well, here's how I read/understood it from my own personal reading:

 

We are ALAWAYS travelling throught the 4-dimensions of our universe at the speed of light. This might seem bizzare, because according to relativity we cannot achieve the speed of light, merely because we have mass. Think of it this way: there are 4 dimensions: x,y,z (the 'normal' spacial dimensions) and then theres t (time dimension). Just as a car moving along at 10m/s due north goes faster in the 'y' dimension than a car moving at 10m/s @ 45degrees North of East (because in the second instance the velocity now has to split into components), if you move faster in the spacial dimensions, then it would follow that you have to move slower through the time dimension... but heres the catch... RELATIVE TO A STATIONARY OBSERVER, ie. an observer that is not moving through the spacial dimensions.

 

So, now for the proof.

Think of vector-magnitude calculations when you know the value of the components.

 

For a 2-D vector, R^2=x^2+y^2, where x and y are the components of Vector R.

 

Expand this to a 4-d vector, with the total magnitude equalling the speed of light, c, and you get the following:

c^2=x^2+y^2+z^2+t^2

with c=speed of light, x=x-component of motion, y=y-component of motion, z=z-component of motion, and t=velocity through time.

 

Following this, Einsteins time-based special relativity equation can be derived. (for the proof of that, email me and i'll send you a scan of my proof. its too tedious to type up on this)

 

Hope this helps,

LazerFazer

[timo]

Hi LazerFazer and welcome to these forums. The idea of your previous post, namely that every body moves through spacetime with a velocity of magnitude c, is correct. However, your assumption on how to calculate the magnitude of the velocity -and therefore probably also your proof- is at least not conform to the standard notation used in relativity.

 

To stay within your naming convention, the magnitude of the 4-velocity is calculated by c² = t² - x² - y² - z². Therefore, if either the magnitude of x, y or z increases, t must also increase to "compensate" for it.

For relativistic calculation, one usually uses the so-called "natural units" with c=1. I´ll take the freedom to also use them to save me from headaches caused by units transformations. So for a moving particle, you have a 4-velocity of for example (t>1, x>0, y=0, z=0).

Now, how does this translate to time dilatation? Well, within one unit of the particles eigentime (the time measured by the particle), it moves t units of coordinate time (4-position = original position + 1* 4-velocity). Since t>1, the cooridnate time passed "during" this one eigentime unit is >1. Therefore, coordinate time "passes" faster than eigentime. In other words: Eigentime -which is the time measured by the particle- passes slower than coordinate time -which is the time measured by the "outside observer".

 

The object which causes this strange magnitude of t²-x²-y²-z² is called the Minkowsky Metric. It really is a bit strange and it takes a bit of time to get used to this metric (which strictly speaking isn´t even a metric). But it plays an essential -perhaps even THE essential- role in the formulation of relativity.

[eon_rider]

Hi LazerFazer and welcome to these forums. The idea of your previous post, namely that every body moves through spacetime with a velocity of magnitude c, is correct.

 

It’s correct? After I read three million sources (exaggeration ) telling me this is not possible. Now two good people say we are all travelling at C. Is this some kind of paradox?

 

A second question: Given that all movement of A wrt to B is relative (and Viceversa), then as a photon of light (A) travels towards us (B) at speed c, could we not just switch to the photon’s reference frame to show that

we are travelling towards the photon at speed c? (light speed).

 

To me, this supportes the idea that we are all travelling at the speed of light all the time but this can't be so. Is this another paradox?

If NO or I’ve got it confused. Feel free to explain if you wish.

 

Cheers.

 

Also. I read that if you point a laser at the moon and then rotate it a few degrees, the laser appears to move across the moon at faster than light speed. If that laser point was considered to be a binary 1 then when you rotate it you are moving information from point A on the moon to point B on the moon also at faster than light speed. Correct?

 

Feel free to let me know what I’ve misunderstood in either question.

Hopefully with more then just “NO.” Or “Wrong”

LOL.

 

best,

 

Eon,

[timo]

You probably found the only place where I wrote "velocity" instead of "4-velocity". I did this to get in touch with LazerFazers post. 4-veocity is the relativistic analogon to what you know as velocity (3-velocity) and it´s restriction is simply that the magnitude described in my previous post is one... except for photons (see below). This constraint on the magnitude of the 4-velocity directly translates into the constraint that the magnitude of the 3-velocity has to be <c (=c if the magnitude of the 4-velcity is 0).

 

An exception are massless particles. The magnitude of massless particles´ 4-velocity is zero. This is also a reason why you cannot switch to the photon´s frame of reference. The 4-velocity of a particle is always a base vector in a particle´s frame of rest (the base vector of the time component). It is not possible to construct a useful base with a base vector of magnitude 0. Well, the point is: There is no frame of reference in which a photon was at rest.

 

 

Also. I read that if you point a laser at the moon and then rotate it a few degrees, the laser appears to move across the moon at faster than light speed. If that laser point was considered to be a binary 1 then when you rotate it you are moving information from point A on the moon to point B on the moon also at faster than light speed. Correct?

The red point might move across moon´s surface faster that c. The photons making up that red dot move from the laser to the moon at c. For the "movement of information" part. I have yet to see a definition of "information" I understand. You can argument in a way that the information didn´t travel with more than the speed of light. But in the end, I personally see little sense in talking about abstract terms like "information" at all. All particles are bound to have a 3-velocity <= c. That´s sufficient for me to know and therefore that´s also all I know and can say here.

[eon_rider]

EDIT:

An exception are massless particles. The magnitude of massless particles´ 4-velocity is zero. This is also a reason why you cannot switch to the photon´s frame of reference. The 4-velocity of a particle is always a base vector in a particle´s frame of rest (the base vector of the time component). It is not possible to construct a useful base with a base vector of magnitude 0. Well, the point is: There is no frame of reference in which a photon was at rest.

 

Great point. I'll take it on board.

 

I thought it was possible to assign a "relativistic mass" to a photon that depended on its wavelength. This must be a different thing, and I assume you must be refering to the proper mass of a photon? (not sure....still learning.)

 

But I hear what you're saying.

 

The red point might move across moon´s surface faster that c. The photons making up that red dot move from the laser to the moon at c. For the "movement of information" part. I have yet to see a definition of "information" I understand. You can argument in a way that the information didn´t travel with more than the speed of light. But in the end, I personally see little sense in talking about abstract terms like "information" at all. All particles are bound to have a 3-velocity <= c. That´s sufficient for me to know and therefore that´s also all I know and can say here.

 

That's cool. Fair enough. It's all good.

 

Respect,

 

Eon.

 

We are ALAWAYS travelling throught the 4-dimensions of our universe at the speed of light.

 

Can anyone clarify this?

 

best again,

 

Eon.

[swansont]

Can anyone clarify this?

 

 

The length of the 4-vector is constant. If you aren't moving, the temporal term is ct (colloquially, moving through time at the speed of light) and other terms are zero. But if you are moving, the time component gets smaller (dilation) because you have a velocity component.

[eon_rider]

Swansont: The length of the 4-vector is constant. If you aren't moving, the temporal term is ct (colloquially, moving through time at the speed of light) and other terms are zero. But if you are moving, the time component gets smaller (dilation) because you have a velocity component.

 

Sweet. Clearly put. Hopefully I'll retain it.

Cheers.

 

BTW...

 

"a little song, a little dance, a little seltzer down your pants or a little soda water spilled on your clothing?"

 

Is that right? Anyway...that's funny