tachyons

tachyons are particles that travel faster then the speed of light and can never go slower then the speed of light and travel back in time. they also have negative energy. Do they break any laws of physics and what would they mean for the universe.

The Star Trek convention called, they want their warp core back.

Just because it was in star trek does not mean that it is an idiotic theory.

Do they break any laws of physics

In terms of FTL, the tachyon definitely breaks a few laws in special relativity, but it seems reasonable in general relativity due to space-time distortions. E.g. worm holes. However, the tachyon and FTL are still only hypothetical terms in modern science.

and what would they mean for the universe.

Obviously, it's most likely used to propagate information.

In terms of FTL, the tachyon definitely breaks a few laws in special relativity, but it seems reasonable in general relativity due to space-time distortions. E.g. worm holes. However, the tachyon and FTL are still only hypothetical terms in modern science.

For the most part tachyons agree with special relativity, don't they?  What laws do they actually break?

Quote from: Jack on February 25, 2009, 06:40:11 PM

In terms of FTL, the tachyon definitely breaks a few laws in special relativity, but it seems reasonable in general relativity due to space-time distortions. E.g. worm holes. However, the tachyon and FTL are still only hypothetical terms in modern science.

For the most part tachyons agree with special relativity, don't they?  What laws do they actually break?

They would only break the law of causality if they were used to transmit data theoretically. The effect of a passing tachyon would be similar to the effect of a fighter jet breaking mach 1.

There's a wiki article on the subject, but it deals partially with string theory which I don't particularly subscribe to.

In terms of FTL, the tachyon definitely breaks a few laws in special relativity, but it seems reasonable in general relativity due to space-time distortions. E.g. worm holes. However, the tachyon and FTL are still only hypothetical terms in modern science.

Obviously, it's most likely used to propagate information.

You know, it could help if you actually opened your mouth when you had some understanding. Tachyons don't have any special or general relativity issue. They were hypothesized precisely because they are consistent with the relevant equations. They have nothing to do whatsoever with worm holes. Tachyons would not travel through odd topological structures but in functionally normal space.

Tachyons also cannot be used to propagate information faster than light speed. Roughly speaking, that would require them to violate causality in somebody's light cone something which would make special relativity a sad panda.  The physics behind why they don't violate causality is more complicated (and the details are a bit beyond me).

For the more technically inclined: The total energy of a particle under special relativity is (mc^2)/(1- v^2/c^2) (There may be some normalization of units to get this equation. Not sure. Haven't done this in a while). Now, when v exceeds c, (that is you have a tachyon) the bottom becomes the square root of a negative number, so either energy or mass needs to be thought of as an imaginary number. This turns out to be more or less ok when tachyons are interacting only with each other but leads to bad stuff if they need to interact with normal particles. Thinking further along these lines is what leads morally speaking to the conclusion that tachyons can't go slow down to the speed of light or below it.  

There's an important alternative definition of a tachyon: A gluon that isn't quite dry.

Tachyons don't have any special relativity issue.

Uh, yes they do. Special relativity forbids any object to travel faster than the speed of light. Relative to all inertial observers, massless particles travel at c. Relative to all inertial observers, massive particles (or any particles with mass) may approach c but never get to or past c. Get your facts straight.

They have nothing to do whatsoever with worm holes.

I never said they have anything to do with worm holes. I said general relativity may allow FTL due to space-time distortion, e.g. wormholes.

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#20

For the most part tachyons agree with special relativity, don't they?  What laws do they actually break?

Special relativity forbids anything to travel faster than the speed of light.

Quote from: JoshuaZ on February 25, 2009, 06:59:16 PM

Tachyons don't have any special relativity issue.

Uh, yes they do. Special relativity forbids any object to travel faster than the speed of light. Relative to all inertial observers, massless particles travel at c. Relative to all inertial observers, massive particles (or any particles with mass) may approach c but never get to or past c. Get your facts straight.

Quote from: JoshuaZ on February 25, 2009, 06:59:16 PM

They have nothing to do whatsoever with worm holes.

