Your opinion on"exceeding the speed of light means the ability to return to the past"

yuiop

They are called "spacetime diagrams" and yes, basically graph 2 is how things look in Cindy's rest frame. The diagrams conventionally have space (distance) along the horizontal axis and time along the vertical axis. Try out the applet posted by George http://www.reagenix.com/personal/sci...time/test.html. If you draw a line at 45 degrees to the vertical representing the null worldline of a photon and move the slider you will notice that the line remains at 45 degrees for all observers demonstrating the constancy of the speed of light for all observers.

Also note that in graph 2 produced by George, it can be interpreted that Cindy fired two tachyon shots at evil Alex and Alex looks like the innocent victim of an unprovoked (double) attack by Cindy. Once we accept that FTL interactions, then notions of what was the cause and what was the effect no longer make any sense. Cindy's claim that she was acting in self defence and that Alex fired the first shot, looks pretty week because Alex was dead before he made the alleged initial attack. The prosecution claim that Cindy fired the first shot instantly killing poor Alex and then fired another shot into his dead body for good measure. We also have the problem of defining histories in a universe that allows FTL interactions. For example, was Alex alive or dead between events E and H?

If we take a series of events along an FTL worldine and then carry out a Lorentz boost, then the transformation makes perfect sense if we only consider the events as a series of independent (non causally linked) spacelike events. If we claim that the events are the worldline of a particle then nothing makes sense as explained elsewhere in the current thread.

Drakkith

So the graph uses a lorentz transformation correct? The tachyons appear to travel back in time because the lorentz transformation is set up as c as the speed limit? IE if 10c was the speed limit then the tachyons would not travel back in time? I'm just asking about the math aspect, not the real physical aspect.

yuiop

I think that is correct. If c is the speed limit and the speed of light was c/10 (in a given reference frame because the speed of light would no longer be invariant) then particles travelling at greater than the speed of light, but less than the maximum speed c, would not go back in time. Tachyons are generally described as particles that exceed the speed of light, but that is only accurate if we assume that the speed of light is exactly the maximum speed c (and that photons have no residual rest mass that is currently unmeasurable). If we define tachyons as particles that exceed the maximum possible speed limit c (the invariant speed), then all tachyons will appear to go backwards in time in certain reference frames.

Drakkith

Got it.

GeorgeDishman

Looking at events E and F, although F seems to happen "first", it is the burn on Cindy's arm produced by the firing of the gun at E by the remains of Alex, so the effect precedes the cause.

Of course that's the point, the gun was fired by the corpse unless we insist that the timelike loop must be self-consistent.

GeorgeDishman

Correct, the transforms are built into the applet to calculate the coordinates of the lines and events as you move the slider.

The transforms are actually set up on the screen with c=1, if you draw a line and then move the slider, it limits at one horizontal unit per vertical unit. The word "tachyon" means going faster than that limiting value, there aren't two different quantities being represented either in the applet or the math or the real world physics.

Drakkith

Ok, so if the lorentz transformation is correct and the limiting speed is c, then any hypothetical tachyon would go back in time in certain frames? Thus there cannot be faster than light travel?

Fredrik

Yes, they do, but keep in mind that every Lorentz transformation is associated with a velocity of magnitude less than c. So there are no Lorentz transformations that boost to a frame in which a FTL particle is at rest.

There are some really counterintuitive things about FTL particles. In particular, if I measure a particle going to the right at 10c, then someone going to the right at 0.5c will measure the particle going faster than 10c, not slower.

Yes.

No. It's not obvious that this implies that tachyons don't exist. You need a more sophisticated argument that involves two tachyon transmitters (like the one I linked to in post #6), and even then the conclusion is just that either FTL particles don't exist, or they have some really counterintuitive properties. (Much more counterintuitive than the weird thing I mentioned in this post).

Austin0

Hi Fredrik
Teleportation came up in another similar thread.
Instantaneous translation between points. Absolute simultaneity of events at separate locations.

Assuming teleportation to a distant location in the same frame; How do you calculate the proper time at the point of arrival?? Given t=0 at point of departure.

