Relative Time

It's undefined. The calculations include the term 1/(1-v²/c²)^0.5, so if v=c, it's 1÷0.

Ok, I see,so only a fractional part of C can be calculated.

So, how fast would one have to travel for one day(relative to the traveler),to equal

1000 years Earth time?

Back of my envelope reckons about 0.999999999996 x c (but it could be wrong).

I make it 0.999999999996247*c

Think you're 2.5 days out (not counting leap-years).

Depends on the gravitation field you are travelling in...

To be more specific the time dilation equation (Wikipedia) is

As v→c simple algebra does say that this formula alone makes an undefined value. However, applying L'Hospital's rule shows that the relativistic time difference approaches infinity for any time happening in the real world. Thus the real world must experience an infinite amount of time to change for the relativistic time to notice any change. In simpler terms time stops for the one travelling at the speed of light, if that were possible.

Yes, and wee see right there that this equation is quadratic(2nd order) not linear, just near the undefined is an enormous value (magnitude).

Depends on how many rest stops were made.

1 Day: he left his clock at home on earth.

I saw Relative time and thought my in-laws were within range . . .

He wouldn't experience 1 day. At the speed of light, time stops.

Nope, it doesn't stop, I've been there with James Stewart, believe me

???What the????

Do you want it to stop? Time really slows down when one is having fun. Have you tried running really fast, and right before you hit that concrete wall, just ducking your head slightly?

I guess 1 day. No matter what they do, how fast they travel, whatever they see,

if their time is by the same clock 1 day is one day. Yes. ?

jt.

They said go for it... but it had went.

So if our space-time vector always sums to C, and the velocity component is C, time stops, and so is therefore one cannot ask for how long or how far from the reference frame of the traveler, no?

By his clock. One day on earth would be the same by his clock. The question should be if traveling at the speed of light would that cause his clock to stop?

Brings back memories of Einsteins tram ride.

Regards JD.

There was a young lady named Bright
who travelled much faster than light.
She set off one day
(in a relative way)
and got back on the previous night.

I wonder if that question was ever addressed on Star Trek (the original), where they traveled at "warp speed 7", e.g.? (Warp speed meant speed of light, didn't it?)

Well, In the pilot, they mentioned that it was 'Time Warp factor 7'and later mentioned to colonists from a 'sleeper' ship colony that the Federation had broken the 'Time Barrier' to allow such fast travel. In the regular series, however, it was more of a 'Space Warp' effect, with the 'Warp Field' or 'Warp Bubble' enclosing the ship, 'separating' it from normal spacetime in some way. (believe be the Treknobabble gets REALLY dense on this topic)

If we were to look at modern physics, the 'Warp Drive' is most likely a version of the 'Ambercluie Drive' (assuming I didn't mangle the name too much for search engines) which allows effective FTL travel by compressing spacetime in front of the ship, and expanding spacetime behind it. Spacetime expansion has no speed limit, as the Observable Universe ends right where the percieved redshift of galaxies places their relative speed away from us at near C. anything on the far side of them will be invisible and undetectible to us, as it's effective speed is greater than C, light from there will NEVER reach us.Actually, we can't even see stars close to the 'edge' of the Observable universe, as even a Gamma Ray Burster would have it's ultra-high energy rays 'downshifted' below infrared, below RF, even below ELF (Extreme Low Frequency, a 'radio wave' that can penetrate the ocean, used to send messages to subs. The recieving antenna is a cable several MILES long the sub trails behind it, the transmitter is a MASSIVE array on land, again MILES long.).

But I'm digressing, the FTL of Star Trek is by Warp Bubbles, where the ships 'surf' on a fast traveling 'wave' of spacetime distortion.

I believe you are talking about the Alcubierre drive.

Thank you, I knew someone would be able to find it, even if I have "ABsoutely NO-CLUEY" how to spell that name.

Too bad it manipulates spacetime and not inertia. If it were an inertia nullifer type drive, I could just call it a "Bergenholm Drive," which I can spell easily.

A question without a possible answer---because the question does not state the location of the observer. Who is to say that the person on earth didn't travel at the speed of light and the "traveler" stand still? The question asks about time lapse on earth while the other was traveling at C for 1 day. If the observer is at a speed exactly 0.5C in relation to each one, then this observer would find that the elapsed time for both was exactly 1 day.

Again, the question is without a possible answer.

--JMM

I believe that's a misunderstanding of special relativity. The situations of the traveller and Earth are not symmetrical. If the traveller goes to a star say 10 light years away and back time taken can be as short as you like if he goes fast enough, and he has aged that amount, while Earth has aged 20 years. The difference (I think) is because the traveller is accelerating (relative to all the matter in the universe, or to absolute space, according to your viewpoint).

That approach implies that there is a "fixed" reference point, from which all other objects' speed is compared. I thought we went past that some time after Copernicus. We were geocentric, then heliocentric, then...

