# Einstein's theory of relativity?

1. Oct 15, 2006

### Indian_2006

Einstein's theory of relativity?

In Length contraction and Time dialation, the distance between the two frames is also a determining factor. i guess so
but why do they are not taken into account.

why they are not included in the equation?
I mean in m =[mo/root of one minus V^2/c^2]

why the distance between the two frames is not considered

2. Oct 15, 2006

### HallsofIvy

Staff Emeritus
You start by asserting "the distance between the two frames is also a determing factor". What reason do you have for saying that? in fact, now that I think of it, what do you mean by the "distance between two frames". A "frame" is basically a coordinate system. I suppose you might mean the distance between the origins of the two coordinate systems but since a given distance would be measured the same at any point of a single coordinate system, that can't have any effect on the distance as measured in two different frames.

3. Oct 15, 2006

### pess5

If a body moves at v, it matters not where it is, its still v. Light moves at c always. The relativistic distortion factor is gamma = 1/(1-v^2/c^2)^1/2, as you pointed out. It arises strictly from the 2 observers of relative v comparing how long a lightpath is in the one frame versus the other, over some common spacetime segment they both can see. Since v is v and c is c irregardless of where something is precisely located, then relative seperation plays no role.

Mass, is a scalar. It doesn't matter whether a 1 gram mass is here or there, it is still 1 gram. By relativity theory however, total mass is proportional to gamma, so m=m0(gamma), where m0 is the rest mass. None the less, mass is still a scalar. What is a vector is the momentum, ie p=mv. Since mass is a scalar, it doesn't matter where it is located. All that matters is its rest mass, and its relative speed.

On the other hand, if one wanted to determine precisely where the massive body was located, or where precisely the front of a body (or aft end of a body) is located at any time, then the Lorentz Transformations are used and relative seperation is vital. However here, your are considering the material body. Mass is just a scalar property of the material body.

pess

4. Oct 15, 2006

### MeJennifer

Interesting topic.

I believe the issue here is, what our distinguished member JesseM frequently calls, the difference between "observing" and "seeing".

If we take a "Doppler" view of reality, in other words a world view based on when light pulses are actually received then distance is most certainly a factor.

Actually my preference goes towards treating relativistic effects by avoiding the construction of a plane of simultaneity as some idea of reality, but instead to use the actual times when light pulses are received. I would be interested to hear what distinguished member bernhard.rothenstein has to say on this topic.

I would venture that if we ever get space traveling at relativistic speeds there would be more of a need to measure and predict the time of receiving light signals then a need to construct a plane of simultaneity.

Last edited: Oct 15, 2006
5. Oct 16, 2006

### pmb_phy

That is an excellant observation. If you read either Taylor or Wheeler's texts on relativity they will often use the term reckon so as not to confuse it with what the eye sees.

Best wishes

Pete

6. Oct 16, 2006

### ZapperZ

Staff Emeritus
Humm... then are you saying that when a police officer does a radar scan on you moving at 80 mph, there is a difference other than the "time of flight" if he/she is doing this when you are 1/2 a mile away versus when you're 10 miles away?

Zz.

7. Oct 16, 2006

### Severian

I think she is refering to the difference of whether the frame of reference has one observer sitting at the origin, or infinitely many little helpers sitting at every point in space, at rest with respect to the observer.

In other words, the time coordinate of an event is the time as measured by the 'helper' at the space-coordinate on the event - not the time at which the observer at the origin would 'see' the event happen.

8. Oct 16, 2006

### ZapperZ

Staff Emeritus
Er.. then I don't see the connection here with the OP, especially with regards to the observed time dilation and length contraction.

Are these two values dependent on the distance between the two frames? If it is, then I'd like to see it worked out for when those two aren't moving.

Zz.

9. Oct 16, 2006

### bernhard.rothenstein

If you have in mind the distance between the origins of the two inertial reference frames, you should have in mind that the Lorentz-Einstein transformations are derived considering that at t=t'=0 the origins O and O' are located at the same point in space x=x'=0 considering that the reference frames are in the standard arrangement. The distance between the two origins is a function of the relative velocity of the two frames and of the time. Taking into account that fact, there are no special problems with lenght contraction and time dilation.

10. Oct 16, 2006

### bernhard.rothenstein

I used to say to my students that the concept of event is fundamental in physics. As an Einstenian observer located at a given point in space I can attribute to an event which takes place in front of me my own space coordinates and the reading of my wrist watch which is synchronized using Einsten's clock synchronization procedure with the clock of my chief observer located at the origin of my rest frame. Located at the origin of my rest frame I can register simultaneously light signals which have left at different times the different points of a luminous profile (photographic detection of the space-time coordinates of an event and we can say visual detection as well). Located at the origin of my rest frame I can handle a radar detection device sending out a light signal at a given time displayed by my wrist watch and receiving it back after reflection on the point where the event takes place at another time displayed by my wrist watch as well. The two times enable me to reckon the space-time coordinates of the event associated with the reflection of the light signal on it. I can use the parallax method as well. Physicists, cleaver as they are could invent other ways to do the same job. Special relativity, with its postulates becomes involved when I try to establish a relationship between the space time coordinates of the same event detected from two inertial reference frames in relative motion taking into account the peculiarities of the different procedures mentioned above. The procedure I prefere is a question of taste and "de gustibus...". Reading the lines above take please in to account that I told all that to my students not in English.
The best things a physicist can offer to another one are information and criticism

11. Oct 16, 2006

### bernhard.rothenstein

mass formula

When we speak about the mass formula you mention, we should say that it holds only in a given inertial reference frame relative to which the particle with rest mass mo moves with velocity V. You will also find in the literature the formula
m=mogamma(1+u'V/cc)
where u' represents the velocity of the same particle relative to an inertial reference frame which moves at its turn with speed V relative to your rest frame.