BTW Congrats.

yuiop

Well it is not clear that Cindy's arm would be burnt as we go forward in time again, because Alex, perhaps along with his tachyon gun, has been destroyed so he is not in a position to do anything. In this case it looks like "evil" Alex is killed in a single unprovoked attack by "nice" Cindy.

As mentioned in #18, the first time around the loop, Alex is alive between events E and H and the second time around he is dead between those same two events. This requirement for different histories probably requires the concept of parallel universes to make sense. Can we say FTL interaction not only implies travelling backward in time, but also implies parallel universes?

yuiop

An energy paradox involving time travel.

Let us say we have one very large uncharged lead battery and a small solar panel to charge the battery. We follow these steps:

1)We connect the solar panel to the uncharged battery.
2)We put a note on the uncharged battery saying "When this battery is charged please send it back to time 1"
3)Our future self obliges and sends the charged battery back in time.

The first time a battery is sent back fully charged, we still have the initial uncharged battery. the second time a charged battery is sent back, we have the initial uncharged battery and two fully charged batteries. Repeat as often as required. We could in principle end up with more batteries than there is lead on the Earth to make them with and with a greater energy store than the total energy impinging on the Earth from the Sun between times 1 and 3.

Sean Pan

Thanks a lot and I have a clearer understand of this problem now. I actually knew that if there were FTL particles, causality would be violated. My opinion is that FTL observers can never actually traveling backwards. And thanks for all above that I now understand what other physicsts mean when they are saying 'returing to the past', it's just an illusion caused by the limited speed of information-carrier. But still, to an FTL particle, γ is no longer real, so I think lorentz boost can't be applied directly here. For example, how can time dilation effect being discussed here?

GeorgeDishman

Exactly, FTL and time travel in this sense are synonymous. Whether that makes them impossible or not is another question.

GeorgeDishman

Hence he didn't shoot, Cindy didn't respond and the third time round Albert is alive. What you have built is the same as an electrical logic circuit with an inverter in a feedback loop, it creates an oscillator switching between two states.

Possibly, that's one way out in sci-fi stories. The other is "cosmic censure" which would require the history round the loop to be consistent, for example forcing a misfire of one of the guns or a non-fatal injury to Albert allowing him to fire (though he could die immediately thereafter).

If you think of the quantum wavefunction going round the loop and Young's Slits as an analogy, we could surmise that non-consistent outcomes lie in the dark bands of destructive interference when calculating their probabilities using the sum over histories method.

Personally, I think they are independent. Albert's shot has an infinite number of points on which it might graze Cindy's arm so alone generates an infinite number of universes and the same is true of every other particle interaction throughout the period. IMHO, any one universe either sees a paradox or a consistent outcome hence you need something more than parallel universes which acts in each. That said, it won't stop the sci-fi authors using it though ;-)

GeorgeDishman

That is an opinion most share as you can see from the replies.

No, that is exactly the opposite of what everyone has said here! What Cindy or Albert can see is on a cone into the past at 45 degrees to the vertical from each event. They never see the tachyons coming but the shots still travel into the past in the frames of both. Albert is killed at event H before he even picks up his gun to start the fight at event E.

It sounds as though you are disregarding what has been said so that you can believe in FTL without dealing with its consequences.

The time dilation factor simply becomes negative. A Lorentz boost is nothing more than a geometric rotation so still applies perfectly to tachyonic particles. For example it would have applied to the reported FTL neutrinos last year (which turned out to be a faulty connection to a clock).

Fredrik

Hi Austin0.

I don't think I understand the question. Since you mentioned absolute simultaneity, you seem to be asking about instantaneous messages in Galilean spacetime. If there's absolute simultaneity, the question of "simultaneous in what coordinate system?" doesn't even arise. So if t=0 at the departure, then isn't t=0 at the arival too, by definition of "instantaneous".

"Proper time" is a property of a curve in Minkowski spacetime, not a point. The concept of proper time isn't needed in Galilean spacetime. (We would have to define it as the coordinate time difference between the endpoints).

The post I linked to in #6 deals with instantaneous messages in Minkowski spacetime.

DrGreg

Within the theory of relativity, if two events are simultaneous in some frame then the proper time between those events is an undefined concept.