What is the relationship between units of time and space in relativity?

[BernieM]

Einstein said that matter was just a special form of energy then later came up with the equation of Energy(in ergs)=Mass(in grams) * C(speed of light in cm)^2 ... well ... what would the equation be if the standard unit of energy measurement were C(speed of light in cm)^2 ergs? ... seems to me it would be E = M ... well wasn't that what he really said to begin with? =o

 

[Lord Einstein]

Einstein said that matter was just a special form of energy then later came up with the equation of Energy(in ergs)=Mass(in grams) * C(speed of light in cm)^2 ... well ... what would the equation be if the standard unit of energy measurement were C(speed of light in cm)^2 ergs? ... seems to me it would be E = M ... well wasn't that what he really said to begin with? =o

yes he meant special as if not normal. not normal meaning that the mass had some unconventional properties when reaching the velocity of speed of light thus relating to energy. which is entirely different from E=M.

 

[Fredrik]

It's not the c that's cool, it's the E=m part. It's quite common to use units in which c=1.

 

[BernieM]

by moving the c2 over to the left side of the equation you imply the 'speed of light part of his equation'

 

[Crazy Tosser]

E=M tells you that anything that has energy has a mass and visa-versa. For example, a moving photon has a mass.

 

[Pythagorean]

it's not like the c^2 just goes away. It becomes 1, but the units are still there.

It's not E = M as in (energy = mass).

it's still E = MC^2, but C^2 isn't just 1 it's 1 (velocity units)^2


so
E = M*C^2
E = M*(velocity units)^2

 

[Crazy Tosser]

it's not like the c^2 just goes away. It becomes 1, but the units are still there.

It's not E = M as in (energy = mass).

it's still E = MC^2, but C^2 isn't just 1 it's 1 (velocity units)^2


so
E = M*C^2
E = M*(velocity units)^2

Velocity has no units :P Remember, time and position are just two dimensions, so their units cancel out when you are talking about speed. Pretty much it's E=M.

 

[tanker]

I'm pretty sure velocity has units...

 

[Pythagorean]

Velocity has no units :P Remember, time and position are just two dimensions, so their units cancel out when you are talking about speed. Pretty much it's E=M.

are you trolling me?

position and time do not cancel each other. You have E = M (change in position/change in time)^2

 

[CRGreathouse]

I'm pretty sure velocity has units...

It doesn't in relativistic units, which are commonly used for problems of this sort.

 

[Pythagorean]

It doesn't in relativistic units, which are commonly used for problems of this sort.

but is it a matter of convenience (I.e. you ignore the units since the value is constant and always 1)?

Surely:

kg*(m/s)^2 != kg

do they?

addendum:

from http://www.sparknotes.com/physics/specialrelativity/dynamics/terms/term_6.html

This simplifies calculations immensely. If you need to find an exact answer it is always possible to put the right number of factors of c back in at the end of a calculation by looking at the units and working out where factors of m/s are missing.

so the units don't actually cancel, you just ignore them for convenience. You put them back when you're done with calculations to make the statement physically true.

 

[Jimmy Snyder]

I don't get it. Doesn't relativity theory put time and space on an equal footing? If so, then isn't velocity (space / time) a pure number?

 

[Crazy Tosser]

are you trolling me?

position and time do not cancel each other. You have E = M (change in position/change in time)^2

No, I am not trolling you. And please bear with me if you think that my understanding of relativity is inferior to yours. What I learned from GR is that time and space are both just dimensions. Just like you can't say that units of one space coordinate and another are different, you cannot say that units of time and space are different, so velocity is nothing but a slope - a number with no unit.

 

[Pythagorean]

No, I am not trolling you. And please bear with me if you think that my understanding of relativity is inferior to yours. What I learned from GR is that time and space are both just dimensions. Just like you can't say that units of one space coordinate and another are different, you cannot say that units of time and space are different, so velocity is nothing but a slope - a number with no unit.

I don't really think that your understanding is inferior. I was thinking special relativity, actually. And my only exposure to it is in electromagnetism. We never canceled different units there.

We did have terms like sqrt(1 + (v/c)^2) so that velocity is canceled with velocity.

It would be nice to have a relativity expert answer this. Perhaps I'm more ignorant than I assume, but it's really hard for me to justify that so far from what I'm looking up.

 

[tmc]

No, I am not trolling you. And please bear with me if you think that my understanding of relativity is inferior to yours. What I learned from GR is that time and space are both just dimensions. Just like you can't say that units of one space coordinate and another are different, you cannot say that units of time and space are different, so velocity is nothing but a slope - a number with no unit.

Actually, it is normally 'c * dt' which is used as the dimension (with c=1), not just dt. This is done exactly so that units work out.

 

[BernieM]

Simple question here:

If i took C^2 (in cm) which i believe is approximately 898755178736817640000, and therefore decided that my unit of measurement should be 898755178736817640000 ergs as my standard unit ... then my E would be 898755178736817640000 ergs = 1 gm of matter ... correct?

 

[Tac-Tics]

No, I am not trolling you. And please bear with me if you think that my understanding of relativity is inferior to yours. What I learned from GR is that time and space are both just dimensions. Just like you can't say that units of one space coordinate and another are different, you cannot say that units of time and space are different, so velocity is nothing but a slope - a number with no unit.

Length has units. We typically use meters.

Times has units. We typically use seconds.

Using the speed of light as a conversion factor, we could define one in terms of the other. In fact, sometimes we use the unit of a lightsecond to mean 1 second of length.

We could say that velocity is then measured without units (an object's velocity is then it's ratio to the speed of light). Acceleration would be in hertz. Force would be in kilogram hertz.

But that's not the canonical way to do it, and people won't understand you unless you go to lengths to make it clear you are treating them as equal. Even though meters and seconds are isomorphic, we treat them as if they were distinct. A nickle is five pennies, but that doesn't mean a nickle is made out copper. Similarly, a meter is c seconds, but it isn't a measurement of time.

Additionally, spatial measurement is a vector, and must be multiplied by a unit-vector. Time is scalar.