# Tachyon riddle!

#### Tyger

Someone is shooting faster than light particles at you and you accelerate toward the shooter. Do the tachyons speed up, slow down or remain the same speed?

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#### jcsd

Gold Member
If you add the velocities 2c and 0.5c using the correction in special relativity you get:

(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.

#### Janus

Staff Emeritus
Gold Member
Originally posted by Tyger
Someone is shooting faster than light particles at you and you accelerate toward the shooter. Do the tachyons speed up, slow down or remain the same speed?
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.

#### Inertia

Einstein's special theory of relativity predicts that nothing can exceed the speed of light. But special relativity applies when spacetime is flat. When spacetime is curved, the theory applies only "locally"--that is, over regions of spacetime small enough to be considered flat. Consider the analogy of a plane that is tangent to a sphere. The flat geometry of the plane is a good approximation to the geometry of the sphere when the size of the plane is very small compared to the sphere's radius of curvature.
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.

#### Marts Liena

Faster Than Light Musings

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.

#### Marts Liena

Laser spots and tachyons

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?

#### jcsd

Gold Member
Faster than light particles are not forbidden by relativity as long as they never travel at or below the speed of light. Tachyons have never been observed and they have interesting properties like imaginary rest mass.

#### futz

Technically SR does not forbid faster than light travel. It forbids an object that is traveling at v < c from ever reaching c. If the object were created already moving at v > c, that would be perfectly fine in the framework of SR (the same rule applies -- this object would not be allowed to slow down to less than c). Tachyons are such objects.

#### wimms

Re: Laser spots and tachyons

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

#### 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=v1+v2/1+v2&times;v2

and for FTL speeds is

V=1+v1&times;v2/v1+v2

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

Staff Emeritus
Gold Member
What do you mean most correct? What more are you looking for?

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.

#### Tyger

Originally posted by Hurkyl
What do you mean most correct? What more are you looking for?

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.

#### jcsd

Gold Member
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=v1+v2/1+v2&times;v2

and for FTL speeds is

V=1+v2&times;v2/v1+v2

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).

#### Tyger

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+v1&times;v2/v1+v2

only applies when both speeds are greater than light.

#### bdkeenan00

If tachyons do travel at a speed greater than c does that mean that it would be impossible to send information upon them? Since that would be against Einsteinian Locality and could possibly violate causality?

Staff Emeritus
Gold Member
Dearly Missed
Re: Laser spots and tachyons

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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