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

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    E=mc2
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Discussion Overview

The discussion revolves around the relationship between units of time and space in the context of relativity, particularly focusing on the implications of Einstein's mass-energy equivalence equation E=mc². Participants explore the meaning of the equation, the nature of velocity, and the treatment of units in relativistic contexts.

Discussion Character

  • Debate/contested
  • Conceptual clarification
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that if energy is measured in units of c² ergs, the equation simplifies to E=M, suggesting a fundamental equivalence between energy and mass.
  • Others argue that the c² term in E=mc² is essential and cannot simply be disregarded, emphasizing that it represents a conversion factor between mass and energy.
  • A participant mentions that in certain units, c can be set to 1, which leads to simplifications in calculations, but the units still play a role in the underlying physics.
  • There is a contention regarding whether velocity can be treated as a dimensionless quantity, with some asserting that time and space are fundamentally different and should not cancel out.
  • Another viewpoint suggests that while time and space can be treated as dimensions in relativity, their units remain distinct and should not be conflated.
  • One participant questions the convenience of ignoring units in relativistic calculations, arguing that they must be accounted for to maintain physical accuracy.
  • Discussions also touch on the implications of defining units of measurement in terms of the speed of light and how that affects the interpretation of energy and mass.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the treatment of units in relativity and the interpretation of E=mc². There is no consensus on whether velocity can be considered unitless or how to properly account for units in relativistic contexts.

Contextual Notes

Some participants highlight the complexity of defining units in relativity, noting that while certain simplifications can be made, the underlying relationships between time, space, and velocity remain nuanced and context-dependent.

Who May Find This Useful

This discussion may be of interest to those studying relativity, physics students grappling with the implications of mass-energy equivalence, and individuals curious about the conceptual foundations of time and space in physics.

BernieM
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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
 
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BernieM said:
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.
 
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.
 
by moving the c2 over to the left side of the equation you imply the 'speed of light part of his equation'
 
E=M tells you that anything that has energy has a mass and visa-versa. For example, a moving photon has a mass.
 
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
 
Pythagorean said:
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.
 
:confused:

I'm pretty sure velocity has units...
 
Crazy Tosser said:
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
 
  • #10
tanker said:
:confused:

I'm pretty sure velocity has units...

It doesn't in relativistic units, which are commonly used for problems of this sort.
 
  • #11
CRGreathouse said:
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.
 
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  • #12
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?
 
  • #13
Pythagorean said:
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.
 
  • #14
Crazy Tosser said:
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.
 
  • #15
Crazy Tosser said:
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.
 
  • #16
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?
 
  • #17
Crazy Tosser said:
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.
 

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