I never said they have anything to do with worm holes. I said general relativity may allow FTL due to space-time distortion, e.g. wormholes.

http://math.ucr.edu/home/baez/physics/Relativity/SpeedOfLight/FTL.html#20

Quote from: Soul Eater on February 25, 2009, 06:52:50 PM

For the most part tachyons agree with special relativity, don't they?  What laws do they actually break?

Special relativity forbids anything to travel faster than the speed of light.

Special relativity doesn't forbid FLT.  It forbids anything from accelerating past the speed of light, which would require infinite energy.  Tachyons are always moving faster than light, thus there is no energy barrier to cross.

Special relativity forbids anything to travel faster than the speed of light.

No it doesn't. This is a common misconception. Please take a physics course.

If a particle's rest mass is a positive real number then the particle cannot accelerate to or beyond the speed of light. If a particle's rest mass is zero then it must travel at the speed of light. If a particle's rest mass is imaginary then the particle travels faster than the speed of light and cannot accelerate below it. (I'm abusing notation slightly with the term rest mass only being strictly valid for the first of the three cases)

Tachyons were in fact first thought about because they turned up as apparent consistent solutions to the equations for special relativity much as how the positron was first conjectured to exist because they turned up as additional solutions to Dirac's equation.

Also wormholes strictly speaking are not a form of FLT. Any traveler cannot beat light traveling through the wormhole.

wouldn't tachyons not interact with matter anyway. They have negative mass which would give them negative gravity so they would be repelled by the galaxy.

No it doesn't. This is a common misconception. Please take a physics course.

Yes it does, especially to objects with mass. No information can travel faster than the speed of light. Massless particles travel at c. It's compelling to think SR allows FTL due to the tachyon; that's a common misconception.

Space-time distortion

Although the theory of special relativity forbids objects to have a relative velocity greater than light speed, and general relativity reduces to special relativity in a local sense (in small regions of spacetime where curvature is negligible), general relativity does allow the space between distant objects to expand in such a way that they have a "recession velocity" which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light years from us today have a recession velocity which is faster than light.

As I've said, GR may allow FTL, but not SR.

The proof that faster-than-light (FTL) propagation is not allowed by nature is simple. Special relativity (SR) forbids it because, in that theory, time slows and approaches a cessation of flow for any material entity approaching the speed of light. One might immediately object that, in particle accelerators, the behavior predicted by SR is observed to happen as speeds approach c. No matter how much energy is added, the particles cannot be made to reach or exceed speed c.

As I've said before, relative to all inertial observers, a massless particle travel at c, whereas a massive particle may accelerate and approach c.

If a particle's rest mass is imaginary then the particle travels faster than the speed of light and cannot accelerate below it. (I'm abusing notation slightly with the term rest mass only being strictly valid for the first of the three cases)

So, what is the value of this imaginary mass of a tachyon?

Also wormholes strictly speaking are not a form of FLT.

Please read my link.

It forbids anything from accelerating past the speed of light

I'm pretty sure that's what I just said.

Quote from: Soul Eater on February 25, 2009, 06:52:50 PM

Quote from: Jack on February 25, 2009, 06:40:11 PM

In terms of FTL, the tachyon definitely breaks a few laws in special relativity, but it seems reasonable in general relativity due to space-time distortions. E.g. worm holes. However, the tachyon and FTL are still only hypothetical terms in modern science.

For the most part tachyons agree with special relativity, don't they?  What laws do they actually break?

They would only break the law of causality if they were used to transmit data theoretically. The effect of a passing tachyon would be similar to the effect of a fighter jet breaking mach 1.

There's a wiki article on the subject, but it deals partially with string theory which I don't particularly subscribe to.

Tachyons wouldn't break causality from what I understand. If you made a tachyon detector it would create tachyons that would create Something that would be considered static so you couldn't figure out which tachyon sent the info and which were created by the tachyon detector. thus no information is sent into the past.
Also tachyons would have been going faster then the speed of light since the big bang and would have never passed the speed of light

wouldn't tachyons not interact with matter anyway. They have negative mass which would give them negative gravity so they would be repelled by the galaxy.

