Specific Relativity/Light-Speed Question

[EWright]

I guess I need to spend a year in a room with calculus and physics texts, a toilet and a years supply of speghettio's (with meatballs!) until I can emerge with a mathematical "proof" of my theory. I'm off to Barnes & Noble and then the Grocery store. Hopefully I can work out a little time dialation in there to make things go quicker!

[CraigD]

Question: If you travel towards a light source that is 10-light days away, at .5c, how soon will you reach the light given off from that source at the time you began to move towards it? (please do not reaspond by stating the obvious fact that a person can't travel at .5c)

~ 5.77 days

And similarly, how long will it take you to reach the actual source, which is 10 light days away.

~ 17.32 days.

 

I assume all the timings are made by “me” moving toward the light source at .5c, and that the distance and the simultaneous start of the light given of by the source is measured by me when I am stationary with respect to the source.

[EWright]

~ 5.77 days~ 17.32 days.

 

I assume all the timings are made by “me” moving toward the light source at .5c, and that the distance and the simultaneous start of the light given of by the source is measured by me when I am stationary with respect to the source.

 

Then recalculate please. You are not stationary relative to the source. You are moving towards it at .5c. I'm ok with its motion being negligable.

[CraigD]

~ 5.77 days~ 17.32 days.

 

I assume all the timings are made by “me” moving toward the light source at .5c, and that the distance and the simultaneous start of the light given of by the source is measured by me when I am stationary with respect to the source.

Then recalculate please. You are not stationary relative to the source. You are moving towards it at .5c. I'm ok with its motion being negligable.

If you are traveling at .5c when you measure the distance to the light source as being 10 light-days, no relativistic corrections are necessary. You’ll reach the light in ~ 6.67 days, the source in 20.

[EWright]

If you are traveling at .5c when you measure the distance to the light source as being 10 light-days, no relativistic corrections are necessary. You’ll reach the light in ~ 6.67 days, the source in 20.

 

At what point do you reach the half way point to the light source?

[CraigD]

At what point do you reach the half way point to the light source?

By definition, you reach the halfway point to the light source half of the way to the light source. Since you measured the distance to the light source to be 10 light-days, you will measure the halfway point to be 5 light-days from both your starting place and the light source.

 

This dialog is begining to seem strange to me.

[EWright]

By definition, you reach the halfway point to the light source half of the way to the light source. Since you measured the distance to the light source to be 10 light-days, you will measure the halfway point to be 5 light-days from both your starting place and the light source.

 

This dialog is begining to seem strange to me.

 

Sorry, you're right. I misinterpreted something. I'll get back to it in the morning.... I'm off to bed.

[Guest loarevalo]

I have a question also:

 

Someone X leaves earth and travels at the speed of light, then returns to earth, and finds out that 100 years have passed on earth, yet X's watch marks that 0 time has passed.

 

Was that at least theoretically acurate?

 

If so, then in X's reference frame X was traveling at infinite speed ( traveled some distance under 0 time). Is that correct?

 

Thank you all for the responses. So, I take it that we agree that those hypothetical situations are at least theoretically acurate. I didn't mean that anything was traveling backwards in time, or that if what I said was accurate it would imply a paradox.

 

So, traveling at c is comparable to traveling at infinite speed (because we travel non-zero distance under 0 time). If anything could travel faster than c, it would be traveling back in time in its own reference frame, but not actually traveling back in time:

 

It takes about 10 min. for light to reach Mars from Earth. Suppose:

 

I work on Earth, but live on Mars. It's 4:50 and I'm heading home. Luckily, in the past century scientists have discovered a way for humans to travel at the speed of light. So, at 5:00 I get into the travel-at-c machine and therefore get home 10 min. after (according to people on Earth and Mars), but of course, I don't feel anything, my watch still displays 5:00. The experience in the machine is like this: I get inside the machine on Earth, close the door and immediately open it, finding now myself in Mars.

 

Some time later: MIT grads are testing a new travel-faster-than-c machine. I decide to test their machine. It's 4:50 again, I ride to Boston, and get into their machine at 5:00. As expected, I get to Mars 5 minutes later because their machine traveled at twice c, cutting my travel time in half. Also as expected, my watch is ahead (before 5:00), which thought makes me feel a bit younger. ;) Of course, I couldn't tell that to my wife! ;) Yet, she asks me "how was the trip?" What could I tell her?