I realize that my earlier comment leaves open the conundrum of multiple bodies: If "A" and "B" are both moving apart at 0.75C and then "B" and "C" are both moving apart at 0.75C and then "C" and "D" are both moving apart at 0.75 C, how quickly are "A" and "D" moving apart? In real terms, light from a star is moving at C in all directions. Therefore one photon can be moving away from another at 2C.

I have trouble wrapping my mind around this.

--JMM

There may not be a fixed reference point, but acceleration and rotation must be relative to something. Newton thought it was "absolute space", nowadays (I think) it's considered relative to all the matter in the universe (though the exact relation isn't clear). If there were no other matter acceleration and rotation would have no meaning. Newton's bucket experiment, when if bucket and water are got spinning, and the water goes down in the centre, it still does if the bucket is stopped but the water continues spinning.

Difference in aging has been confirmed experimentally. Particles produced by cosmic rays in the high atmosphere are detected at ground level, though their half-life is so short they should have decayed before that. Also with atomic clocks on satellites.

There is a formula for addition of velocities in special relativity (on Wikipedia). The relative velocity is still c even if bodies are approaching, each at velocity c.

Here is a very simplistic answer that is based as you say on relative time. I may be way off base but this is one way to look at it: Let us say we are comparing how long it would take the earth to get from the sun to the earths' orbital position (93 million miles). Using the current speed at which the earth orbits the sun (67,000 mph) it would take the earth 58 days to reach that distance from the sun traveling in a straight line. It takes light 8.3 minutes to go that distance. So, if you are traveling at the speed of light, it would take only 8.3 minutes to get there. However, if you are on the earth, it would take you 58 days. If we do the math, when comparing these two travelers, the traveler going at the speed of light for 24 hours (relative to his frame of reference) would take 28 years for the traveler on earth to go that same distance.

You notice that I have framed this answer relative to time and motion. This is the only way I can answer this, for without motion, there is no time. Time does not exist unless something is moving. And on to my next postulation: There is no gravity until a mass moves through space. And all the heavens are in motion!

#1 - the traveler would die if accelerated to c, due to his apparent mass increase, even the slightest gravitational perturbation could crush him.

#2 - the traveler would die if accelerated to c, due to length forshortening, he is apparently crushed again.

#3 - the traveler would die if accelerated to c, if the duration of accleration is instantaneous he is crushed, if it is not instantaneous, he expires from old age before traveling at precisely c.

#4 - question is irrelevant or irreverant.

#5 - if #1-#4 can somehow be avoided, then for 1000 years to pass on earth, the traveler notices only 1 day when (C-V)/C is 3.74783x10^-12 , so that is going fast for all practical purposes. The calculation is based upon the Lorentz factor, the standard value of the speed of light (although just knowing V/c or (c-v)/c is good enough).

I don't think all that is correct. As I understand it (I'm no expert) the traveller cannot reach the speed of light, but the effects of mass increase and length contraction (only noticeable at speed approaching c) are not experienced by the traveller, but are as seen by a stationary observer.

Yes, in the traveler's frame of reference (which only applies in special relativity where acceleration is not considered, only constant velocity), his time seems normal, his dimensions seem normal to him, but he observes time dilation outside his frame of reference, linear foreshortening of objects outside his frame, and also mass increases outside his frame of reference. Would this not means that any massive object near his flight path should appear to be compressed, exhibit a larger mass? Would this not exert a tremendous gravity well on him and his spacecraft?

Maybe I am wrong, but I think relativity should also be messing with gravity just based on the Lorentz factor between frames of reference. I have never worked out the maths for the General Relativity case of accelerating frames.

Dear Mr.HiTekRedNeck,

About 20 Years back I have studied in special Issue published by a Science Magazine, , which describes, a man travelling at VERY NEAR TO SPEED OF LIGHT at AIR i.e., 1,86,000 Miles/Sec. or 2,97,600 KM/Sec. (5 Miles = 8 KM approx.) for one Year (of Earth Time) in space and when he comes back to Earth, it is described that 3.0 Million Years could have elapsed, on earth, he cannot see his parents or kith and kin which I did not and could not understand even today.

The definition/explanation of "VERY NEAR TO SPEED OF LIGHT" is described as (0.99999999) x 1,86,000 Miles/Sec. or (0.99999999) x 2,97,600 KM.

Let us see what other CR4 MEMBERS explain.

DHAYANANDHAN.S

The effect is one that is covered well in Special Relativity.

The Lorentz factor for time dilation applies to an observer at rest in his own spatial frame of reference (man in space ship), when there is a high relativistic speed to another frame of reference (earth). His hypothetical trips requires that he not be bothered with effects of acceleration/deceleration, nor any time taken with respect to that. The proposed loss of several million years can only take place when (C-V/C) is a tiny tiny fraction. Dear friend, I will let you have the space to perform the calculation for yourself.