Actually, no. Technically, using that logic, knowing that having positive mass expands space-time (thus having positive time passage due to the distance between two masses), having negative mass would be the reverse. I'm not 100% on that, I'm just going by your logic to make more sense, I am not sure if that is actually how it would work, but it would explain why tachyons would be able to travel faster than light. They would not be repelled by any positive mass. If anything, they would be of the same nature of neutrinos as far as interactions go with our current knowledge and technology level.

Tachyons wouldn't break causality from what I understand. If you made a tachyon detector it would create tachyons that would create Something that would be considered static so you couldn't figure out which tachyon sent the info and which were created by the tachyon detector. thus no information is sent into the past.
Also tachyons would have been going faster then the speed of light since the big bang and would have never passed the speed of light

I know they wouldn't. Causality is only possible when handling data. As long as the tachyons aren't being used in a way to transmit data, they will not break causality.

Also, causality is not dependent on detection or any sort of cypher. If ANY data is sent on or by a tachyon, it could cause a breakdown. How much the extent of the breakdown is would be dependent on the type and amount of data transmitted.

Also, Jack, please read the wiki article.

Yes it does, especially to objects with mass.

What does that mean? It either allows them or not, it can't not allow something and especially not in other cases.

No information can travel faster than the speed of light.

Not exactly but not relevant either. You can't use tachyons to transmit information faster than the speed of light.

Quote from: http://en.wikipedia.org/wiki/Faster-than-light#Space-time_distortion

Space-time distortion

Although the theory of special relativity forbids objects to have a relative velocity greater than light speed, and general relativity reduces to special relativity in a local sense (in small regions of spacetime where curvature is negligible), general relativity does allow the space between distant objects to expand in such a way that they have a "recession velocity" which exceeds the speed of light, and it is thought that galaxies which are at a distance of more than about 14 billion light years from us today have a recession velocity which is faster than light.

As I've said, GR may allow FTL, but not SR.

Mein Gott. Please take a physics course, don't just quote Wikipedia. Nothing in that statement is at all contradictory to anything I've said. Expansion of space is a completely separate issue which has nothing at all to do with tachyons.

Quote from: http://metaresearch.org/cosmology/gravity/LR.asp

The proof that faster-than-light (FTL)
propagation is not allowed by nature is simple. Special relativity (SR) forbids it because, in that theory, time slows and approaches a cessation of flow for any material entity approaching the speed of light. One might immediately object that, in particle accelerators, the behavior predicted by SR is observed to happen as speeds approach c. No matter how much energy is added, the particles cannot be made to reach or exceed speed c.

As I've said before, relative to all inertial observers, a massless particle travel at c, whereas a massive particle may accelerate and approach c.

I'm resisting the urge to flame here. Do you maybe want to check out what random websites you are quoting from? Metaresearch is some crank's personal site. In any event, this is a quite poor explanation Time dilation is a related effect but not the reason you can't accelerate an object with mass faster than the speed of light. And again, this is all only relevant if you have positive real rest mass.

Quote from: JoshuaZ on February 25, 2009, 07:28:15 PM

If a particle's rest mass is imaginary then the particle travels faster than the speed of light and cannot accelerate below it. (I'm abusing notation slightly with the term rest mass only being strictly valid for the first of the three cases)

So, what is the value of this imaginary mass of a tachyon?

It is a function of the rest mass and the current velocity. But strictly speaking, there are no restrictions on the rest mass of a tachyon within special relativity beyond that it needs to be a non-zero imaginary number. But like all particles you have E= (mc^2)/(1- v^2/c^2)^(1/2) where m is the rest mass and E is the total energy (you get Einstein's well known equation from setting v=0 in the above).

Please read my link.

Please take a physics course.

Edit:Formatting

Quote from: optimisticcynic on February 25, 2009, 07:53:05 PM

wouldn't tachyons not interact with matter anyway. They have negative mass which would give them negative gravity so they would be repelled by the galaxy.

