Speed of C in all frames of reference

[shamrock5585]

In einsteins theory of how time is dilated at relativistic speeds he assumes that light moves at the same speed in all reference frames... how is that possible?

if we assume this then we come to the conclusion that time slows down relative to a stationary observer at very high speeds... all of this makes perfect sense but only if you make the assumption that light travels at the same speed relative to an observer. How can a photon move at a certain speed but also be moving at a different speed at the same time?

it is very hard to get my head around... i can see how it works but time being relative to velocity and the speed of light being the same in all references seem to depend on each other... if one is true then the other is too... but what if we don't assume that light moves the same speed in all reference frames? time would be the same in all reference frames...

why do we assume light moves the same speed in all reference frames?

 

[LURCH]

The consatncy of lightspeed was verified expirimentally. Einstein's work was largely in response to this observed phenomanon.

 

[shamrock5585]

im guessing you mean consistency...

how was it verified expirimentally?

this is very interesting and hard to bend my mind around...

it is interesting to get to where if you moved at the speed of light, to a stationary observer your watch would stop moving and you would get somewhere instantly based on your own observation... your clock would still be moving at regular speed as observed by yourself but you would get anywhere you wanted to go without your watch moving anyway so it is as if you never moved at that speed anyway... now if you move faster than the speed of light a stationary observer would observe your watch to move backwards but you would observe your watch to move at regular speed which creates a paradox!

 

[mgb_phys]

how was it verified expirimentally?

http://en.wikipedia.org/wiki/Michelson-Morley_experiment

 

[jtbell]

See the sticky post at the top of this forum, titled FAQ: Experimental Basis of Special Relativity.

 

[russ_watters]

One of the neat things about science is when a new theory has broad implications that can't immediately be tested. Time dilation wasn't really directly testable until the atomic clock was invented almost half a century later. But imagine if atomic clocks and satellites (ie, the GPS system) had been invented before Relativity was figured out. The GPS system wouldn't work - it would have been a disaster. But then, fixing it after they figured out time dilation would have required a simple software update.

Even the slightly more indirect tests (via doppler shift and particle decay) didn't happen until many decades after the theory was worked out and had been accepted.

This wik has explanation of time dilation specific experiments: http://en.wikipedia.org/wiki/Time_dilation#Experimental_confirmation

 

[russ_watters]

it is interesting to get to where if you moved at the speed of light, to a stationary observer your watch would stop moving and you would get somewhere instantly based on your own observation... your clock would still be moving at regular speed as observed by yourself but you would get anywhere you wanted to go without your watch moving anyway so it is as if you never moved at that speed anyway... now if you move faster than the speed of light a stationary observer would observe your watch to move backwards but you would observe your watch to move at regular speed which creates a paradox!

Traveling at or above C isn't physically possible, but yes, time dilation (and the other side of the coin, length contraction) means that interstellar travel is theoretically possible in human lifespans. The catch, of course, is while you can travel to a distant star and back (at just below the speed of light), when you get home, everyone you knew will be long dead.

 

[shamrock5585]

so i have been reading at this because i love this whole concept...

http://en.wikipedia.org/wiki/Speed_of_light

can anyone explain what they mean here...

"information propagates to and from a point from regions defined by a light cone. The interval AB in the diagram to the right is "time-like" (that is, there is a frame of reference in which event A and event B occur at the same location in space, separated only by their occurring at different times, and if A precedes B in that frame then A precedes B in all frames: there is no frame of reference in which event A and event B occur simultaneously). Thus, it is hypothetically possible for matter (or information) to travel from A to B, so there can be a causal relationship (with A the "cause" and B the "effect").

On the other hand, the interval AC in the diagram to the right is "space-like" (that is, there is a frame of reference in which event A and event C occur simultaneously, separated only in space; see simultaneity). However, there are also frames in which A precedes C (as shown) or in which C precedes A. Barring some way of traveling faster than light, it is not possible for any matter (or information) to travel from A to C or from C to A. Thus there is no causal connection between A and C."

im having trouble seeing in what frames A would precede C and another frame where C would precede A...

can anyone explain?

