Space-time contraction question

[Rade]

We know from experiment that time (a measure between two events) slows as we approach speed of light, but does the meter stick (a measure between two entities) then shorten as we approach speed of light ? If yes, since time stops at speed of light, then does meter stick disappear at speed of light ?

 

[Andrew Mason]

We know from experiment that time (a measure between two events) slows as we approach speed of light, but does the meter stick (a measure between two entities) then shorten as we approach speed of light ? If yes, since time stops at speed of light, then does meter stick disappear at speed of light ?

Time and space are relative terms that depend on the relative motion between the measuring frame and the rest frame of the object being measured.

The length of a meter stick moving at relativistic speed relative to you would appear shorter than 1 m. But your meter stick would also appear shorter to the relativistically moving observer. The effect is similar for time - time in the moving frame appearing to move slower.

Time does not stop at the speed of light. The speed of light cannot be reached. Light always moves away from the moving observer at the speed of light. A meter stick will never appear to have 0 length in any inertial frame (mind you, receiving a light signal from the moving meter stick in order to measure it could be difficult so it may seem to disappear). For things that travel at the speed of light (e.g. photons), time and space has no meaning. Time and space has meaning only in relation to matter and space.

AM

 

[Rade]

Thank you, but do not these two statements form a contradiction... "The speed of light cannot be reached" & "For things that travel at the speed of light (e.g. photons), time and space has no meaning" Also, if photons are not within "space-time" where are they ? Your answer defines photons as being "things" that exist so they must exist somewhere, but where if not within "space-time" ?

 

[bernhard.rothenstein]

length and time

We know from experiment that time (a measure between two events) slows as we approach speed of light, but does the meter stick (a measure between two entities) then shorten as we approach speed of light ? If yes, since time stops at speed of light, then does meter stick disappear at speed of light ?

i think that the relativistic effects you mention depend on the way in which you measure length, clock reading and time interval. i would avoid to say that clocks are slowing down.

 

[pervect]

Thank you, but do not these two statements form a contradiction... "The speed of light cannot be reached" & "For things that travel at the speed of light (e.g. photons), time and space has no meaning" Also, if photons are not within "space-time" where are they ? Your answer defines photons as being "things" that exist so they must exist somewhere, but where if not within "space-time" ?

The situation is this:

Massive particles and physical objects cannot move at the speed of light. They must always move slower than 'c'.

Photons and other massless particles must move at exactly 'c'.

People often try to think about what a photon would experience as if it had human qualities. This is a mistake.

I would say that the issue here is that one is "anthropormorphizing" the photon -one is treating it as if it were a human being, and it's not.

See for instance

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/headlights.html

I am driving my car at the speed of light and I turn on my headlights. What do I see?

Sadly this question and all others about experiences at the speed of light do not have a definitive answer. You cannot go at the speed of light so the question is hypothetical. Hypothetical questions do not have definitive answers. Only massless particles such as photons can go at the speed of light. As a massive object approaches the speed of light the amount of energy needed to accelerate it further increases so that an infinite amount would be needed to reach the speed of light.

Sometimes people persist: What would the world look like in the reference frame of a photon? What does a photon experience? Does space contract to two dimensions at the speed of light? Does time stop for a photon?. . . It is really not possible to make sense of such questions and any attempt to do so is bound to lead to paradoxes. There are no inertial reference frames in which the photon is at rest so it is hopeless to try to imagine what it would be like in one. Photons do not have experiences. There is no sense in saying that time stops when you go at the speed of light. This is not a failing of the theory of relativity. There are no inconsistencies revealed by these questions. They just don't make sense.

Despite these empty answers, nobody should feel too put down for asking such questions. They are exactly the kind of question that Einstein often asked himself from the age of 16 until he discovered special relativity ten years later.

Of course, part of Einstein's genius was to see that these questions didn't lead anywhere.

In an abstract sense, one can construct coordinate systems in which the trajectory of a photon is stationary.

These are called "null coordinates" and the transformation rules are quite simple. Using geometrized units in which c=1, the transformations to null coordinates are just:

u = x-t
v = x+t

These coordinates are perfectly valid mathematically, and are even used in General Relativity. They describe a coordinate system in whch a photon moving along the x-axis is represented by a single number (u, or v, depending on which way the photon is going).

Combined with standard 'y' and 'z' coordinates, one can construct a complete 3-d coordinate system out of these null coordinates.

This abstract mathematical description is probably as close as one can come to ascribing a "point of view" to a photon. Note that this coordinate system does not have any such thing as a "time" coordinate - instead, one has two null coordinates (one for photons moving in the +x direction, another for photons moving in the -x direction), and two spatial coordinates.

 

[rakeshrocky]

ok,i have a doubt on Alcubierre warp drive. According to this theory if space-time wrap can be created by bending it and establishing a connection through worm hole then interstellar travel is possible more than light speed. what will be the time taken by the bended space from point A to point B to become normal if the gap is about 5 Light year?

 

[DaveC426913]

ok,i have a doubt on Alcubierre warp drive. According to this theory if space-time wrap can be created by bending it and establishing a connection through worm hole then interstellar travel is possible more than light speed. what will be the time taken by the bended space from point A to point B to become normal if the gap is about 5 Light year?

Wormholes do not allow us to travel at faster than light speeds; they allow us to shorten distances. At no point is the craft moving faster than light.

 

[Naty1]

We know from experiment that time (a measure between two events) slows as we approach speed of light, but does the meter stick (a measure between two entities) then shorten as we approach speed of light ?

Keep in mind such time dilation and length contraction is relative to the other observer's frame...not yours. You see those effects relative to another frame of refernce, and from that reference you are observed the identical way; but in your local frame everything remains the same. Unless you are entering a black hole.