LightSpeed & Time: What's the Relationship?

[universalidea]

What exactly is the relationship between the speed of light and Time? or in other words will Time still exists if an object was to travel faster than light speed?
Thanks :)

 

[mfb]

What exactly is the relationship between the speed of light and Time?

They are different concepts in physics without a direct relation.

or in other words will Time still exists if an object was to travel faster than light speed?

Objects cannot travel faster than the speed of light (at least not within the known laws of physics), so that question does not make sense.

 

[Khashishi]

Relationship is here: https://en.wikipedia.org/wiki/Time_dilation
You can't travel faster than the speed of light, so the equations aren't valid at those speeds.

 

[Physics-GEEK]

As people have already said, there are no known particles that can travel faster than the speed of light. The tachyon was once such a particle but then it got proven that it is impossible for a tachyon to exist because Einstein's Special Relativity equations states that no particle can reach the speed of light unless it is massless (and most particles are not).

However, to your question for the relation between the speed of light and time is simple. I read the wikipedia page, but that didn't really answer the question for the relation. When one reaches the speed of light (hypothetically), there will be no concept of time. This is because when one reaches the speed of light, time completely stops. So if you were to reach c, you wouldn't even realize when 100 Earth years had gone by and you will still be the exact same age (not even 1 second older) since when you reached c. This is because of Einstein's theory of special relativity which talks about very fast moving particles, including photons and how time changes in its perspective.

The Relation :
T=T[0]/√1-v^[2]/c^[2]
where is T is the Time in motion(where time goes faster)
T[0] is the time at rest(where time goes slower).

So if v=c then the denominator will be = 1-1 = 0.
So if we multiply any magnitude of time by 0, the answer will be zero and therefore one can conclude that for any given time period for an object traveling at c, the time that the object will experience will always = 0

 

[lifeonmercury]

All of these calculations are based on the assumption that nothing in the universe can travel faster than the speed of light (in a vacuum). And this assumption is based our current state of knowledge about our observable universe. Faster-than-light travel may indeed be possible and we haven't discovered it yet.

 

[DaveC426913]

All of these calculations are based on the assumption that nothing in the universe can travel faster than the speed of light (in a vacuum).

Yes. In other words, based on science.

And this assumption is based our current state of knowledge about our observable universe. Faster-than-light travel may indeed be possible and we haven't discovered it yet.

Perhaps true. The list of things that may be possible some day is infinite.

They are outside the scope of this forum.

 

[phinds]

... When one reaches the speed of light (hypothetically), there will be no concept of time.

you are making the common mistake of positing, whether you realize it or not, that there is an inertial frame in which light is motionless. There isn't, so your conclusion is false.

 

[Physics-GEEK]

@phinds
When I said that there will be no concept of time, I meant that tie would have stopped completely. There would be coefficient of time as time would stop.
It also depends on which inertial frame you are talking about. to an outside observer, he/she will not even see you due to length contraction and to the person inside, he/she will not be able to 'experience' time itself due to a very simple equation :
s = d/t

 

[phinds]

@phinds
When I said that there will be no concept of time, I meant that tie would have stopped completely. There would be coefficient of time as time would stop.
It also depends on which inertial frame you are talking about. to an outside observer, he/she will not even see you due to length contraction and to the person inside, he/she will not be able to 'experience' time itself due to a very simple equation :
s = d/t

AGAIN, I point out that your statement is positing, whether or not you intend it to, that there is an inertial frame in which light is stationary and again I say that there is not, so your statement is not meaningful. This is such a common mistake that there is a FAQ on it somewhere here on PF.

 

[Physics-GEEK]

@phinds
So, correct me if I'm wrong, when traveling at c, we are in an inertial frame of reference?
But also, if my conclusion is wrong, then what actually happens to time if a particle reaches the speed of light?

 

[phinds]

@phinds
So, correct me if I'm wrong, when traveling at c, we are in an inertial frame of reference?
But also, if my conclusion is wrong, then what actually happens to time if a particle reaches the speed of light?

