Thread: Can a dimension be in units of speed?

if we are talking about dimensions. Can I create a dimension with units of velocity or speed? ?

Originally Posted by tom

if we are talking about dimensions. Can I create a dimension with units of velocity or speed? ?

Why not try it.... Do you mean 'dimension' as in 3D or 4D or do you mean 'dimension' such as 60 kts long, 30 kts wide, 15 kts high and the whole 'thing' traveling at 100kts (all kts in seconds)?

Originally Posted by tom

if we are talking about dimensions. Can I create a dimension with units of velocity or speed? ?

You can make it the y axis on a graph if you want.

Many times, a physical problem is analyzed by measuring various dimensions. Color might be one of the dimensions, as well as weight, or (your example) velocity. There might be as many as fifty dimensions, or many more. Often times, some of the dimensions are highly correlated, and are then folded into a single dimension. For instance, mass and weight might've been separate dimensions, but they're basically measuring the same basic quantity, kind of like inches and meters both measure distance, although in the case of mass/weight there are still unresolved philosophical (which elude measurement for now) and practical (like, varying force of gravity) issues.

As usual not really sure where I was going with all of this ...
but I guess here was where my thought process was. On my other post I was discuss FTL objects. for FTL objects it would see to take work to slow it down and you could extract work by making it speed up.

How fast could this stuff speed up?

So I started to think a bit about the unit of c. Could this be a looped dimension or some kind of binary dimension where there are two ... well almost parallel universes ... One for FTL and one for STL particles. So you would have 3 space 1 time and one binary dimension for either FTL or STL

See Tachyon - Wikipedia, the free encyclopedia
There is no evidence that such things exist. It is science fiction.

Rather bizarre, and I'm definitely out of my element here. Some possibly ignorant questions:

a) There is an equation for the energy of a particle



The article notes that if , then the denominator is imaginary, and the numerator must therefore also be imaginary to ensure that the energy is a real number.

The relativistic formula for energy, together with the other formulas of special relativity, has been found to work to a high degree of accuracy in the observable universe, which consists of things that are moving slower than the speed of light. The square root is then applied to a positive number. Within the real number system, only non-negative numbers have square roots.

The real numbers form the only (to within an isomorphism) totally ordered complete field. The numbers some of the folks in the 0.999... = 1 thread are using are rather ill-defined, but are clearly not the real numbers. We can extend the real numbers to the complex numbers; one way of doing so is to introduce complex numbers as pairs of real numbers, and define addition as and multiplication as . The extension is a complete (under product topology) field, but it is not totally ordered. Furthermore, it is useful for lots of things; for example, electrical engineers use complex numbers to represent impedance.

The square root function, defined on complex numbers, has a nasty singularity at zero, and a branch-cut discontinuity. So we have a formula for energy with a square root in it, it works well in the observable universe filled with things moving at less than the speed of light. When we extend this formula to faster-than-light particles for which we have not a shread of evidence, is it reasonable to think that the same mathematical extension of the square root function that is useful in other applications, is also the right one to use here?

b) Why does energy have to be real? Faster-than-light particles are totally outside our realm of experience, how do we know that they have real energy but imaginary mass? Why couldn't they have real mass and imaginary energy?

c) The article says that energy is required to slow them down. That follows by choosing the positive imaginary square root in the denominator, and assigning positive imaginary mass to the particle. Why not have positive imaginary mass, but choose the negative imaginary square root in the denominator, so the hypothesized particles have negative energy? Then it would take positive energy to speed them up to infinity.

d) The article contains this quote.

tachyons are believed by physicists to either not exist, or else to be incapable of interacting with normal matter

Is there a difference between those two?

Originally Posted by Coelacanth

Rather bizarre, and I'm definitely out of my element here. Some possibly ignorant questions:
d) The article contains this quote.

tachyons are believed by physicists to either not exist, or else to be incapable of interacting with normal matter

Is there a difference between those two?

It would appear as if the statement is saying (1) tachyons do not exist or (2) tachyons do exist. Either way, there appears to be an awful lot of work going on regarding a subject that supposedly doesn't exist.

Originally Posted by Coelacanth

Rather bizarre, and I'm definitely out of my element here. Some possibly ignorant questions:

a) There is an equation for the energy of a particle



b) Why does energy have to be real? Faster-than-light particles are totally outside our realm of experience, how do we know that they have real energy but imaginary mass? Why couldn't they have real mass and imaginary energy?

The article went on to develop the equivalent equation to alleviate the imagenary mass 'problem'/question.

Originally Posted by David E. Eaton Sr.

The article went on to develop the equivalent equation to alleviate the imagenary mass 'problem'/question.

Yes, but it transfers the imaginary mass problem to slower-than-light particles.

Seems to me, we could renormalise things in our slower-than-light world, to make energy the negative of what we call it now. Every equation that has energy in it, add a negative sign (in fact, we do often talk about negative graviational potential energy, where the "zero" level is that of an object that is infinitely removed from the gravitational source). We'd still even have the conservation of energy principle, but we could say things like, in order to speed up this slower-than-light particle, we need to remove energy from it.

So this idea that faster-than-light particles need to have energy removed to speed them up, seems completely arbitrary. Define energy to be the negative of that, and you would need to add energy to speed them up, just like in the slower-than-light world. Unless we have some interaction between the faster-than-light and slower-than-light universes, and something like a conservation of energy principle between them, any sign convention, or any assignment of "real" or "imaginary" dimensions to physical quantities, is just arbitrary.

Or am I missing something here?