Actually, no. Technically, using that logic, knowing that having positive mass expands space-time (thus having positive time passage due to the distance between two masses), having negative mass would be the reverse. I'm not 100% on that, I'm just going by your logic to make more sense, I am not sure if that is actually how it would work, but it would explain why tachyons would be able to travel faster than light. They would not be repelled by any positive mass. If anything, they would be of the same nature of neutrinos as far as interactions go with out current knowledge and technology level.

you cant contract space. picture a piece of rubber stretched into a thin sheet. a piece of mass would seem to increase the space time. However if you put a balloon underneath it would do the exact opposite as a object with weight but would still increase the amount of space

Quote from: Hara Taiki on February 25, 2009, 08:06:09 PM

Quote from: optimisticcynic on February 25, 2009, 07:53:05 PM

wouldn't tachyons not interact with matter anyway. They have negative mass which would give them negative gravity so they would be repelled by the galaxy.

Actually, no. Technically, using that logic, knowing that having positive mass expands space-time (thus having positive time passage due to the distance between two masses), having negative mass would be the reverse. I'm not 100% on that, I'm just going by your logic to make more sense, I am not sure if that is actually how it would work, but it would explain why tachyons would be able to travel faster than light. They would not be repelled by any positive mass. If anything, they would be of the same nature of neutrinos as far as interactions go with out current knowledge and technology level.

you cant contract space. picture a piece of rubber stretched into a thin sheet. a piece of mass would seem to increase the space time. However if you put a balloon underneath it would do the exact opposite as a object with weight but would still increase the amount of space

You can contract space-time, though. Space and space-time are two different things.

wouldn't it just stretch space time out the opposite direction. Also matters with a positive mass is attracted to space time that has been warped in that direction tachyons stretch it in the other way so wouldn't it be repelled matters way of stretching it.

What does that mean? It either allows them or not, it can't not allow something and especially not in other cases.

It means objects with mass cannot accelerate past (or, in layman terms, travel past) the speed of light. Make sense now?

Not exactly but not relevant either. You can't use tachyons to transmit information faster than the speed of light.

I said nothing about tachyons.

Mein Gott. Please take a physics course, don't just quote Wikipedia. Nothing in that statement is at all contradictory to anything I've said.

Sure there is.

Metaresearch is some crank's personal site.

Especially when the page cited quite a few sources to back it up?

Expansion of space is a completely separate issue which has nothing at all to do with tachyons.

We're not arguing about that. Please be consistent with the discussion.

Time dilation is a related effect but not the reason you can't accelerate an object with mass faster than the speed of light. And again, this is all only relevant if you have positive real rest mass.

You can't accelerate an object with mass faster than the speed of light, under SR. Period.

It is a function of the rest mass and the current velocity. But strictly speaking, there are no restrictions on the rest mass of a tachyon within special relativity beyond that it needs to be a non-zero imaginary number. But like all particles you have E= (mc^2)/(1- v^2/c^2)^(1/2) where m is the rest mass and E is the total energy (you get Einstein's well known equation from setting v=0 in the above).

So, what is the value of this imaginary mass of a tachyon just so it doesn't violate SR?

Please take a physics course.

Good, so you have nothing to add to your argument. Gotcha.

wouldn't it just stretch space time out the opposite direction. Also matters with a positive mass is attracted to space time that has been warped in that direction tachyons stretch it in the other way so wouldn't it be repelled matters way of stretching it.

Mass creates gravity. Gravity stretches space-time. That's why if you were to fall into the gravity well of a black hole, an outside observer would see your body slow down to a near standstill as you approach it's event horizon. It takes longer and longer to reach the next point. An object such as a tachyon with negative mass would possibly shrink space-time, and could be why it propels through space at FTL speeds. It's basically shrinking the space-time in front of it, and stretching out space-time behind it as it moves.



It's also theorized (this is where Star Trek actually stole the idea from) that if you could somehow make a tachyon "field" you would effectively negate the mass of anything inside this field, which would allow the object to be exempt from GR and SR altogether and move along at FTL speeds. Although, Star Trek adds that it simply shifts the mass into subspace, but that's just to be special I believe.