"We" cannot travel at c and no, when light travels, it is not in an inertial frame. If it were, then it would be in an inertial frame in which light simultaneously is at rest and is also traveling at c. This obvious contradiction is why it is not meaningful to talk about the "point of view" or "frame" or "concept of time" of a photon.

EDIT: and by the way, photons don't "reach the speed of light". They only exist at c. They start their existence traveling at c and neither slow down nor speed up, when in a vacuum.

I suggest you read some of the thousands of threads here on PF which discuss this over and over. A good place to start is the links at the bottom of this page.

 

[DaveC426913]

When one reaches the speed of light (hypothetically), there will be no concept of time.

To elaborate on what Phinds is saying:

One of the two postulates of Einsteinian relativity is that 'the speed of light is the same in all reference frames'.

You propose an object (spaceship, observer or merely a particle) achieving the speed of light.

By definition, one is stationary in one's own frame of reference. So, your reference frame is moving at c. Thus, light will be stationary.
But the above postulate requires that light be c in your reference frame.

Which means you posit a scenaio where light is both moving at c AND stationary at the same time. This is a paradox.

And that is why the speed of light is not a valid reference frame.

[ EDIT ] Aaaaaaand phinds beat me to it.

 

[DaveC426913]

what actually happens to time if a particle reaches the speed of light?

No particle can ever reach the speed of light. It can only get arbitrarily close to it.
The external universe, as observed from that reference frame, will appear to slow down to virtually zero. (Also, the universe will appear compressed to a disc along the direction of travel, meaning you could cross its very thin breadth in an arbitrarily short length of time.)

 

[Physics-GEEK]

@DaveC426913
I am still not exactly comprehending this situation. One cannot propose that the speed of light is existing both at c and stationary, understood. So what will really happen at the speed of light. How is it possible to say that one cannot know for sure, because in many websites it is written that if one could hypothetically reach c, their time would stop. So what will really happen (hypothetically)?

 

[phinds]

@DaveC426913
I am still not exactly comprehending this situation. One cannot propose that the speed of light is existing both at c and stationary, understood. So what will really happen at the speed of light. How is it possible to say that one cannot know for sure, because in many websites it is written that if one could hypothetically reach c, their time would stop. So what will really happen (hypothetically)?

These "websites" you mention pop-sic at best or ignorant blogs at worse. In either case, they are wrong. Asking what would happen hypothetically is exactly asking this: "if the laws of physics did not apply, what would the laws of physics say about <insert nonsense of your choice>".

 

[DaveC426913]

So what will really happen at the speed of light. How is it possible to say that one cannot know for sure, because in many websites it is written that if one could hypothetically reach c, their time would stop. So what will really happen (hypothetically)?

This is not an analogy, I'm just getting across the idea of asymptotic geometry.

Imagine an airplane on an infinite plane. It cannot turn; it can only ever propel itself due North (its jets are pointed exactly due South).
It is flying North at 500mph, but it is in a 50mph Easterly crosswind. This deflects its course from due North by some angle.
The plane has an endless supply of fuel and it can accelerate as fast as it needs to go.

How fast does the plane need to propel itself (due North), in this 50mph crosswind, so that its heading is actually due North?
Would 5000mph do it? No.
It keeps accelerating.
Would 500,000mph do it? No.
50,000,000mph? No.

No matter how fast the plane propels itself, its heading can only ever approach due North asymptotically.
No amount of proplusion in the direction of due North will ever have its actual heading reach due North.

You are asking 'but what if it could go so fast as to have a heading of due North?'
The answer is: it can't. Full stop.

A long-winded way of saying

The geometry of its environment forbids it.

Spacetime is a different kind of geometry, but the same principle of asymptotes applies.

Simplistically, no object with mass can increase its spacelike trajectory such that its timelike trajectory drops all the way to zero.

 

[Physics-GEEK]

Ok thanks so much guys I actually understood it @DaveC426913 @phinds

 

[phinds]

Ok thanks so much guys I actually understood it @DaveC426913 @phinds

Good. It's not intuitive and you are hardly the only one to have trouble with it at first.