# Length contraction v. time dilation

1. Mar 24, 2008

### tomtraxler

Bear with me. I am a lawyer, not a physicist.... I understand how the light clock demonstrates time dilation with special relativity. I think I understand length contraction.

Here is my question: at relativistic speeds, why does length contraction not affect the distance traveled by the light flash? In other words, why isn't the "V" shape of the light (as seen by the external observer) "squashed" and made more narrow by length contraction, thereby affecting the calculation of the distance traveled by the light etc.?

Is it because the external observer would measure the distance using a meter stick on the frame of reference traveling at relativistic speed (which would likewise be contracted) or does the external observer use his own external meter stick that is not contracted?

Thanks!!

2. Mar 24, 2008

### Janus

Staff Emeritus
The external observer uses his own external meter stick. He is measuring how long the light path is in his frame.

3. Mar 24, 2008

### rbj

length contraction does affect the length of the meter stick if it is oriented in the direction of travel. but, even if the speed is relativistic, there is no reason for it to affect lengths (or components of length) along the directions that are perpendicular to the direction of travel.

actually, it would make less sense (or be a less simple model) for length contraction to be observed in for meter sticks that are perpendicular to travel. suppose it did, if moving a meter stick that is parallel to the y axis in solely the x direction contracted length in all the x and y and z directions. then what wound happen if the object were moving in the x and y directions (at a 45o degree direction)? if you slug out the math, would the contraction be the same? not if time dilates by a factor of $(1-v^2/c^2)^{-1/2}$. you would get some contraction for moving in the x direction for $v/\sqrt{2}$ velocity, and another contraction for moving the same speed in the y direction. but if the contraction in the y direction due to movement in the x direction is none, and the contraction in the y direction due to movement in the y direction is what we get in SR, then the math works out.

Last edited: Mar 24, 2008
4. Mar 25, 2008

### bernhard.rothenstein

There are very different methods to measure distances and time intervals (radar detection, photographic detection...) which could lead to length contraction, length dilation or even to the absence of such relativistic effects.

5. Mar 25, 2008

### belliott4488

If the previous responses still leave you uncertain, then maybe you could clarify a bit what it is you're asking.
First of all, what is the situation here? Moving light source? When you say "external observer", do you mean "external to the light source", implying perhaps an observer at rest with respect to the source, and one moving with respect to it? Also, since you're asking about the beam of light, is the light directed in the same direction as the relative motion of the observers, perpendicular to it, or something else?

Also, what "V" shape do you mean? Are you talking about the angular spread of a beam of light, e.g. from a flashlight? If so, and if the beam is parallel to the direction of motion, then rbj's respose is apt. On the other hand, are you talking about the "V" shape of the light cone as drawn on a space-time diagram?

These things weren't clear to me, but they affect the answer. (I know you don't mind my asking for clarification, since clear and unambiguous language is your stock and trade! )