Quote from: optimisticcynic on February 25, 2009, 08:27:28 PM

wouldn't it just stretch space time out the opposite direction. Also matters with a positive mass is attracted to space time that has been warped in that direction tachyons stretch it in the other way so wouldn't it be repelled matters way of stretching it.

Mass creates gravity. Gravity stretches space-time. That's why if you were to fall into the gravity well of a black hole, an outside observer would see your body slow down to a near standstill as you approach it's event horizon. It takes longer and longer to reach the next point. An object such as a tachyon with negative mass would possibly shrink space-time, and could be why it propels through space at FTL speeds. It's basically shrinking the space-time in front of it, and stretching out space-time behind it as it moves.



It's also theorized (this is where Star Trek actually stole the idea from) that if you could somehow make a tachyon "field" you would effectively negate the mass of anything inside this field, which would allow the object to be exempt from GR and SR altogether and move along at FTL speeds. Although, Star Trek adds that it simply shifts the mass into subspace, but that's just to be special I believe.

The fact something seems to slow down as it approaches a black hole has nothing  to do with stretching of space time. it has to do with what happens to the light in the gravity.
So if it did warp space time one way it should be attracted to things that warp it the same way and repelled by thing that warp it the opposite way. So it should still be repelled by the gravity of are galaxy.

wouldn't it just stretch space time out the opposite direction. Also matters with a positive mass is attracted to space time that has been warped in that direction tachyons stretch it in the other way so wouldn't it be repelled matters way of stretching it.

The underlying material with gravity is complicated. I don't understand it well at all (my understanding of GR isn't very good). But I can be sure that the gravitational issues with tachyons are not going to be easily noodlable without a lot more math. This is a waste of time.

And now to deal with Jack...

It means objects with mass cannot accelerate past (or, in layman terms, travel past) the speed of light. Make sense now?

.

Ok, if that's what you meant then it is confused. This is only true for objects with positive real mass.

Quote from: JoshuaZ on February 25, 2009, 08:12:09 PM

Expansion of space is a completely separate issue which has nothing at all to do with tachyons.

We're not arguing about that. Please be consistent with the discussion.

Well excuse me for replying to what you quoted from Wikipedia. You seem to be missing the point. That's about travel within space (roughly speaking, the details are more complicated).

You can't accelerate an object with mass faster than the speed of light, under SR. Period.

You can't accelerate an object with positive real rest mass faster than the speed of light under SR. That's not the same. Tachyons don't have a positive real rest mass.

Quote from: JoshuaZ on February 25, 2009, 08:12:09 PM

It is a function of the rest mass and the current velocity. But strictly speaking, there are no restrictions on the rest mass of a tachyon within special relativity beyond that it needs to be a non-zero imaginary number. But like all particles you have E= (mc^2)/(1- v^2/c^2)^(1/2) where m is the rest mass and E is the total energy (you get Einstein's well known equation from setting v=0 in the above).

So, what is the value of this imaginary mass of a tachyon just so it doesn't violate SR?

Some number of the form ki for k a non-zero real number.

Quote from: JoshuaZ on February 25, 2009, 08:12:09 PM

Please take a physics course.

Good, so you have nothing to add to your argument. Gotcha.

There's no need for a new argument. If you don't understand the relevant equations that's not my fault.  If you don't have time to take a physics course then crack open a book on special relativity.

