# Validity of comparing units ?

What is time ? My maths is so rusty its almost non existant. I'm looking at the energy to mass equivalence formula and trying to work out an equivalent 'unit of time'. With my poor maths I get;

e=mc^2

e^(1/2)=m^(1/2)* c

[In terms of units]

e^(1/2)=m^(1/2)* (d/t)

e^(1/2)*t=m^(1/2)* d

t= d * m^(1/2) / e^(1/2)

So in terms of units, time is related to distance ( einsteins spacetime ) multiplied by a 'small part' of mass over energy. Is doing this valid at all ?

Last edited:

Related Introductory Physics Homework Help News on Phys.org
Kurdt
Staff Emeritus
Gold Member
Energy is not a base unit. if you consider the kinetic energy formula E=1/2m*v^2 then the units of energy are as follows:

E=([M]*[L]^2)/[T]^2

If you replace energy in your expression with its units you'll find that time is equal to time as it should be.

Hi Kurdt

I'm trying to understand time, so its not much use saying that its time.

Does this seem ok ? Kurdt
Staff Emeritus
Gold Member
Comparing units is fine but if you do not use fundamental units then you just have an elaborate way of saying time is equal to time. As one of the fundamental units thats all you will ever get with time. Understanding it is more to do with philosophical arguments i guess although it is defined by the speed of light.

Hi Kurt

Thats my starting point, but what do you mean by "speed". If time is defined by the speed of light, that seems so important. Perhaps we should say veolcity rather than speed ? Phased EM, lazer like, finds its target like a particle. Individual photons spread out like a wave.

So what is the difference between a phased photon and a photon in youngs slit experiment ?

There is no consideration of dimensionaity in these concepts. No one seems to want to move on from Einstein.

Kurdt
Staff Emeritus
Gold Member
Saying time is defined by the speed of light was confusing because you need time to define speed. What you define one second by is how long it takes light to travel a particular distance. I never really felt comfortable with this because you need a definition of time to have a speed in the first place. I prefer the definition that says one second is the time taken for a caesium atom to oscillate so many times (I'm a theoretical physicist thus i have no idea how many times it actually is). Anyway I'm still not clear what it is about time that you're trying to understand. Are you attemting to derive the time dilation formula?

You CAN indeed rederive the unit system by choosing a new set of base units. Take care, though, you need to also rederive all the equations and reinterpret them. Here-in lies the problem. If you choose, say, J, kgm/s, and kg as base units (a system based on conserved quantities), just what does J/kg imply? What is a J/(kgm/s) and what does it mean?

I have messed with this a bit and have yet to find another system that makes any sort of internal logical sense. That doesn't mean there isn't a way to do it, but it is HIGHLY non-trivial.

-Dan

HallsofIvy
Homework Helper
"Base" units are man-made not natural. I remember reading, some years back, a way of choosing "natural" units in which it was necessary to change what you consider "base" units. Since the speed of light, c, is a natural constant, take speed as "base" and c as the unit (that's commonly done in texts on relativity). Since Plank's constant, h, which measures "action" is a natural constant, take that as a base unit. Similarly, take G, the "universal gravitational constant (NOT "g"), as base unit. If I remember correctly, the unit length in that system turns out to be the "diameter" of an electron and the unit time is the time it takes light to cross that distance.

Great answers thanks guys. I will stick to this "Introductory Physics" board as the replies are far more down to earth than on other boards here like QM and cosmology.

What I'm trying to do is use time as a 'constant' in an extra dimensional universe. Einstein's relativity is clearly fundamental. But mass and EM energy seem to occupy fundamentally different realms. When a photon is emitted as light - or when an electron travels down a telephone cable - there is a change in properties of the domain of that energy that is more fundamental than 3D spacial vectors. This is the heart of einsteins theories, but kind of taken for granted. I suspect time is, despite what seems intuitive, the actual connection between these domains. For EM raditation there is no time, and yet it has a very real connection to spacetime in 'relativity'. This is why I'm curious what the difference is between a 'normal' light photon that travels through both slits in youngs experiment, and a 'phased' photon that is part of a lazer beam. By polarising the light, the connection between the matter and EM domains seems to have been changed. Or is this an incorrect assumption I have made - would a photon in a lazer also pass through both slits?

Thanks

Simon

Last edited: