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- Thread starter Tyger
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jcsd

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(2c+0.5c)/(1+ 0.5*2) = 1.75c

but if you sum 3c and 0.5c, you get:

(3c+0.5c)/1+ 0.5*3) = 1.4c

I can't be bothered to work out the limiting cases right now.

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Originally posted by Tyger

Assuming that you are limited to moving at less than c with respect to the person shooting the tachyons, as you accelerate, the tachyons (as measured by you) would slow down approaching the limit of c.

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Inertia

In curved spacetimes, when we compare two observers at large separation, we can no longer use the "locally flat" approximation. In the plane-and-sphere analogy, this situation would correspond to comparing two observers on the sphere separated by a distance comparable to the sphere's radius of curvature. Although each observer could approximate the geometry in his or her local region as a plane, there is no single plane that would be applicable to both observers. Consequently, the two observers in curved spacetime can each apply special relativity in their own local region, but not globally.

A similar situation arises in an expanding universe. Here one should not think of the galaxies as moving through space, but rather that the space between the galaxies is expanding. Einstein's general theory of relativity, on which such models are based, imposes no restrictions on the rate at which the expansion of space can drive the galaxies apart. But special relativity still applies locally, in the sense that a particle chasing a light ray can never catch up to it. An analogy is to imagine bugs crawling on a rubber sheet. By stretching the sheet we can make the bugs recede from each other at arbitrarily high speeds, but no bug can crawl across the sheet faster than a light beam.

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Marts Liena

In the pre-Einsteinian conception of the nature of space and time, there is no limit in principle to how fast an object can travel. But in Einstein's special theory of relativity, the notion of causality--of the past completely determining the future--would break down if any type of matter, energy or signal were able to travel faster than light.

In the pre-Einsteinian framework, time has an absolute character. The time of an event--and thus its time ordering--is the same to all observers; velocities add according to ordinary addition. For very small velocities (small compared to the velocity of light), the same holds in relativity, but for large velocities significant modifications occur. Early in the 20th century the Michelson-Morley experiment established that the speed of light is the same to all observers whatever their relative motion. Therefore the law for adding velocities must be modified. The relative velocity of two objects, one traveling at the same of light and the other traveling at sublight speeds, must equal the speed of light. When both are traveling at sublight speeds, the relative velocity must be less than the speed of light.

One surprising consequence is that time loses its absolute character. The times perceived by observers moving with respect to each other do not coincide. But observers always agree on the ordering of events. If we admit the possibility of faster-than-light speeds, some observers would perceive one event as occurring before another, others would perceive them as occurring simultaneously, and a third group would perceive the reverse order. The time ordering is invariant only when the two events can be linked by a signal traveling at a speed slower than or equal to the speed of light.

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Marts Liena

If i stand in the centre of a wide meteor crater with a powerful laser on a spinning turntable I can easily get my laser spot on the crater wall to travel superluminally. Does this mean the spot is a virtual tachyon?

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jcsd

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I wonder, if i stand in the centre of a small meteor crater with a powerful d..k on a spinning turntable can I easily get my pee spot on the crater wall to travel supersonically?Originally posted by Marts Liena

If i stand in the centre of a wide meteor crater with a powerful laser on a spinning turntable I can easily get my laser spot on the crater wall to travel superluminally. Does this mean the spot is a virtual tachyon?

I guess if you spin fast enough, you'd get spiral shaped lightray, and spot would still travel at c.

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Janus' answer is the most correct one so far.

jcsd is correct insofar as the speed decreases, but the derivation and values are incorrect. The first one has a clerical error, but that aside the derivation for STL speeds is

V=v_{1}+v_{2}/1+v_{2}×v_{2}

and for FTL speeds is

V=1+v_{1}×v_{2}/v_{1}+v_{2}

but the one for combining both types of speeds involves separating the space and time parts and putting them together another way. Unfortunately I haven't worked out all the details yet, but I do know that in a sense the FTL and STL regimes are inverses of each other.

jcsd is correct insofar as the speed decreases, but the derivation and values are incorrect. The first one has a clerical error, but that aside the derivation for STL speeds is

V=v

and for FTL speeds is

V=1+v

but the one for combining both types of speeds involves separating the space and time parts and putting them together another way. Unfortunately I haven't worked out all the details yet, but I do know that in a sense the FTL and STL regimes are inverses of each other.

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Hurkyl

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I guess I'm presuming by the statement of the problem that you observe the tachyons as moving from the shooter towards yourself; if you perceive the tachyons going the other way, then as you accelerate towards the shooter you will perceive their speed shoot off towards infinity and then they will slow back down, now going the "right" way.

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Originally posted by Hurkyl

I guess I'm presuming by the statement of the problem that you observe the tachyons as moving from the shooter towards yourself; if you perceive the tachyons going the other way, then as you accelerate towards the shooter you will perceive their speed shoot off towards infinity and then they will slow back down, now going the "right" way.

Tachyons are tricky, very counterintuitive, but if you try to "chase" them they will just keep speeding up.

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jcsd

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Originally posted by Tyger

Janus' answer is the most correct one so far.

jcsd is correct insofar as the speed decreases, but the derivation and values are incorrect. The first one has a clerical error, but that aside the derivation for STL speeds is

V=v_{1}+v_{2}/1+v_{2}×v_{2}

and for FTL speeds is

V=1+v_{2}×v_{2}/v_{1}+v_{2}

but the one for combining both types of speeds involves separating the space and time parts and putting them together another way. Unfortunately I haven't worked out all the details yet, but I do know that in a sense the FTL and STL regimes are inverses of each other.

Erm, where did you get that equation for FTL travel, it's incorrect as it cannot produce values above c, meaning when you add 2 and 0 you get 1/2 which is nonensical (as essientally says that you can change the observed value for the speed of an object without changing reference frames).

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Originally posted by jcsd

Erm, where did you get that equation for FTL travel, it's incorrect as it cannot produce values above c, meaning when you add 2 and 0 you get 1/2 which is nonensical (as essientally says that you can change the observed value for the speed of an object without changing reference frames).

The FTL speed quation, corrected,

V=1+v

only applies when both speeds are greater than light.

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selfAdjoint

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Originally posted by Marts Liena

If i stand in the centre of a wide meteor crater with a powerful laser on a spinning turntable I can easily get my laser spot on the crater wall to travel superluminally. Does this mean the spot is a virtual tachyon?

The spot is not a thing and does not travel. Rather a succession of spots falls along the path. Each spot is illuminated by new rays as you swing the laser (in my day they just used a flashlight).

What relativity says is,

If your invariant mass is a real number and > 0, you must travel at < c

If your invariant mass is 0, you must travel at c

If your invariant mass is a pure imaginary number you must travel at > c

Relativity has nothing to say about other cases (mass real and < 0, or a general complex number).

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