Ok. Last attempt to explain this. Trying another tact. Let's think what goes wrong when we try to accelerate an object to the speed of light. Quick change of notation. I'm going to use capital M as the rest mass and little m as the relativistic mass. SR says in part that for normal particles relative mass is increases as we increase velocity. In fact, it says a bit more, namely that for any particle we have m(1- v^2/c^2)^(1/2)= M or if you prefer m= M/(1- v^2/c^2)^(1/2).  Now, if M and m are non-zero then we get a problem if v=c because in that case we would have 1-v^2/c^2=0 and so we would get M*0=0=m which would be bad. Now, if m=M=0 this isn't a problem. That's why particles with mass zero can go the speed of light (for other reasons they have to go the speed of light). We similarly get a problem if we let v exceed c because we get an imaginary number if we have v>c. But, that's ok if we allow M or m to be imaginary numbers. The equations are consistent. If you look at the other relevant equations of SR you'll find that they are also consistent but you get strange acting particles. In particular, these particles still have the same problem if you try to set v=c so you can't ever get these particles to the speed of light. There are some other weird issues here and I'm a number theorist not a physicist so I don't feel comfortable going into that much more detail without picking up a textbook but that's the basic idea.

Quote from: Hara Taiki on February 25, 2009, 08:37:19 PM

Quote from: optimisticcynic on February 25, 2009, 08:27:28 PM

wouldn't it just stretch space time out the opposite direction. Also matters with a positive mass is attracted to space time that has been warped in that direction tachyons stretch it in the other way so wouldn't it be repelled matters way of stretching it.

Mass creates gravity. Gravity stretches space-time. That's why if you were to fall into the gravity well of a black hole, an outside observer would see your body slow down to a near standstill as you approach it's event horizon. It takes longer and longer to reach the next point. An object such as a tachyon with negative mass would possibly shrink space-time, and could be why it propels through space at FTL speeds. It's basically shrinking the space-time in front of it, and stretching out space-time behind it as it moves.



It's also theorized (this is where Star Trek actually stole the idea from) that if you could somehow make a tachyon "field" you would effectively negate the mass of anything inside this field, which would allow the object to be exempt from GR and SR altogether and move along at FTL speeds. Although, Star Trek adds that it simply shifts the mass into subspace, but that's just to be special I believe.

The fact something seems to slow down as it approaches a black hole has nothing  to do with stretching of space time. it has to do with what happens to the light in the gravity.
So if it did warp space time one way it should be attracted to things that warp it the same way and repelled by thing that warp it the opposite way. So it should still be repelled by the gravity of are galaxy.

No. Please educate yourself on newtonian physics and general relativity and how the two interact with one another as far as black holes and gravity are concerned.

Quote from: optimisticcynic on February 25, 2009, 08:52:47 PM

Quote from: Hara Taiki on February 25, 2009, 08:37:19 PM

Quote from: optimisticcynic on February 25, 2009, 08:27:28 PM

wouldn't it just stretch space time out the opposite direction. Also matters with a positive mass is attracted to space time that has been warped in that direction tachyons stretch it in the other way so wouldn't it be repelled matters way of stretching it.

Mass creates gravity. Gravity stretches space-time. That's why if you were to fall into the gravity well of a black hole, an outside observer would see your body slow down to a near standstill as you approach it's event horizon. It takes longer and longer to reach the next point. An object such as a tachyon with negative mass would possibly shrink space-time, and could be why it propels through space at FTL speeds. It's basically shrinking the space-time in front of it, and stretching out space-time behind it as it moves.



It's also theorized (this is where Star Trek actually stole the idea from) that if you could somehow make a tachyon "field" you would effectively negate the mass of anything inside this field, which would allow the object to be exempt from GR and SR altogether and move along at FTL speeds. Although, Star Trek adds that it simply shifts the mass into subspace, but that's just to be special I believe.

The fact something seems to slow down as it approaches a black hole has nothing  to do with stretching of space time. it has to do with what happens to the light in the gravity.
So if it did warp space time one way it should be attracted to things that warp it the same way and repelled by thing that warp it the opposite way. So it should still be repelled by the gravity of are galaxy.

No. Please educate yourself on newtonian physics and general relativity and how the two interact with one another as far as black holes and gravity are concerned.

The light closer to the event horizon of a black hole takes longer to reach you. SO the image that you see of someone who is almost about to fall into a black hole takes longer to reach you then it would without the gravity well. As you get closer and closer it takes the light longer and longer to escape. So you would never actually see someone fall into a black hole they would just get exponentially closer. even though the object probably fell through along time ago.