 

I personally went back in time, though not backwards in the history of Earth and Mars. What actually happened to me during those 5 min. in route to Mars?

[CraigD]

… Also as expected, my watch is ahead (before 5:00), which thought makes me feel a bit younger. …

If you actually moved at 2c as measured by observers on Earth and Mars (This may not actually be impossible. If “you” are a statistical property of the wave description of light … see this interesting link that jerryo posted in “Speed of Light is limited by what?”, though - fair warning - superluminal wave characteristic propagation is mind-boggling, difficult stuff), you watch would not read “4:??”, it would read 5:00 + ?i (where i = -1^.5), a complex number. I can’t imagine a sensible interpretation of this.

 

There’s a way you could make the 10 light-minute trip to Mars in only 5 minutes that doesn’t require you experience the passage of nonsensical time. You just need a traversable “worm hole” – a region of space that is shorter on the inside than on the outside – with movable ends. Place on end of the in a spaceship. Accelerate the ship to .0051 c. Let it travel for a year, eventually arriving back at Earth.

 

Now step throught the end of he worm hole that wasn’t moved. You emerge from the other end 5 minutes in your own past (Check my math, but I believe I’ve picked the right number - v = (1-((1–(300/22917600))**2))**.5). Hop in your travel-at-c machine to Mars. In a subjective (your) instant, you’re at Mars, 5 minutes after an observer on earth saw you step into the wormhole.

 

Of course, a more effective thing to do with a movable, traversable wormhole, is to just put one end on Earth, and one on Mars, allowing for subjective and externally observed trips in near zero time. A more interesting thing to do is take the time-dilated one in the first example, put its ends near one another, then use it to go back in time and tell yourself not to step thought the machine in the next 5 minutes.

 

Postulating the possibility of traversable worm holes is a big speculation, but one that many serious physicists (and their grad-student slaves) have given a lot of consideration. It the subject of one of Kip Thorne’s famous wagers with Steven Hawking, with an entertaining connection to the late Carl Sagan, and fills a chapter of Thorne’s excellent “Black Holes and Time Warps: Einstein's Outrageous Legacy”

[Guest loarevalo]

Thanks, I see that it's far more complex that how I would put it.

 

How could one theoretically travel back in time in the history of Earth? Would one need to travel at negative speed (not -x/t but like x/-t) meaning faster than infinity (not faster than c but actually faster than infinity)?

[CraigD]

... How could one theoretically travel back in time in the history of Earth? Would one need to travel at negative speed (not -x/t but like x/-t) meaning faster than infinity (not faster than c but actually faster than infinity)?

As far as I know, there are at present only 2 scientifically reasonable approaches to time travel. Neither requires any sort of weird velocity.

 

The first is as I described in my last post, and requires a traversable, movable wormhole.

 

The Second is a “Tippler Machine”, and requires a rapidly spinning cylinder with the mass of a planet or more.

 

There’s no consensus among top physicists that either of these would actually work, even if the engineering could be accomplished.

 

Both have the limitation that they cannot be used to travel to time-space where the machine does not exist, so, unless ancient time machines are somewhere for the finding, they won’t be any good for going back in time to witness events in the 1st century Middle East, the Jurassic era, etc. Assuming such machine could be preserved, they should be good for trips thousands of years into the future, to bring back cool knowledge, technology, etc.

 

There was a time travel thread recently that asked this question – you might want to hunt it down for more.

[Tormod]

It takes about 10 min. for light to reach Mars from Earth.

 

(ta-ta! interlude)

 

Here is a basic chart:

http://www.astromax.com/planets/images/mars2003.gif

 

Mars is at 1.5 AU from the Sun, AU being an Astronomical Unit and equals the mean distance from the Sun to the Earth (approximately).

 

At the most Mars is about 2.5 AU from the Earth (opposition), which means that light takes at most 20 minutes. The shortest distance is about 0.23 AU which means that light covers the distance in less than 2 minutes.

 

Okay, nuff nitpicking.