 

[cmos]

That diagram you speak of is taken from the reference frame of A. In that frame, C occurs at a different point in both space and time. What the diagram is saying is that to move through spacetime starting at A, you must stay within the light cone. The way the diagram is drawn, there is no way to reach the event C when starting at the event A. From your reference frame, C occurs after A and at a different point in space.

For event C to occur simultaneously with A, we would place event C on the space axis (t=0).

 

[Fredrik]

im having trouble seeing in what frames A would precede C and another frame where C would precede A...

can anyone explain?

It's simply a matter of moving fast enough in the right direction to give your simultaneity lines (lines of constant time coordinate) a greater slope than the line from A to C. This will give A a higher value of the time coordinate than C.

If you're moving in the positive x direction with speed v, the slope of your world line is 1/v. (You move a distance v*dt in time dt), and your simultaneity lines have slope v. This means that the angle between your simultaneity lines and the x-y plane is the same as the angle between your world line and the t axis. (This ensures that the speed of light is =1 in the new coordinates too).

This also answers the "how is that possible" question from your first post. All of the weirdness of SR is possible because the "slices" of spacetime that one observer thinks of as "space, at different times" are not parallel to the slices that another observer would use.

 

[yuiop]

...
im having trouble seeing in what frames A would precede C and another frame where C would precede A...

can anyone explain?

There is only one frame in which events A and C happen exactly simultaneously. That is the frame of an observer that is exactly at rest with respect to A and C. If the observer is midway between A and C and walking towards C then it seems to him that event C happened before event A and if he is walking in the opposite direction it seems as if event A happened before event C.

Mathematically if two objects A and C are at rest with respect to each other and are separated by a proper distance L, and two events happen simultaneously at locations A and C then to an observer moving with velocity v relative to the rest frame of A and C the events are separated by a time interval of L*v/c^2. If two clock are syncronised at locations A and C in their own rest frame then to an observer with relative velocity v the two clocks are out of sync by that factor of L*v/c^2. This is what is commonly called the relativity of simultaneity.

If a light signal is sent from A at time tA and arrives at C at time tC, then there is no reference frame where events tA and tC are simultaneous* or where tC happens before tA.

*The exception of course is where the spatial separation L of events A and C is zero and then technically they are the same event.

 

[shamrock5585]

but if A is at rest and C is at rest are they not in the same reference frame? the observer is out of sync with both clocks because he is moving at a differenct velocity but he is out of sync from both clocks by the same amount... no?

 

[Doc Al]

but if A is at rest and C is at rest are they not in the same reference frame?

Yes. And according to that frame, the clocks at A and C read the same time.

the observer is out of sync with both clocks because he is moving at a differenct velocity but he is out of sync from both clocks by the same amount... no?

No. The issue is not simply that the moving observer is out of synch with A and C clocks, but that according to the moving observer the clocks at A and C are out of synch with each other.

Reread kev's explanation.

 

[shamrock5585]

"two events happen simultaneously at locations A and C then to an observer moving with velocity v relative to the rest frame of A and C the events are separated by a time interval of L*v/c^2."

i don't understand how events can happen simultaneously but be separated by a time interval?

 

[Doc Al]

i don't understand how events can happen simultaneously but be separated by a time interval?

That's because whether the events are simultaneous or not depends on who is doing the observing. Viewed from their own frame events at A and C are simultaneous; viewed from a moving frame they are not.

Strictly speaking, a statement like "two events happen simultaneously at locations A and C" is incomplete without specifying the frame doing the observing. One can assume, lacking any further details, that the statement refers to observations from a frame in which A and C are at rest.

Lots of things once thought to be universal turn out to be frame-dependent: Length, time, & simultaneity are the big three.

 

[shamrock5585]

i see that if you know the distances from A and C and they are not moving and the observer is moving... obvserver will see different measures for the speed of light than A and C but A and C will see the same measurement for the speed of light... so the observer may see that the light from A got there first but based on the speed of light in that frame (of the moving observer) you can figure out when that event happened... and then when receiveing the light from C after you measure the same speed for the light and you figure out that C was further away and that A and C occurred at the same time... now if A and C are moving at different speeds, then the observer, A, and C will all observe different measurements for the speed of light and you cannot figure out when each event happened... I am just confused why if A and C are in the same reference frame you cannot tell which happened first... i guess I am just not recognizing any contradictions...