No, that's not how it works at all. It has NOTHING to do with light at all, as light is subject to the same effects. As I said, please educate yourself a bit more, it's clear you don't understand how it works fully.

Ok, if that's what you meant then it is confused. This is only true for objects with positive real mass.

What is a real mass?

Some number of the form ki for k a non-zero real number.

Right, you can't give me a number. Talk about hypothetical nonsense...

There's no need for a new argument. If you don't understand the relevant equations that's not my fault.  If you don't have time to take a physics course then crack open a book on special relativity.

I'm not asking for a new argument.

I'm going to use capital M as the rest mass and little m as the relativistic mass.

No, it's the other way around: m = invariant mass, M = relativistic mass.

SR says in part that for normal particles relative mass is increases as we increase velocity.

Not necessarily. Please, replace relativistic mass with energy, as it removes confusion. In fact, even Einstein disliked the idea of relativistic mass. When we say mass, we mean invariant (rest) mass.

Ok. Last attempt to explain this. Trying another tact. Let's think what goes wrong when we try to accelerate an object to the speed of light. Quick change of notation. I'm going to use capital M as the rest mass and little m as the relativistic mass. SR says in part that for normal particles relative mass is increases as we increase velocity. In fact, it says a bit more, namely that for any particle we have m(1- v^2/c^2)^(1/2)= M or if you prefer m= M/(1- v^2/c^2)^(1/2).  Now, if M and m are non-zero then we get a problem if v=c because in that case we would have 1-v^2/c^2=0 and so we would get M*0=0=m which would be bad. Now, if m=M=0 this isn't a problem. That's why particles with mass zero can go the speed of light (for other reasons they have to go the speed of light). We similarly get a problem if we let v exceed c because we get an imaginary number if we have v>c. But, that's ok if we allow M or m to be imaginary numbers. The equations are consistent. If you look at the other relevant equations of SR you'll find that they are also consistent but you get strange acting particles. In particular, these particles still have the same problem if you try to set v=c so you can't ever get these particles to the speed of light. There are some other weird issues here and I'm a number theorist not a physicist so I don't feel comfortable going into that much more detail without picking up a textbook but that's the basic idea.

I've yet to see a contradiction to my claim:

Relative to all inertial observers, massless particles travel at c. Relative to all inertial observers, massive particles (or any particles with mass) may approach c but never get to or past c.

What is a real mass?

A mass that is a real number.

Quote from: JoshuaZ on February 25, 2009, 08:53:48 PM

Some number of the form ki for k a non-zero real number.

Right, you can't give me a number. Talk about hypothetical nonsense...

I can't give you a specific number because any specific number will do, just as the standard equations for SR are valid for any chosen mass as long as you adjust energy and other values accordingly. You might as well ask for a specific mass for a regular particle.

Quote from: JoshuaZ on February 25, 2009, 08:53:48 PM

I'm going to use capital M as the rest mass and little m as the relativistic mass.

No, it's the other way around: m = invariant mass, M = relativistic mass.

Sorry, screwed the notation up there.

I've yet to see a contradiction to my claim:

Quote from: Jack on February 25, 2009, 07:20:02 PM

Relative to all inertial observers, massless particles travel at c. Relative to all inertial observers, massive particles (or any particles with mass) may approach c but never get to or past c.

Ok. Let's be explicit: Your statement is wrong.
Because that's only true for massive particles whose mass is a real number. If the mass is an imaginary number then the particle has to start out faster than c and can't slow down past c. See the issue?

No, that's not how it works at all. It has NOTHING to do with light at all, as light is subject to the same effects. As I said, please educate yourself a bit more, it's clear you don't understand how it works fully.

here is a source http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html I can find more if you don't trust this one.

lol some people in this thread haven't got a clue about physics or relativity.

I teach university physics I have a PhD, admitedly in condensed matter physics.

A particle can travel faster than the speed of light if it has zero rest mass i.e. the mass of the particle at rest in ALL inertial frames of reference. Any particle that moves has a mass associated with it due to it's movement.

Some of the physics stated in this thread is shocking tbh.