 

(this has been a message from your friendly forum troll. now back to our regular programming)

[Qfwfq]

MIT grads are testing a new travel-faster-than-c machine. I decide to test their machine. It's 4:50 again, I ride to Boston, and get into their machine at 5:00. As expected, I get to Mars 5 minutes later because their machine traveled at twice c, cutting my travel time in half. Also as expected, my watch is ahead (before 5:00), which thought makes me feel a bit younger.

:wave:

There is no reason to expect your watch to read a time previous to 5:00, on what do you base this statement?

 

The time interval between the two events, departure from Boston and arrival on Mars, would be negative for some coordinate frames but what would happen to your watch can't be extrapolated from SR. The square of ds between these two events is negative, it can't really be considered the square of a proper time, it wouldn't be a negative real proper time anyway but an imaginary one.

[Southtown]

Thank you all for the responses. So, I take it that we agree that those hypothetical situations are at least theoretically acurate. I didn't mean that anything was traveling backwards in time, or that if what I said was accurate it would imply a paradox.

 

So, traveling at c is comparable to traveling at infinite speed (because we travel non-zero distance under 0 time). If anything could travel faster than c, it would be traveling back in time in its own reference frame, but not actually traveling back in time:

 

It takes about 10 min. for light to reach Mars from Earth. Suppose:

 

I work on Earth, but live on Mars. It's 4:50 and I'm heading home. Luckily, in the past century scientists have discovered a way for humans to travel at the speed of light. So, at 5:00 I get into the travel-at-c machine and therefore get home 10 min. after (according to people on Earth and Mars), but of course, I don't feel anything, my watch still displays 5:00. The experience in the machine is like this: I get inside the machine on Earth, close the door and immediately open it, finding now myself in Mars.

 

Some time later: MIT grads are testing a new travel-faster-than-c machine. I decide to test their machine. It's 4:50 again, I ride to Boston, and get into their machine at 5:00. As expected, I get to Mars 5 minutes later because their machine traveled at twice c, cutting my travel time in half. Also as expected, my watch is ahead (before 5:00), which thought makes me feel a bit younger. :rant: Of course, I couldn't tell that to my wife! :wave: Yet, she asks me "how was the trip?" What could I tell her?

 

I personally went back in time, though not backwards in the history of Earth and Mars. What actually happened to me during those 5 min. in route to Mars?

You're clock was distorted by motion. Set it forward to 5:00.

 

It would appear that the laws of physics would reverse themselves past c, because bosonic transfer would be in the wrong direction from your rest frame. Who knows what length contraction would become. Maybe we would revert back to energy?

[Guest loarevalo]

Someone said in previous post that the watch would not display 4:?? but 5:00 + ?i , so it isn't as simple as "because time goes forward being traveling at < c, then at >c time goes backward." The equations does not show it and it seems reasonable.

 

I read somewhere that time is a bit different from other dimensions. A formula to calculate

time-space distance:

 

square root ( x^2 + y^2 + z^2 - t^2)

Notice the negative in front of t, so instead of adding -t^2, we could add + (t i)^2.

 

My idea of traveling through time by means of speed spurred from the movie "Back to the future." I'm sure we all have some serious disagreements with the science of it, yet the idea of time travel must have come from somewhere.

[Qfwfq]

Notice the negative in front of t, so instead of adding -t^2, we could add + (t i)^2.

This is but a choice of notation, Landau and Lifschitz use it in their classic textbook, it doesn't show that your watch would read a time previous to 5:00 after the journey. You would have covered a spacelike interval, something there is no experience we know of. As I said, ds^2 is negative for this interval but this doesn't imply a negative real proper time. We do not know ant interpretation of an imaginary proper time, we can't deduce any answer from Lorentz and Minkowski about what would happen to an object travelling faster than c. What we can deduce is that superluminal propagation of causality would be paradoxical.

[Qfwfq]

What I said was:

 

"There is no reason to expect your watch to read a time previous to 5:00, on what do you base this statement?"

 

I did not say that it would read a time after 5:00 or even exactly 5:00. We can't predict any of the three things. We can't even make any sense of what would happen to an object travelling a spacelike curve.